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Your FREE Admission Test for Dental Hygiene (ATDH) Practice Test 2026 – 280+ Q&A

Prepare with realistic, Admission Test for Dental Hygiene-style questions — take a full ATDH practice test or drill one section at a time.

How ready are you?

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ATDH exam by the numbersStandard mode

Where the ATDH exam's points come from

ADA Department of Testing Services' official outline weights, the exam rules and our 288 free practice questions mapped domain by domain. Use it to plan your study hours.

  • Question type:Multiple choice (computer-based)
  • Time limit:Approximately 4 hours 50 minutes total (290 minutes, with two optional 15-minute breaks)
  • Result:Scaled scores 200-500 (no pass/fail); compared by programs
  • Administered by:ADA Department of Testing Services at Prometric centers
  • Eligibility:Candidates seeking admission to a U.S. dental hygiene education program
  • Retakes:Tested year-round; 60-day wait between attempts; permission needed after 3 attempts
Facts from ADA Department of Testing Services' official exam outline and rules
240
Questions
$150
Cost

Where the ATDH points are

ADA Department of Testing Services' official weight for each of the six domains. Hover or tap a domain to see how many questions that means on your exam.

See these numbers as a table
Weights from ADA Department of Testing Services' ATDH exam outline. Questions on your exam = weight × 240 questions, rounded. Practice questions: Career Employer's ATDH bank.
DomainOfficial weightQuestions on your examOur practice questions
Reading Comprehension17%4147
Language Usage17%4141
Quantitative Reasoning17%4153
Perceptual Ability25%6057
Biology12%2936
General Chemistry12%2954

What to do: Perceptual Ability is the biggest domain at 25%, which means 60 of your questions. Biology and General Chemistry are the smallest at 12% each. The other three domains are within a point of each other, so don't skip any.

Career Employer study data · ATDH exam

What 357 ATDH studiers got right (and wrong) on their first try

9,347 first-try answers on our free ATDH practice questions. Each part below switched on by itself once it had enough people behind it.[5]

Data through Nov 10, 2026 · updates daily
50.5%
first-try accuracy across the exam
357
people studying ATDH with us
69.4%
accuracy on the second try, up from 50.5%
3%
of people who start a full exam finish it

Where ATDH points are lost

Out of 100 questions on a real exam, how many a typical studier would miss in each section. Accuracy alone hides this: a big section with average accuracy costs more points than a small, hard one.

Not shown yet (below our sample-size minimum): Reading Comprehension.

See these numbers as a table
First-try answers from 357 ATDH studiers on Career Employer, through Nov 10, 2026. Weights from ADA Department of Testing Services at Prometric centers's ATDH content outline.
SectionExam weightScored questionsFirst-try accuracyPoints lost per 100First-try answersStudiers
Perceptual Ability25%6063.4%9.1454226
Language Usage16.7%4049.3%8.41,607218
Quantitative Reasoning16.7%4050%8.31,071217
General Chemistry12.5%3042.6%7.21,323206
Biology12.5%3044.1%7.01,473204

SurePass, Capital Prep’s 1-year ATDH pass with an exam pass guarantee: your $150 retake fee covered if you don’t pass, plus your money back and another year of study access. Limited-time CE student deal: 50% off SurePass →

Split your study time

Your hours, divided by ADA Department of Testing Services' domain weights.

Reading Comprehension
10 hrs
Language Usage
10 hrs
Quantitative Reasoning
10 hrs
Perceptual Ability
15 hrs
Biology
7.2 hrs
General Chemistry
7.2 hrs

More ATDH student data is on its way

We’ve logged 9,347 first-try answers on our ATDH questions so far. This section switches to real ATDH student results by itself once each part has enough people behind it:

What switches onNeeds
Accuracy by domain300 answers + 50 people per domain
First full exam score100 full exams

Then it shows you vs everyone.

How hard are the questions?

246 ATDH questions with at least 15 first-try answers, grouped by the share of people who got them right first time.

See these numbers as a table
Every version of each question since Aug 29, 2026, through Nov 10, 2026.
Got it right first tryQuestions
0–10%1
10–20%8
20–30%18
30–40%49
40–50%44
50–60%46
60–70%28
70–80%31
80–90%17
90–100%4

What it means: 120 of 246 questions (49%) trip up more than half of studiers on the first try. That's on purpose: our free ATDH bank is built to be hard, so a passing score here means something.[5]

ATDH study activity, week by week

How much ATDH studying happens on Career Employer each week. Hover or tap a week for details.

See these numbers as a table
Site analytics, week of Jul 6 through Nov 8, 2026.
Week ofQuestions answeredPractice tests startedFlashcard sessions
Nov 2779969
Oct 26690716
Oct 192,78118115
Oct 121,2081136
Oct 51,1121224
Sep 282,30618223
Sep 217867848
Sep 1497610017
Sep 7965895
Aug 319021007
Aug 241,0549726
Aug 171,6231589
Aug 102,50715217
Aug 31,6471498
Jul 271,2876010
Jul 20846322
Jul 132964–
Jul 695320–

Source: anonymous first-try answers on Career Employer ATDH practice tests, Aug 29, 2026 – Nov 10, 2026. Staff traffic, repeats and peeked answers excluded. Our practice questions are written to the official outline, not the official exam; self-selected sample; a studier is one browser.

Weights and rules from ADA Department of Testing Services' published ATDH exam outline and certification pages. Practice-question counts from Career Employer's ATDH bank. Fees and requirements can change; check ADA Department of Testing Services before you register.

The Admission Test for Dental Hygiene (ATDH) is a standardized admission exam used by dental hygiene education programs in the United States to assess an applicant’s readiness and potential for success.

It is administered by the American Dental Association’s Department of Testing Services and delivered by computer at Prometric test centers.[1] The ATDH measures critical thinking and academic ability across six sections.

These practice questions follow the published ATDH content domain and test specifications, mirroring the content and pacing of the real exam so you can build readiness across every section.[4]

To build readiness across every section, pair these with our free study guide, flashcards, and cheat sheet. Want extra insurance for exam day? For a limited time, Career Employer students get 50% off SurePass, Capital Prep’s 1-year ATDH pass with an exam pass guarantee: your $150 retake fee covered if you don’t pass, plus your money back and another year of study access.

Prices, schedules, and policies change — always verify the current details at ADA.org/ATDH before applying.

What’s Changed on the ATDH Exam (2026–2027)

Checked against official sources: Sep 30, 2026

No changes announced by ADA Department of Testing Services as of Sep 30, 2026. Official ADA Department of Testing Services page checked (opens in a new tab)

What changed on this page

Every real change, with the date.

  1. Interactive charts added. Built from the official outline and our question bank.
  2. 23 new practice questions. The bank now has 288 questions.
  3. 54 new practice questions. 101 questions removed that the official outline doesn't test. The bank now has 265 questions.
  4. 66 new practice questions. 3 verified quotes from people who took the real ATDH. The bank now has 312 questions.
  5. 246 questions rewritten.
  6. 5 questions corrected, including 1 answer key.
Earlier changes (2)
  1. 8 questions retired. The bank now has 246 questions.
  2. 27 new practice questions. 12 questions retired. 8 answer keys corrected. The bank now has 254 questions.

What Is on the ATDH Exam?

The ATDH exam covers six sections totaling 240 multiple-choice questions: Perceptual Ability (60 questions), Reading Comprehension (40), Language Usage (40), Quantitative Reasoning (40), Biology (30), and General Chemistry (30).[2]

These sections come from the ADA’s ATDH content domain and test specifications, with Perceptual Ability the largest. Our full practice test mirrors these proportions.

ATDH practice test — practice questions by domain with answer explanations

Practice Questions by Section

Use Start Test for a full weighted ATDH simulation, or open the hub and pick a single section to drill your weak area. After each full exam, your results show a per-section breakdown so you know exactly where to focus — most applicants need the most reps on Perceptual Ability and the sciences.

Who Is Eligible to Take the ATDH?

The ATDH is open to anyone seeking admission to a dental hygiene education program in the United States — there is no formal degree prerequisite to register.[1]

The test is designed for prospective dental hygiene students, and most successful examinees have completed prerequisite college coursework in sciences such as biology and chemistry.

Because admission requirements vary, confirm whether your target programs require the ATDH and what scores or coursework they expect. Additional eligibility details are provided in the official ATDH Candidate Guide.

How Do You Register for the ATDH?

You register for the ATDH online through the ADA Department of Testing Services using a DENTPIN, pay the $150 examination fee (2026 Candidate Guide), and then schedule your exam at a Prometric test center.[3]

The DENTPIN is the unique identifier used for all ADA dental testing. Verify the current fee at ADA.org/ATDH before applying, as fees change.[2]

After your application is accepted you schedule your exam at a Prometric professional testing center. The ADA recommends submitting your application 60 to 90 days before you intend to test.

Testing fees are non-refundable and non-transferable, and the name on your application must exactly match your government-issued ID.

How Is the ATDH Scored?

The ATDH is scored on a scaled range of 200 to 500 with no national pass/fail standard — dental hygiene education programs use the scores to meaningfully compare applicants.[2]

Section results allow programs to see relative strengths and weaknesses across Reading Comprehension, Language Usage, Quantitative Reasoning, Perceptual Ability, Biology, and General Chemistry.

The ATDH is offered year-round, and official results are reported to your selected programs within three to four weeks of your testing date.[2] If you retest, you must wait 60 days between attempts. Each individual program decides what scores it considers competitive and whether results are recent enough for admission.

How Hard Is the ATDH?

The ATDH is demanding mainly for its breadth and pacing — 240 questions across six distinct sections in about 4 hours and 50 minutes — rather than any single hard section.[2] The practical challenge is sustaining focus and managing time across very different skills.

The 60-question Perceptual Ability section is unfamiliar to most applicants because it tests visual-spatial reasoning — mentally rotating and manipulating three-dimensional objects — rather than recalled knowledge.

Biology and General Chemistry reward solid foundational science, Quantitative Reasoning rewards fluency with algebra and mental math, and Reading Comprehension and Language Usage test how quickly you can extract and edit information under time pressure.

200-500
Scaled score range
no pass/fail
60
Perceptual Ability Qs
largest section

The takeaway: drill until you’re consistently scoring above your target programs’ competitive thresholds on full-length, section-weighted practice — especially Perceptual Ability and the sciences — before you book your exam date.

On Career Employer, ATDH students get 51% right on the first try and miss General Chemistry most[5] — see the ATDH student data above.

What to Expect on Exam Day

Arrive at your Prometric test center at least 15 minutes early to check in — bring a valid, unexpired government-issued photo ID whose name matches your ATDH application.[3] You’ll store phones and personal items in a locker; no notes are allowed, but you’re given materials for scratch work.

A short tutorial precedes the exam, then you work through 240 multiple-choice questions across six sections, with two optional 15-minute breaks built into the roughly 4 hour 50 minute appointment.

The ADA processes your results and reports them to you and your programs within three to four weeks of your testing date. Having simulated the full timing with practice tests makes that long clock feel routine.

What ATDH Test-Takers Report

What people who recently sat the ATDH said about the real exam in public forums, quoted word for word:

PAT hardest, chem/QR time

“First of all the PAT section was HARD! … Gen chem and QR were the other sections I struggled with I was running low on time in both of these sections so most of my answers were just educated guesses”

— u/z3bra_cake17r/ATDH, Jun 2026

Time pressure across sections

“I had to guess on over half the questions in almost every section because I didn’t have enough time left and the perceptual ability was SO HARD!!”

— u/toadybearisawesomer/DentalHygiene, Jan 2025

Unscored items, guessing still scores

“Not all of the questions are even real don’t stress I feel like I guessed on most of chemistry and scored a 400 in that section.”

— u/LetterheadUpstairs20r/ATDH, Jan 2026

How to Use This ATDH Practice Test

  • Recreate exam conditions. Take the full test timed, with no notes.[2]
  • Diagnose, then drill. Use a full ATDH simulation to find weak sections, then drill them.
  • Prioritize Perceptual Ability + sciences. They’re the biggest score-movers.
  • Learn the why. Read every explanation — understanding beats memorizing.
  • Answer everything. There’s no guessing penalty, so never leave a question blank.

Plan for the full sitting. Only 3% of ATDH students on Career Employer who start a full-length practice exam finish one (11 of 340)[5] — set aside the full sitting before you press Start Test.

Mind the calendar. ATDH students who set an exam date on Career Employer had a median of 23 days until their exam, and 72% were within 30 days (n = 57)[5] — if you have more runway than that, use it to work through every section.

Why the ATDH Matters

A strong ATDH score is one of the clearest ways to stand out when you apply to a competitive dental hygiene program — it gives admissions committees an objective, section-by-section measure of your academic readiness alongside your coursework.[1] Because programs set their own competitive thresholds, scoring well across all six sections widens the range of programs where you’re a strong candidate. These free ATDH practice tests are the most efficient way to get there.

Conclusion

Performing well on the ATDH comes down to broad academic readiness — sciences, reasoning, language, and visual-spatial skill — and the stamina to sustain it across a long exam. Use this free ATDH practice test to find your weak sections, drill them to mastery, and pair it with our free study guide, flashcards, and cheat sheet. On Career Employer, ATDH students lose the most points on Perceptual Ability (63% correct on the first try), so start your drilling there.[5]

ATDH Practice Test FAQ

The ATDH (Admission Test for Dental Hygiene) is a standardized admission test administered by the American Dental Association's Department of Testing Services. It is designed to help dental hygiene education programs assess an applicant's readiness and potential for success, and it is intended for candidates seeking admission to a dental hygiene program in the United States.

Career Employer ATDH practice-test data, through Nov 10, 2026 · 357 students
Every published Career Employer ATDH practice-test number, with its sample size, source and date
MetricValuenStudentsSourceData through
Students who answered practice questions357—357all question versionsNov 10, 2026
First-try answers (all question versions)9,3479,347357all question versionsNov 10, 2026
First-try accuracy, whole exam50.5%9,347 answers357current question setNov 10, 2026
First-try accuracy: General Chemistry (12.5% of the exam; costs 7.2 of every 100 exam points)42.6%1,323 answers206current question setNov 10, 2026
First-try accuracy: Biology (12.5% of the exam; costs 7 of every 100 exam points)44.1%1,473 answers204current question setNov 10, 2026
First-try accuracy: Language Usage (16.7% of the exam; costs 8.4 of every 100 exam points)49.3%1,607 answers218current question setNov 10, 2026
First-try accuracy: Quantitative Reasoning (16.7% of the exam; costs 8.3 of every 100 exam points)50%1,071 answers217current question setNov 10, 2026
First-try accuracy: Perceptual Ability (25% of the exam; costs 9.1 of every 100 exam points)63.4%454 answers226current question setNov 10, 2026
Median days from setting an exam date to the exam23 days57 exam dates57first date each student setNov 10, 2026
Exam dates within 30 days of being set71.9%57 exam dates57first date each student setNov 10, 2026
Started a full-length practice exam340—340all question versionsNov 10, 2026
Finished a full-length practice exam11of 340 starters11all question versionsNov 10, 2026
Full-length practice exam finish rate3.2%340 starters340all question versionsNov 10, 2026

Sections below our sample-size minimum (not published yet): Reading Comprehension.

First attempt at each question only; repeats, answers after revealing the explanation, bots and staff excluded. Aug 29, 2026 – Nov 10, 2026. Our practice questions written to the official outline, not the official exam; self-selected sample; a student is one browser. Free to reuse under CC BY 4.0 — cite “Career Employer practice-test data, careeremployer.com/data”.

ATDH question bank

All 288 questions, by domain

A reference copy of every question in this practice test. Each answer stays hidden until you choose to show it. To practice with scoring, timing and your readiness score, use Start Test at the top of the page.

Reading Comprehension (47)

  1. Read the passage, then answer the question. Cells rarely make more of a product than they need, and one of the fastest ways they avoid waste is feedback inhibition. In many biosynthetic pathways, the final product binds to the first enzyme of the pathway at a site separate from the active site. This binding changes the enzyme's shape and lowers its affinity for its substrate, so the whole pathway slows. When the product is used up, it leaves the enzyme and activity returns. A classic example comes from bacteria that make the amino acid isoleucine from threonine: isoleucine inhibits threonine deaminase, the first enzyme of that pathway. Regulating the first committed step, rather than a later one, matters because it keeps intermediate compounds from piling up. Unlike changes in gene expression, which can take minutes to hours, this form of control acts within seconds, because it alters the activity of enzyme molecules that already exist rather than the number of molecules the cell makes. Which statement best expresses the main idea of the passage?

    • A.Acting on the first committed step keeps intermediate compounds of a pathway from piling up
    • B.A pathway's end product can quickly slow its own synthesis by binding the first enzyme
    • C.Isoleucine slows its own pathway by binding threonine deaminase away from its active site
    • D.Cells mainly regulate metabolic pathways by changing how many enzyme molecules they make
    Show answerHide answer

    Correct answer: A pathway's end product can quickly slow its own synthesis by binding the first enzyme

    The passage as a whole explains feedback inhibition: a pathway's end product can quickly slow its own synthesis by binding the first enzyme, with every other sentence elaborating that mechanism. The isoleucine example is a true detail that illustrates the idea but is too narrow to be the main idea, and the point about intermediates explains only why the first step is chosen. The passage contrasts this fast control with changes in enzyme number rather than calling enzyme number the main method.

  2. Read the passage, then answer the question. When a pathogen enters the body for the first time, only a small number of lymphocytes carry receptors that happen to fit its antigens. Those few cells are selected: binding to the antigen, together with signals from helper T cells, triggers them to divide repeatedly, producing a clone of identical cells. Some members of the clone become effector cells, such as plasma cells that secrete antibodies, while others become long-lived memory cells. Because the starting population is so small, this primary response takes one to two weeks to reach its peak, and the person may become noticeably ill in the meantime. If the same antigen appears again, the memory cells, which far outnumber the original precursors, respond within days and produce more antibody, much of it binding the antigen more tightly. This secondary response is often fast enough that the infection is cleared before symptoms develop. Vaccines take advantage of this pattern by building the memory population without the risks of the disease itself. Which of the following best summarizes the passage?

    • A.Lymphocytes that fit an antigen multiply into clones that speed up any later response
    • B.Helper T cells kill infected cells directly, so antibodies matter only on second exposure
    • C.Memory cells formed in a first infection give lifelong protection against any later illness
    • D.Vaccines build a population of memory cells without exposing a person to the disease itself
    Show answerHide answer

    Correct answer: Lymphocytes that fit an antigen multiply into clones that speed up any later response

    The passage traces how lymphocytes that fit an antigen multiply into clones that speed up any later response, through memory cells, which is the full arc from first to second exposure. The lifelong-protection summary overstates the passage, which says the secondary response is often, not always, fast enough to prevent symptoms. The vaccine statement is accurate but covers only the final sentence, and the passage never says helper T cells destroy infected cells.

  3. Read the passage, then answer the question. Blood pH normally stays between 7.35 and 7.45. This stability depends less on the chemical strength of any single buffer than on the fact that the bicarbonate buffer system is linked to two organs. In the blood, carbonic acid and bicarbonate ions exist in equilibrium with dissolved carbon dioxide. When a strong acid enters the blood, bicarbonate accepts the extra hydrogen ions and forms carbonic acid, which breaks down into water and carbon dioxide. By itself, this reaction would soon use up the available bicarbonate. What makes the system effective is that both of its components can be adjusted: the lungs can exhale the added carbon dioxide within minutes, and the kidneys can, over hours to days, excrete hydrogen ions and generate new bicarbonate. Phosphate ions and proteins also bind hydrogen ions, and hemoglobin in particular buffers large amounts of acid inside red blood cells, but the body cannot replenish these buffers in the same way. Which detail from the passage most directly supports its central claim about what keeps blood pH stable?

    • A.Hemoglobin buffers a large amount of acid inside the body's red blood cells
    • B.Phosphate ions and proteins in the blood also bind some of the hydrogen ions
    • C.Bicarbonate accepts the hydrogen ions from a strong acid and forms carbonic acid
    • D.The lungs exhale carbon dioxide and the kidneys generate new bicarbonate ions
    Show answerHide answer

    Correct answer: The lungs exhale carbon dioxide and the kidneys generate new bicarbonate ions

    The central claim is that pH stability comes from the bicarbonate system being linked to the lungs and kidneys, so the detail that the lungs exhale carbon dioxide and the kidneys generate new bicarbonate ions is its direct support. The reaction of bicarbonate with a strong acid is mentioned, but the passage says that reaction alone would soon use up the bicarbonate, so it does not support the claim. The hemoglobin and phosphate details are offered as contrasts, buffers the body cannot replenish the same way.

  4. Read the passage, then answer the question. (1) Bone looks inert, but adult bone is constantly being rebuilt. In a process called remodeling, osteoclasts dissolve small pockets of old bone, and osteoblasts then fill each pocket with new matrix that later mineralizes. Roughly a tenth of the adult skeleton is replaced each year, which allows tiny fatigue cracks to be repaired before they spread. Remodeling also lets bone serve as a calcium reserve for the rest of the body. (2) The two cell types do not work independently. Cells of the osteoblast lineage produce a signaling protein called RANKL, which binds receptors on osteoclast precursors and drives them to mature into active osteoclasts. The same cells also release osteoprotegerin, a decoy receptor that binds RANKL and keeps it from acting. The balance between these two signals therefore sets how much bone is resorbed. Conditions that raise the ratio of RANKL to osteoprotegerin, such as the fall in estrogen after menopause, tip remodeling toward a net loss of bone. What is the main point of the second paragraph?

    • A.Osteoclasts release a decoy protein that keeps osteoblasts from maturing
    • B.Bone-forming cells set the amount of resorption through opposing signals
    • C.Adult bone is continually broken down and rebuilt instead of staying inert
    • D.Falling estrogen after menopause raises RANKL and leads to net bone loss
    Show answerHide answer

    Correct answer: Bone-forming cells set the amount of resorption through opposing signals

    The second paragraph explains that osteoblast-lineage cells control resorption by releasing RANKL, which activates osteoclasts, and osteoprotegerin, which blocks it, so bone-forming cells set the amount of resorption through opposing signals. That adult bone is continually rebuilt is the point of the first paragraph, not the second. The menopause sentence is a single example of the paragraph's idea, and the decoy protein comes from osteoblast-lineage cells and blocks osteoclast maturation, not the reverse.

  5. Read the passage, then answer the question. The concentration of calcium ions in blood plasma is held within a narrow range because nerves, muscles and blood clotting all depend on it. When calcium falls too low, nerves and muscles become overly excitable. When plasma calcium falls, cells of the parathyroid glands detect the change and release parathyroid hormone (PTH). PTH acts on two organs directly. In bone, it indirectly stimulates osteoclasts, which release calcium from the mineral matrix. In the kidneys, it increases the reabsorption of calcium from the filtrate, so less is lost in urine, and it stimulates the conversion of vitamin D to its active form, calcitriol. Calcitriol, in turn, increases the absorption of calcium from food in the small intestine. When plasma calcium rises, PTH secretion falls. The thyroid gland releases calcitonin when calcium is high, and calcitonin inhibits osteoclasts, but in adult humans, removing the thyroid does not noticeably disturb calcium balance, which suggests that calcitonin plays a minor role compared with PTH. Which statement is NOT supported by the passage?

    • A.PTH raises blood calcium by acting directly on the intestine to absorb more
    • B.PTH reduces the amount of calcium that the kidneys allow to be lost in urine
    • C.PTH frees calcium from bone by way of its indirect effect on the osteoclasts
    • D.Calcitonin seems to matter less than PTH for calcium balance in adult humans
    Show answerHide answer

    Correct answer: PTH raises blood calcium by acting directly on the intestine to absorb more

    The passage says PTH acts directly only on bone and the kidneys, and it raises intestinal absorption indirectly, through the calcitriol the kidneys make, so the statement that PTH raises blood calcium by acting directly on the intestine to absorb more is not supported. The kidney statement restates the passage's point about reabsorption, and the calcitonin statement matches the conclusion drawn from removing the thyroid. The bone statement is supported because the passage says PTH stimulates osteoclasts indirectly.

  6. Read the passage, then answer the question. The kidneys filter about 180 liters of plasma a day, and with it about 180 grams of glucose. In a healthy person, almost none of this glucose appears in the urine, because cells lining the proximal tubule reclaim it. On the side of these cells facing the tubule, a protein called SGLT2 moves glucose into the cell together with sodium ions. The sodium flows down a concentration gradient that is maintained by sodium-potassium pumps on the opposite side of the cell, and the glucose is carried along against its own gradient. Glucose then leaves the cell through a separate carrier and returns to the blood. SGLT2 accounts for about 90 percent of the glucose recovered; a related transporter farther along the tubule, SGLT1, recovers most of the rest. Because the number of transporters is limited, reabsorption has a maximum rate. When plasma glucose is so high that the filtered load exceeds this maximum, as in uncontrolled diabetes, the excess glucose stays in the filtrate and is excreted. Based on the passage, a drug that blocks SGLT2 in a person with normal plasma glucose would most likely have which effect?

    • A.SGLT1 would reclaim the extra glucose, so the urine would stay nearly glucose-free
    • B.Much more glucose would be excreted while blood levels remained in the usual range
    • C.Glucose would reach the urine only after plasma glucose rose well above normal
    • D.The sodium-potassium pumps would stop, so less glucose would leave the cells
    Show answerHide answer

    Correct answer: Much more glucose would be excreted while blood levels remained in the usual range

    SGLT2 recovers about 90 percent of filtered glucose, and SGLT1 normally handles only part of the remaining tenth, so blocking SGLT2 would mean much more glucose would be excreted while blood levels remained in the usual range. Linking urine glucose only to very high plasma glucose describes the untreated transport maximum, which the drug lowers. SGLT1 is described as recovering most of the small remainder, not the nine-tenths SGLT2 handles, and the passage gives no reason the pumps on the other side of the cell would stop.

  7. Read the passage, then answer the question. Allergic diseases such as hay fever and asthma became markedly more common in wealthy countries during the second half of the twentieth century. In 1989, the epidemiologist David Strachan reported that children with several older siblings were less likely to develop hay fever, and he proposed that early infections, passed between siblings, might protect against allergy. This idea, later called the hygiene hypothesis, has been attractive because it offers a single explanation for a broad trend. The evidence, however, is mixed. Children raised on traditional farms do show lower rates of allergy, but many common childhood infections do not appear to protect, and some infections are linked to more asthma, not less. Many researchers now suspect that what matters is not infection itself but early contact with a diverse range of harmless microbes. Even this revised version rests largely on observational studies, in which families who differ in exposure may also differ in other ways. It would be premature to conclude that cleanliness causes allergy, though the pattern is too consistent to dismiss. The author's attitude toward the hygiene hypothesis is best described as

    • A.firm skepticism, treating its pattern as a likely artifact of flawed studies
    • B.qualified support, treating early infection as the most likely protective cause
    • C.cautious interest, treating the trend as genuine but its explanation as open
    • D.measured approval, treating microbial contact as a proven cause of less allergy
    Show answerHide answer

    Correct answer: cautious interest, treating the trend as genuine but its explanation as open

    The author calls the evidence mixed and a causal conclusion premature, yet says the pattern is too consistent to dismiss, which is cautious interest, treating the trend as genuine but its explanation as open. Firm skepticism is ruled out because the author explicitly refuses to dismiss the pattern. Qualified support for infection fails because the passage reports that many infections do not protect and that researchers now favor harmless microbes, and nothing in it calls microbial contact proven.

  8. Read the passage, then answer the question. People with periodontitis, a chronic bacterial infection of the tissues that support the teeth, are more likely than people with healthy gums to develop cardiovascular disease. Several large observational studies have reported this association, and some investigators have proposed a causal explanation. Periodontitis produces persistent, low-grade inflammation, and bacteria from inflamed gums can enter the bloodstream during chewing or brushing. Because inflammation plays a central role in the formation of arterial plaques, these investigators argue that gum disease itself helps drive heart disease and that treating it might lower cardiovascular risk. Other researchers urge caution. Periodontitis and heart disease share several risk factors, including smoking, diabetes and older age, and people who neglect their gums may differ from others in diet, exercise and access to medical care. Separating these influences from any direct effect of the gum infection has proved difficult, and an association alone cannot show which factor, if any, is responsible. Which finding, if true, would most weaken the investigators' proposal that gum disease helps cause heart disease?

    • A.Bacteria from the patients' inflamed gums were found inside arterial plaques
    • B.The link vanished once the analysis adjusted for smoking and diabetes
    • C.The link grew stronger as the severity of the patients' gum disease rose
    • D.Gum treatment lowered the blood markers of inflammation in the patients
    Show answerHide answer

    Correct answer: The link vanished once the analysis adjusted for smoking and diabetes

    If the link vanished once the analysis adjusted for smoking and diabetes, the shared risk factors the passage names would explain the association, leaving no evidence that the gum infection itself contributes. A link that grows stronger with severity is a dose-response pattern, which supports rather than weakens a causal reading. Finding gum bacteria inside arterial plaques and lowering inflammation through gum treatment both strengthen the investigators' proposed mechanism.

  9. Cells lining the small intestine and the kidney's proximal tubules absorb glucose against its concentration gradient, often moving it from a region where it is scarce into a cell where it is already abundant. They manage this without spending ATP at the transporter itself. The protein responsible, a sodium-glucose cotransporter, binds a glucose molecule together with sodium ions and carries them inward at the same time. Because sodium is far more concentrated outside the cell than inside, sodium's movement down its gradient supplies the energy that drags glucose up its own gradient. The arrangement works only as long as the sodium gradient persists. That job falls to a separate protein on the opposite side of the cell, the sodium-potassium pump, which uses ATP to export three sodium ions for every two potassium ions it brings in. Glucose that accumulates inside the cell then leaves through a third protein, a carrier that lets it diffuse passively into the blood. Physiologists call the cotransporter's mechanism secondary active transport: active because it moves glucose uphill, secondary because the energy was spent earlier, by the pump. Based on the passage, if a drug completely blocked the sodium-potassium pump in these cells but left the cotransporter itself undamaged, which outcome would be expected?

    • A.Glucose uptake would rise as sodium built up outside the cell
    • B.Glucose uptake would dwindle as the gradient it relies on faded
    • C.Glucose uptake would go on, but glucose could not exit to the blood
    • D.Glucose uptake would go on, as the cotransporter uses no ATP itself
    Show answerHide answer

    Correct answer: Glucose uptake would dwindle as the gradient it relies on faded

    The passage says the cotransporter works only as long as the sodium gradient persists and that the pump is what maintains that gradient, so with the pump blocked sodium leaks in and glucose uptake dwindles as the gradient it relies on fades. The tempting idea that uptake would go on because the cotransporter uses no ATP itself ignores the word secondary: the energy was spent earlier by the pump. Sodium would build up inside the cell, not outside, and the exit carrier is described as passive, so blocking the pump would not stop glucose leaving for the blood.

  10. Bacteria acquire antibiotic resistance in two broad ways. A random mutation in the chromosome may alter the drug's target, and if the antibiotic is present, cells carrying that mutation survive and multiply while their neighbors die. Resistance can also arrive from outside. Many resistance genes sit on plasmids, small circles of DNA separate from the chromosome, which can be copied and passed from one cell to another through a bridge-like connection in a process called conjugation. Because plasmids can cross between different species, a gene that arose in a harmless soil bacterium may eventually turn up in a pathogen. A single plasmid often carries several resistance genes at once, so exposure to one antibiotic can select for resistance to drugs the cells have never encountered. Plasmids impose a cost, however: copying the extra DNA consumes resources, and in drug-free conditions plasmid-free cells sometimes outgrow their plasmid-carrying relatives. This observation has encouraged hopes that reducing antibiotic use will let resistance fade, although some plasmids acquire compensating mutations that lower their cost, allowing them to persist for many generations even when no drug is present. Which statement is NOT supported by the passage?

    • A.A resistance gene found in a pathogen may have arisen in another species
    • B.Chromosomal mutation is the more common source of resistance in bacteria
    • C.Plasmid-bearing cells can be outgrown by plasmid-free cells without drugs
    • D.Exposure to one antibiotic can select for resistance to another drug
    Show answerHide answer

    Correct answer: Chromosomal mutation is the more common source of resistance in bacteria

    The passage names chromosomal mutation and plasmid transfer as the two routes but never says which is more common, so the claim that chromosomal mutation is the more common source is not supported; listing a route first is not ranking it. The other three are each stated: one plasmid carrying several resistance genes means one drug can select for resistance to another, plasmids cross species, and plasmid-free cells sometimes outgrow plasmid carriers in drug-free conditions.

  11. Many flowering plants depend on animals to carry pollen between individuals, and biologists have long asked whether flower color alone can steer a pollinator's choices. In a meadow where a single wildflower species grows in both purple and white forms, a team of ecologists recorded bumblebee visits over two summers. Purple plants received nearly twice as many visits as white plants and, by the end of each season, had produced substantially more seed. The team concluded that bumblebees prefer purple flowers and that this preference gives purple plants a reproductive advantage. The conclusion fits a broader pattern: bumblebees see violet and blue wavelengths well, and in laboratory trials with artificial flowers, naive bees often approach blue-violet targets first. Yet a meadow is not a laboratory. Flowers differ in more than color, and the plants that bees visit most may also be the ones growing where conditions favor both nectar production and seed set. The team acknowledged this limitation and proposed a follow-up in which purple and white plants would be grown in pots and set out side by side at randomly chosen spots. Which finding, if true, would most seriously weaken the team's conclusion?

    • A.At night, moths visited white plants more often than they visited purple plants
    • B.In laboratory trials, naive bees approached white targets as often as blue ones
    • C.Purple plants grew mostly in moist, sunny patches where white plants were rare
    • D.In the potted follow-up, bees again visited purple plants about twice as often
    Show answerHide answer

    Correct answer: Purple plants grew mostly in moist, sunny patches where white plants were rare

    If purple plants grew mostly in moist, sunny patches where white plants were rare, their extra visits and seed could come from the richer site rather than from color, which is exactly the confound the passage warns about and undercuts both parts of the conclusion. A laboratory result showing no preference for blue would only remove one piece of background support; it says nothing about what happened in this meadow. The potted result would strengthen the conclusion, and moth visits to white plants do not explain why purple plants drew more bees and set more seed.

  12. Large population surveys consistently find that adults who report sleeping fewer than six hours a night are more likely to have high blood pressure than adults who sleep seven to eight hours. The association persists after researchers adjust for age, body weight, and smoking, which makes it harder to dismiss as a by-product of those factors. Several plausible pathways have been suggested. Short sleep is accompanied by heightened activity of the sympathetic nervous system, which constricts blood vessels and raises heart rate, and the normal nighttime dip in blood pressure is blunted when sleep is cut short. Even so, the direction of the relationship is not settled. Obstructive sleep apnea both fragments sleep and raises blood pressure, so some short sleepers may have an undiagnosed disorder driving both. Work stress, shift schedules, and depression can likewise shorten sleep while independently straining the cardiovascular system. Short-term laboratory experiments that restrict healthy volunteers' sleep for a few nights do produce small rises in blood pressure, but whether those changes persist over years, and whether lengthening sleep would lower pressure in people who already have hypertension, remains under study. Which statement is most strongly supported by the passage?

    • A.Sleep apnea, not short sleep itself, explains the association the surveys found
    • B.Lengthening sleep would lower blood pressure in adults who have hypertension
    • C.Cutting sleep for a few nights can modestly raise pressure in healthy adults
    • D.Short sleep raises blood pressure in adults regardless of their age or weight
    Show answerHide answer

    Correct answer: Cutting sleep for a few nights can modestly raise pressure in healthy adults

    The passage directly reports that restricting healthy volunteers' sleep for a few nights produces small rises in blood pressure, so the statement that cutting sleep for a few nights can modestly raise pressure in healthy adults is supported. The most tempting wrong choice treats the adjustment for age and weight as proof of cause, but adjustment only makes the survey association harder to dismiss; the passage says the direction of the relationship is not settled. Sleep apnea is offered as one possible explanation for some short sleepers, not the whole association, and the effect of lengthening sleep in hypertension is described as still under study.

  13. For most of the twentieth century, physicians attributed peptic ulcers to excess stomach acid, often blamed on stress and spicy food. The stomach, with a pH that can fall below 2, was assumed to be too hostile for bacteria to colonize, and treatment centered on antacids and acid-suppressing drugs. Ulcers healed on these regimens but frequently returned once the drugs were stopped. Around 1980 the Australian pathologist Robin Warren observed curved bacteria in biopsies taken from inflamed stomach linings, and the physician Barry Marshall succeeded in growing the organism, later named Helicobacter pylori, in culture. Their claim that the bacterium caused gastritis and ulcers met resistance, and in 1984 Marshall drank a culture of it, developing gastritis within days. Later clinical trials showed that eradicating H. pylori with antibiotics sharply reduced ulcer recurrence. The bacterium survives in the stomach by burrowing into the mucus layer and producing urease, an enzyme that generates ammonia to neutralize the acid around it. Marshall and Warren received the Nobel Prize in Physiology or Medicine in 2005. Which choice best states the primary purpose of the passage?

    • A.To explain how a bacterium manages to survive the acid conditions of the stomach
    • B.To compare how well antacid drugs and antibiotics prevent ulcers from returning
    • C.To recount how new evidence overturned an accepted explanation for a disease
    • D.To describe the method by which a stomach bacterium was first grown in culture
    Show answerHide answer

    Correct answer: To recount how new evidence overturned an accepted explanation for a disease

    The passage opens with the long-held acid-and-stress view of ulcers and then traces the observations, self-experiment, and trials that replaced it, so its primary purpose is to recount how new evidence overturned an accepted explanation for a disease. The sentence on urease and mucus explains how the bacterium survives acid, but it is one supporting detail answering the old objection, not the passage's purpose. The culturing is mentioned in a single clause with no method described, and recurrence rates are mentioned only in passing.

  14. Penicillin and its relatives kill bacteria by sabotaging construction rather than attacking a finished structure. The bacterial cell wall is built from peptidoglycan, long sugar chains linked to one another by short peptide bridges, forming a mesh that resists the pressure of water pushing into the cell. As a bacterium grows and prepares to divide, it must continually loosen this mesh in places and insert new material. The final cross-linking step is carried out by enzymes called penicillin-binding proteins, and penicillin binds to them irreversibly. When cross-linking fails while the cell is still loosening its old wall, the mesh weakens, and the cell eventually bursts. Human cells have no peptidoglycan, which is why penicillin can be given in large doses with relatively little direct toxicity. Not all bacteria are equally vulnerable, though. In many Gram-negative species, an outer membrane surrounds the thin peptidoglycan layer and can slow the drug's entry, while some bacteria produce beta-lactamase enzymes that cut the penicillin molecule apart before it reaches its target. Which conclusion about penicillin can most reasonably be inferred from the passage?

    • A.It would kill Gram-negative bacteria faster, since their wall layer is thinner
    • B.It would have little effect on bacteria that have stopped growing and dividing
    • C.It would work better when paired with drugs that halt the growth of bacteria
    • D.It acts mainly by digesting peptidoglycan already present in a finished wall
    Show answerHide answer

    Correct answer: It would have little effect on bacteria that have stopped growing and dividing

    The passage ties penicillin's killing to the moment a growing cell loosens its wall and inserts new material, so a bacterium that has stopped growing and dividing gives the drug little to sabotage. Pairing penicillin with a growth-halting drug sounds like stronger treatment, but by the same reasoning it would weaken penicillin rather than help it. The passage says the drug sabotages construction rather than attacking a finished wall, and it presents the Gram-negative outer membrane as slowing the drug's entry, not speeding killing.

  15. Mitochondria, the organelles that carry out most of a eukaryotic cell's aerobic respiration, resemble bacteria living inside a larger cell. They are about the size of a typical bacterium, they are surrounded by two membranes, and they divide by splitting in two rather than being assembled by the cell from scratch. They also carry their own DNA, a small circular molecule resembling a bacterial chromosome, and their ribosomes are closer in size and structure to bacterial ribosomes than to those in the surrounding cytoplasm. These observations underlie the endosymbiotic theory, which holds that mitochondria descend from free-living bacteria that were engulfed by an ancestral cell and, rather than being digested, were retained as partners. Chloroplasts are thought to have arisen in a similar way from photosynthetic bacteria. Nevertheless, a mitochondrion today could not survive on its own. Over hundreds of millions of years, most of the genes its ancestor carried have been lost or transferred to the nucleus, so the great majority of mitochondrial proteins are now encoded by nuclear genes, made in the cytoplasm, and imported into the organelle. In the passage, the word "Nevertheless" primarily serves which purpose?

    • A.To introduce a contrast between how chloroplasts and mitochondria arose
    • B.To introduce a finding that casts doubt on the endosymbiotic theory itself
    • C.To introduce more evidence that mitochondria descend from free-living bacteria
    • D.To introduce a limit on how far the comparison with bacteria can be taken
    Show answerHide answer

    Correct answer: To introduce a limit on how far the comparison with bacteria can be taken

    After listing the ways mitochondria resemble bacteria, the author uses nevertheless to introduce a limit on how far the comparison with bacteria can be taken: unlike a bacterium, a mitochondrion can no longer live on its own. The most tempting misreading treats the contrast as an attack on the endosymbiotic theory, but the following sentence explains the dependence as gene loss from the bacterial ancestor, which fits the theory. The word marks a contrast, so it does not add supporting evidence, and the chloroplast sentence describes a similar origin rather than a different one.

  16. The human immune system operates in two broad tiers. The innate immune system is present from birth and responds within minutes to hours of an infection. Its cells, such as neutrophils and macrophages, recognize molecular patterns shared by many kinds of microbes, for example components of bacterial cell walls, so a single receptor type can detect a wide range of invaders. Because these receptors are inherited and fixed, the innate response to a given microbe is essentially the same on the second encounter as on the first. The adaptive immune system works differently. Its lymphocytes, the B cells and T cells, each carry receptors generated by the random rearrangement of gene segments, so that collectively they can recognize an enormous variety of specific molecular shapes, or antigens. When a lymphocyte meets its matching antigen, it multiplies into a large population of identical cells, a process that takes several days during a first infection. Some of these cells persist as memory cells, so that a later exposure to the same antigen triggers a faster and stronger response. The two tiers are not independent, however: innate cells display fragments of microbes to T cells, helping to launch the adaptive response. According to the passage, the innate and adaptive immune systems differ in each of the following respects EXCEPT which one?

    • A.Whether a second exposure brings a faster response than the first
    • B.How quickly each responds at the start of a first infection
    • C.Whether its receptors are inherited or built by gene rearrangement
    • D.Whether it can respond to a microbe the body has not met before
    Show answerHide answer

    Correct answer: Whether it can respond to a microbe the body has not met before

    Both tiers respond to a microbe the body has not met before: innate cells detect shared patterns at once, and adaptive lymphocytes respond during a first infection, only more slowly, so this is not a difference the passage draws. The tempting confusion is to equate the adaptive system with memory and assume it needs a prior exposure, but memory is what makes the second response faster and stronger, not what allows the first. Speed of the first response, inherited versus rearranged receptors, and an unchanged versus boosted second response are all contrasts the passage states.

  17. Fish that live in fresh water and fish that live in the ocean face opposite water problems. A freshwater fish's body fluids are saltier than the water around it, so water constantly moves into its tissues by osmosis, especially across the thin membranes of the gills. To cope, the fish rarely drinks, and its kidneys produce large volumes of very dilute urine. Specialized cells in the gills also take up salt ions from the surrounding water, replacing what is lost in the urine. A marine bony fish, by contrast, has body fluids less salty than seawater. It therefore loses water to its surroundings and must drink seawater almost continuously. Its kidneys produce only small amounts of urine, and its gill cells pump excess salt out of the body. Sharks and rays, however, take a different route. They retain high concentrations of urea in their blood, which raises the concentration of their body fluids to roughly that of seawater. As a result, they gain little water and lose little by osmosis, and they need not drink nearly as much as bony marine fish do. In the passage, the word "however" in the sentence beginning "Sharks and rays" mainly serves to mark sharks and rays as

    • A.an exception to the marine pattern described just before
    • B.an exception to the rule that water moves by osmosis
    • C.facing the opposite water problem from marine bony fish
    • D.an exception to the freshwater pattern described at the start
    Show answerHide answer

    Correct answer: an exception to the marine pattern described just before

    "However" follows the account of marine bony fish, which lose water and must drink, and it introduces sharks and rays as ocean animals that solve the same problem differently. The freshwater fish were already contrasted earlier with "by contrast," so the new contrast is with the marine pattern just described. Sharks do not escape osmosis; the passage says urea raises their fluid concentration so that osmosis moves little water either way.

  18. Most plants, called C3 plants, fix carbon dioxide directly with the enzyme rubisco inside the mesophyll cells of the leaf. Rubisco has a costly flaw: it can bind oxygen instead of carbon dioxide, triggering a wasteful process called photorespiration that releases carbon the plant had already fixed. Photorespiration becomes more frequent on hot, dry days, when plants close their stomata to save water, so oxygen builds up inside the leaf while carbon dioxide runs low. Plants such as corn and sugarcane, called C4 plants, divide the work between two cell types. In the mesophyll, a different enzyme, PEP carboxylase, captures carbon dioxide; this enzyme does not react with oxygen. The captured carbon is passed as a four-carbon compound to tightly packed bundle-sheath cells deeper in the leaf, where it is released and concentrated around rubisco. Because rubisco there is surrounded by carbon dioxide, photorespiration is nearly eliminated. The arrangement is not free: shuttling carbon between the two cell types costs the plant extra ATP for each molecule of carbon dioxide fixed. In cool, moist climates, where photorespiration is modest, C3 plants often grow as well as or better than C4 plants. According to the passage, which statement correctly describes a difference between C4 plants and C3 plants?

    • A.In C4 plants, rubisco works in bundle-sheath cells instead of mesophyll cells
    • B.In C4 plants, PEP carboxylase takes over rubisco's job in the bundle sheath
    • C.In C4 plants, each carbon dioxide fixed costs less ATP than it does in C3 plants
    • D.In C4 plants, photorespiration is avoided by keeping stomata open on hot days
    Show answerHide answer

    Correct answer: In C4 plants, rubisco works in bundle-sheath cells instead of mesophyll cells

    The passage says C3 plants use rubisco in the mesophyll, while C4 plants capture carbon in the mesophyll and release it around rubisco in the bundle-sheath cells. PEP carboxylase does not replace rubisco; it only captures carbon in the mesophyll and hands it on, and rubisco still does its work in the bundle sheath. The passage also states that the C4 shuttle costs extra ATP, and it never says C4 plants keep their stomata open.

  19. A skeletal muscle contracts only after a chain of events that begins in a motor neuron, although the chain is often easiest to describe from its end backward. The final step is mechanical: myosin heads bind to actin filaments and pull on them, shortening the muscle fiber. Myosin can reach actin only after calcium ions, released from a storage network inside the fiber called the sarcoplasmic reticulum, bind to regulatory proteins and shift them off actin's binding sites. That calcium release is triggered by an electrical signal, an action potential, that travels along the muscle fiber's membrane and dives into the fiber through small tunnels called T-tubules. The muscle's action potential, in turn, starts where the nerve meets the muscle. There, the neuron's own action potential opens channels that let calcium flow into the nerve ending, and this influx causes the nerve ending to release the neurotransmitter acetylcholine. Acetylcholine crosses a narrow gap and binds to receptors on the muscle membrane, opening channels that let sodium ions rush in. This depolarization is what launches the action potential in the muscle fiber. Based on the passage, which event occurs immediately before calcium is released from the sarcoplasmic reticulum?

    • A.Regulatory proteins shift off the binding sites along actin
    • B.Calcium ions flow into the nerve ending of the motor neuron
    • C.An action potential spreads along the membrane and T-tubules
    • D.Acetylcholine binds to receptors on the muscle fiber membrane
    Show answerHide answer

    Correct answer: An action potential spreads along the membrane and T-tubules

    Read forward, the chain is: calcium enters the nerve ending, acetylcholine is released and binds the muscle membrane, sodium rushes in, the muscle action potential travels along the membrane and T-tubules, and only then does the sarcoplasmic reticulum release calcium. Calcium entering the nerve ending is a different calcium step much earlier in the chain. Acetylcholine binding also comes earlier, and regulatory proteins shift only after the released calcium binds them.

  20. Plants cannot walk, yet their seeds routinely travel far from the parent. Ecologists sort these journeys by the agent that carries the seed. In anemochory, wind does the work: dandelion seeds ride on feathery parachutes, and maple fruits spin like propellers. In hydrochory, moving water is the carrier, as when a coconut floats for weeks before washing ashore. Zoochory, dispersal by animals, is split in two. In epizoochory, seeds travel on the outside of an animal, hooked into fur or stuck to feathers with sticky coatings. In endozoochory, an animal eats a fruit, and the seeds pass through its gut and are deposited, often with a ready supply of fertilizer, far from where they were swallowed. Researchers stress that the category follows the carrier, not the landscape the seed passes through or the shape of the seed itself. A seed that sticks to a duck's feet and crosses a lake is therefore classed with the hooked seeds in fur, not with the floating coconut. Many plants hedge their bets, and a single species may use more than one route; the classification then applies to each journey separately, not to the plant as a whole. Which journey would the passage's system classify as epizoochory?

    • A.A sedge seed caught in the mud on a heron's legs as it flies to a pond
    • B.A fig seed swallowed by a fish and released in its droppings downstream
    • C.A mangrove seedling that drops into a creek and drifts to a new bank
    • D.A hooked burr snapped off a dry stalk and rolled across a plain by wind
    Show answerHide answer

    Correct answer: A sedge seed caught in the mud on a heron's legs as it flies to a pond

    Epizoochory is defined as an animal carrying a seed on its outside, and the passage says the category follows the carrier, so mud on a heron's legs is epizoochory just like the seed on the duck's feet. The hooked burr is the trap: its shape suits fur, but the passage says shape does not decide the category, and wind carried it, which makes it anemochory. The fig seed travels with water around it, but the fish carries it inside its gut, so it is endozoochory, and the drifting mangrove is hydrochory.

  21. Over the past two decades, several large observational studies have tracked thousands of adults for many years, recording how much they slept and whether they later developed memory problems. Taken together, these studies suggest that people who regularly sleep fewer than six hours a night are more likely to experience cognitive decline in later life. Laboratory work offers a possible mechanism. In mice, sleep appears to speed the flow of fluid through the brain, which may help clear away proteins such as beta-amyloid that build up in Alzheimer's disease. Still, the human findings must be read with care. People in the early, undiagnosed stages of dementia often sleep poorly, so it is possible that the brain changes cause the short sleep rather than the reverse. Depression, chronic pain, and shift work can also disturb sleep and independently affect memory. Only randomized trials, in which some participants are helped to sleep longer and are then compared with those who are not, could show that improving sleep protects the brain, and such trials are difficult to run over the decades that dementia takes to develop. The author's choice of the word "suggest" in the second sentence indicates that the author views the observational studies as

    • A.evidence of a cause that the mouse research has confirmed
    • B.too small and too brief to show any real link between them
    • C.evidence that short sleep causes the cognitive decline later
    • D.evidence of a link whose direction of cause is unproven
    Show answerHide answer

    Correct answer: evidence of a link whose direction of cause is unproven

    "Suggest" signals a real but unproven finding, and the passage backs that reading by noting that early dementia may cause short sleep rather than the reverse and that only randomized trials could show cause. The mouse work is offered only as a possible mechanism, with its own hedges ("appears," "may"), so it confirms nothing in people. The studies are not dismissed as weak either; the passage calls them large and long-running.

  22. Cytochrome c is a small protein that shuttles electrons between two large complexes in the inner membrane of the mitochondrion, a step essential to aerobic respiration. Because nearly every eukaryote depends on this step, biochemists have sequenced the protein from hundreds of species, from yeast to sunflowers to humans. The results are striking. Of the roughly 104 amino acids in the human version, a substantial share occupy the same positions in organisms whose last common ancestor lived more than a billion years ago. Researchers describe these positions as highly conserved. Their explanation is functional: residues that hold the heme group in place or form the docking surface for the partner complexes cannot change without crippling electron transport, so mutations at those sites are removed by natural selection almost as quickly as they arise. Positions on the protein's outer surface, by contrast, tolerate substitution, and they differ widely among species. This uneven pattern has made cytochrome c useful in two ways. The variable positions accumulate differences at a fairly steady pace, so counting them helps estimate how long ago two lineages diverged. The conserved positions, meanwhile, point experimenters toward the parts of the molecule that matter most for its job. A molecule only a hundred or so amino acids long can therefore preserve, in its sequence, a record stretching back to the earliest eukaryotes. As used in the passage, the word "conserved" most nearly means

    • A.kept in reserve by the cell until a later demand arises
    • B.kept shielded from damage by the protein's outer surface
    • C.kept nearly unchanged across distantly related species
    • D.kept at steady levels by the cell to sustain respiration
    Show answerHide answer

    Correct answer: kept nearly unchanged across distantly related species

    In the passage, conserved positions are the ones that occupy the same places in organisms separated by more than a billion years, because selection removes mutations there, so the word means kept nearly unchanged across distantly related species. The everyday sense of saving something for later, kept in reserve by the cell, does not fit a sequence position. The passage contrasts conserved sites with variable surface sites; it never says the surface protects them or that the cell holds the protein at steady levels.

  23. The marine bacterium Vibrio fischeri lives freely in seawater and also colonizes the light organ of the Hawaiian bobtail squid. A single free-living cell produces almost no light, yet the dense population packed inside the squid glows brightly. The switch depends on small diffusible molecules called autoinducers. Each cell releases autoinducers continuously at a low rate, and the molecules pass easily across cell membranes. In open water, they diffuse away almost as soon as they are made, so their concentration around any one cell stays negligible. In the confined light organ, where cell numbers reach very high densities, the molecules accumulate. Once their concentration crosses a threshold, they bind a receptor protein inside each cell, and the receptor-autoinducer complex switches on the lux genes, which encode the enzyme luciferase and the other proteins needed for light production. Because the response depends on how many neighbors are present, biologists call this kind of communication quorum sensing. The squid benefits too: the glow, matched to moonlight from above, hides the animal's shadow from predators below. Similar systems control toxin release and biofilm formation in many pathogens, which has prompted interest in drugs that block the signal rather than kill the bacteria. Based on the passage, autoinducers are best described as

    • A.signal molecules whose local concentration rises with the density of the population
    • B.receptor proteins that switch on the lux genes when enough neighboring cells are present
    • C.enzymes encoded by the lux genes that produce light once a signal threshold is crossed
    • D.signal molecules that cells begin releasing only after they colonize the squid's organ
    Show answerHide answer

    Correct answer: signal molecules whose local concentration rises with the density of the population

    The passage says each cell releases autoinducers continuously, that they diffuse away in open water but accumulate where cells are packed densely, so they are signal molecules whose local concentration rises with the density of the population. The receptor protein is a separate molecule that autoinducers bind, and luciferase is the light-producing enzyme the lux genes encode. The claim that release begins only after colonization contradicts the statement that cells release autoinducers continuously, even in open water.

  24. Cells die in more than one way, and the manner of death matters to the tissue around them. Necrosis is typically the result of injury, such as a loss of blood supply, a toxin, or a burn. The damaged cell cannot keep water out, so it swells; its organelles break down, and eventually its outer membrane ruptures. The cell's contents spill into the surrounding tissue, where they attract immune cells and set off inflammation, which can injure neighboring cells that were otherwise healthy. Apoptosis, in contrast, is an orderly, energy-requiring program that the cell carries out on itself. Enzymes called caspases cut up proteins in a controlled sequence, the cell shrinks, its DNA is chopped into regular fragments, and the cell breaks into small membrane-wrapped packages. Because the membrane around each package stays intact, nothing leaks out; nearby phagocytes recognize signals on the packages' surfaces and engulf them quietly, without inflammation. Apoptosis is not only a response to damage. During embryonic development, it removes the webbing between the fingers, and throughout life it eliminates cells whose DNA is beyond repair. Which statement is NOT supported by the passage?

    • A.A cell without working caspases would struggle to finish apoptosis
    • B.A cell dying by necrosis shrinks before its membrane ruptures
    • C.A cell unable to make ATP would be unlikely to die by apoptosis
    • D.A cell can undergo apoptosis even when it has suffered no injury
    Show answerHide answer

    Correct answer: A cell dying by necrosis shrinks before its membrane ruptures

    The passage says a necrotic cell swells because it cannot keep water out; shrinking belongs to apoptosis, so the statement that a cell dying by necrosis shrinks before its membrane ruptures is not supported. The most tempting wrong choice is the ATP statement, which is a fair inference because the passage calls apoptosis an energy-requiring program. Apoptosis without injury is supported by the webbing removed during development, and the caspase statement follows from caspases carrying out the controlled sequence.

  25. Read the passage, then answer the question. For decades after community water fluoridation began, most dentists believed that fluoride worked mainly from the inside. Swallowed fluoride, the reasoning went, was carried by the blood to developing teeth and built into the enamel crystals as they formed, producing teeth that were permanently harder to dissolve. That view shaped advice for years, including the idea that fluoride mattered chiefly for young children whose teeth were still forming. Later laboratory and clinical work changed the picture. The amount of fluoride built into enamel during development turned out to be too small to explain the large drop in decay. What mattered far more was fluoride present in the mouth at low concentration, in saliva and in the film of plaque on the teeth. There it slows the dissolving of enamel when bacteria produce acid, and it speeds the rebuilding of mineral once the acid is cleared; the rebuilt mineral resists acid better than the original did. This shift explains why public health agencies now stress frequent exposure to small amounts of fluoride, from toothpaste and fluoridated water, throughout life rather than only in childhood. Adults, whose enamel formed long ago, still benefit. Which of the following best expresses the main idea of the passage?

    • A.Fluoride was added to water supplies long before scientists understood how it protected the teeth from acid
    • B.Fluoride protects teeth chiefly through its presence in the mouth throughout life, not through forming enamel
    • C.Fluoride rebuilds enamel after an acid attack, and the rebuilt mineral resists acid better than the original did
    • D.Fluoride must be swallowed during childhood so that the blood can carry it into the enamel of forming teeth
    Show answerHide answer

    Correct answer: Fluoride protects teeth chiefly through its presence in the mouth throughout life, not through forming enamel

    The passage is built around a shift in understanding: the old belief that swallowed fluoride hardened developing enamel gave way to evidence that low levels of fluoride in saliva and plaque do most of the work, which is why exposure throughout life matters. The statement that fluoride rebuilds enamel into more acid-resistant mineral is true in the passage but is one supporting detail of how topical fluoride acts. The childhood-swallowing statement is the older view the passage says was replaced, and the claim about water supplies is only implied background, not the point.

  26. Read the passage, then answer the question. (1) Saliva is the mouth's main defense against acid. After a person eats sugar, bacteria in dental plaque ferment it, and within minutes the pH at the tooth surface can fall below about 5.5, the level at which enamel begins to dissolve. Saliva reverses this drop. Its bicarbonate neutralizes acid, its calcium and phosphate ions allow lost mineral to be redeposited, and its flow washes sugar away. When saliva flow is stimulated, for example by chewing, its bicarbonate concentration rises and recovery is faster. (2) This protection has limits, however, and they depend on timing rather than on saliva itself. Recovery to a resting pH typically takes from twenty minutes to an hour after each sugar exposure. A person who sips a sweetened drink over an afternoon restarts the acid attack before saliva can finish its work, so the teeth spend much of the day below the critical level. The same amount of sugar taken at a single meal produces only one such period. For this reason, how often sugar is consumed can matter as much as how much is consumed. The main point of the second paragraph is that

    • A.saliva neutralizes plaque acid faster when chewing increases the flow it delivers
    • B.sweetened drinks harm enamel more than meals do because they contain more sugar
    • C.saliva's defense can fail when acid attacks come too close together for it to recover
    • D.the total amount of sugar consumed sets how long the enamel stays below its critical pH
    Show answerHide answer

    Correct answer: saliva's defense can fail when acid attacks come too close together for it to recover

    The second paragraph qualifies the first: saliva's protection is real, but if sugar exposures are frequent, each new attack begins before the roughly twenty- to sixty-minute recovery is finished, so saliva's defense can fail when acid attacks come too close together. The point about chewing speeding neutralization is accurate but comes from the first paragraph. The paragraph says frequency can matter as much as total amount, so the amount-based statement reverses it, and sipped drinks are harmful because of how often they are sipped, not because they contain more sugar.

  27. Read the passage, then answer the question. For much of the twentieth century, tooth decay was explained by the specific plaque hypothesis. In this view, caries was an infection caused by a few particular species, above all Streptococcus mutans, and the logical goal was to suppress or eliminate those organisms, perhaps one day with a vaccine. The ecological plaque hypothesis, proposed in the 1990s by the microbiologist Philip Marsh, places the cause elsewhere. It holds that acid-producing and acid-tolerant bacteria, S. mutans among them, are normal minor members of a healthy plaque community. Disease follows when the environment changes, most often through frequent sugar intake, so that repeated drops in pH favor these species over their neighbors and shift the whole community toward one that makes and survives acid. The two views predict different things. The first predicts that people without S. mutans should be free of decay; in fact, caries occurs in some people in whom S. mutans is scarce or undetected, with other acid-tolerant species present instead. The second predicts that changing the conditions, by reducing how often sugar is eaten or by raising plaque pH, should restore a healthy balance without eradicating any single species. The primary purpose of the passage is to

    • A.argue that a vaccine against a single species could one day prevent most cases of decay
    • B.contrast two accounts of what causes tooth decay and the different outcomes each predicts
    • C.explain how frequent sugar intake lowers plaque pH and lets acid-tolerant species take over
    • D.recount how researchers identified the one species of bacteria responsible for tooth decay
    Show answerHide answer

    Correct answer: contrast two accounts of what causes tooth decay and the different outcomes each predicts

    The passage lays out the specific plaque hypothesis, then the ecological plaque hypothesis, and closes by setting their predictions side by side, so its purpose is to contrast two accounts of what causes tooth decay. The sugar-and-pH mechanism is described only as part of the second account, so explaining it is too narrow a purpose. The vaccine idea is mentioned only as a goal of the older view, and the passage never presents one species as established as the single cause; it reports evidence against that idea.

  28. Read the passage, then answer the question. When Frederick McKay opened a dental practice in Colorado Springs in 1901, he was puzzled to find that many local residents had brown stains on their teeth, a condition people there called Colorado brown stain. No dental textbook described it. McKay spent years documenting the mottling, at one point enlisting the noted dental researcher G. V. Black, and he observed two things: the stains appeared in people who had grown up in the area, and the stained teeth, though unsightly, seemed unusually resistant to decay. He came to suspect something in the water. The answer arrived in 1931, when chemical analysis of water from a town where the stain was common revealed unusually high levels of fluoride. Public health researchers then asked a new question: was there a level of fluoride low enough to avoid the staining while keeping the protection against decay? Surveys of many communities suggested that there was, and in the 1940s several cities began adding controlled amounts of fluoride to their water to test the idea. The passage is primarily concerned with

    • A.showing that the stain found in one town was a cosmetic concern rather than a danger to health
    • B.explaining how a mineral in water stains the enamel of children's teeth as the enamel is forming
    • C.tracing how a puzzling stain led researchers to connect a water mineral with resistance to decay
    • D.arguing that public water should hold the mineral levels once found in the water of Colorado towns
    Show answerHide answer

    Correct answer: tracing how a puzzling stain led researchers to connect a water mineral with resistance to decay

    The passage follows a sequence of events from McKay's first puzzle in 1901, through the 1931 water analysis, to the community trials of the 1940s, so it is primarily concerned with tracing how a puzzling stain led researchers to connect a water mineral with resistance to decay. It never explains how fluoride produces staining, so the mechanism option goes beyond it. The passage says researchers sought a level low enough to avoid staining, which is the opposite of recommending the high levels found in those towns, and the cosmetic point is one observation within the story, not its focus.

  29. Read the passage, then answer the question. Diabetes has long been recognized as a risk factor for periodontitis: people whose blood glucose is poorly controlled develop more severe gum disease and lose supporting bone faster. A newer claim runs the other way, holding that periodontitis may worsen diabetes. The idea is biologically plausible. Infected gum tissue releases inflammatory signals such as tumor necrosis factor and interleukin-6 into the bloodstream, and these signals are known to interfere with the action of insulin. Clinical trials have tested the claim directly by treating periodontitis and then measuring HbA1c, a marker of average blood glucose over roughly the previous three months. A pooled analysis of these trials reports a drop of about 0.4 percentage points three to four months after treatment, an encouraging result for a treatment that targets the mouth rather than the pancreas or the liver. Still, many of the trials were small, several followed patients for only a few months, and it is not yet clear how long the benefit lasts. Periodontal care is worth offering to people with diabetes, but it cannot be regarded as a substitute for medical management of the disease. The author's attitude toward the claim that treating periodontitis improves blood glucose control is best described as

    • A.measured optimism, treating the benefit as real but modest and of uncertain duration
    • B.firm conviction, treating the benefit as proven large enough to replace some diabetes drugs
    • C.deep doubt, treating the benefit as an artifact of trials too small and brief to be trusted
    • D.even-handed neutrality, treating the benefit as equally likely to be genuine or illusory
    Show answerHide answer

    Correct answer: measured optimism, treating the benefit as real but modest and of uncertain duration

    The author calls the result encouraging and recommends offering periodontal care, yet notes small trials, short follow-up and an unknown duration of benefit, which is measured optimism about a real but modest effect. Even-handed neutrality is tempting because the author hedges, but the author is not balanced between real and illusory; the plausible mechanism and the recommendation tilt toward real. Firm conviction is contradicted by the statement that periodontal care cannot substitute for medical management, and deep doubt ignores the author's word 'encouraging.'

  30. Read the passage, then answer the question. Fever is often treated as a malfunction to be suppressed, but the body raises its temperature deliberately. When immune cells detect an infection, they release signaling molecules called pyrogens, which act on the hypothalamus and raise the temperature at which the body tries to hold itself. The person shivers and feels cold, not because the body is losing heat but because its normal temperature now falls below the new set point. Several lines of evidence suggest that this response is useful. Many bacteria and viruses multiply more slowly at temperatures a few degrees above normal, and some immune cells move and respond more effectively when warmed. Lizards, which cannot generate much body heat, seek out warm places when infected with bacteria, and in experiments those kept from doing so were more likely to die. Fever also has costs: each degree of increase raises the body's energy use, and very high fevers can damage tissue. Its benefit, then, is real but bounded, which is why physicians weigh comfort and risk rather than lowering every fever by reflex. Which of the following titles best fits the passage?

    • A.Fever as a Reset of the Hypothalamic Set Point
    • B.Fever as a Regulated Defense That Carries Costs
    • C.Fever as a Defense Best Left Untreated by Doctors
    • D.Fever as a Failure of Body Temperature Control
    Show answerHide answer

    Correct answer: Fever as a Regulated Defense That Carries Costs

    The passage argues that fever is a deliberate, regulated response that helps fight infection, then weighs that benefit against energy use and tissue damage, so the best title presents fever as a regulated defense that carries costs. The set-point title names a mechanism described in two sentences, which is too narrow. The untreated title drops the author's qualifier that the benefit is bounded and that physicians weigh comfort and risk, and the failure title restates the view the passage opens by rejecting.

  31. Read the passage, then answer the question. Nearly all infants produce lactase, the enzyme that splits milk sugar in the small intestine, but in most of the world's adults its production falls sharply after weaning. Adults who lack the enzyme can feel bloating and cramps after drinking milk, because undigested lactose passes to the colon, where bacteria ferment it. In some populations, however, most adults continue making lactase throughout life. This trait, called lactase persistence, is common in northern Europe and in some herding peoples of East Africa and the Middle East, and it is rare in East Asia. Genetic studies have shown that the trait is caused by different mutations in different regions, each lying in a stretch of DNA that controls the lactase gene rather than in the gene itself. That several separate mutations produce the same result, and that each became common only in populations with a long history of keeping animals for milk, points to strong natural selection: where fresh milk was a reliable food, adults who could digest it had an advantage. Which of the following best states the main idea of the passage?

    • A.Lactase persistence arose more than once and spread where digesting milk gave adults an advantage
    • B.The mutations behind lactase persistence alter DNA that controls the gene, not the gene's own code
    • C.Lactase persistence arose in northern Europe and was later carried to herding peoples of East Africa
    • D.Adults who lack lactase feel discomfort because bacteria in the colon ferment the undigested lactose
    Show answerHide answer

    Correct answer: Lactase persistence arose more than once and spread where digesting milk gave adults an advantage

    The passage builds toward its final sentence: separate mutations in different regions, each common only where milk was a staple, point to natural selection, so lactase persistence arose more than once and spread where digesting milk helped adults. The regulatory-DNA statement is accurate but is one piece of evidence for that conclusion, and the discomfort statement explains symptoms rather than the passage's argument. The claim that the trait spread from Europe to Africa contradicts the passage, which says different mutations caused it in different regions.

  32. Read the passage, then answer the question. Many people feel a sharp, brief pain when cold air or a cold drink touches an exposed root surface. The most widely accepted explanation is the hydrodynamic theory. Dentin, the tissue beneath the enamel of the crown and the cementum of the root, is riddled with microscopic tubules that run from its outer surface toward the pulp, and each tubule is filled with fluid. Normally the tubule openings are covered by enamel or cementum. When the gums recede and the thin cementum wears away, the openings are exposed. A stimulus such as cold, a blast of air, or a sugary solution then makes the fluid inside the tubules move rapidly, and this movement deforms nerve endings near the pulp, which fire and produce pain. Treatments for sensitivity follow from this chain of events. Some toothpastes contain potassium salts that make the nerve less excitable, reducing its response to the fluid movement. Others deposit minerals or other particles that plug the tubule openings. Based on the passage, a treatment that completely plugged the exposed tubule openings would most likely reduce sensitivity by

    • A.keeping the drop in temperature from reaching the nerve endings near the pulp
    • B.stopping a cold stimulus from setting the fluid inside the tubules in motion
    • C.lowering how excitable the nerve endings near the pulp become when fluid moves
    • D.reducing the amount of fluid held inside each tubule between surface and pulp
    Show answerHide answer

    Correct answer: stopping a cold stimulus from setting the fluid inside the tubules in motion

    In the passage, pain results when a stimulus at the open tubule makes the fluid move, and that movement deforms the nerve endings; sealing the openings breaks the chain at that step, stopping a cold stimulus from setting the fluid in motion. Lowering nerve excitability is how the potassium salts work, a different link in the same chain. The passage attributes pain to fluid movement rather than to temperature reaching the nerve, and nothing in it says plugging changes how much fluid the tubules hold.

  33. Read the passage, then answer the question. Some bacteria living on the back of the tongue convert nitrate, a compound abundant in leafy vegetables and also secreted in saliva, into nitrite. Once swallowed, nitrite can be converted in the body to nitric oxide, a molecule that relaxes blood vessels and lowers blood pressure. Nitric oxide made by this route adds to the supply that the lining of the blood vessels produces on its own. In small short-term trials, volunteers who used a strong antiseptic mouthwash for a week had much less nitrite in their saliva and blood plasma and showed small rises in blood pressure. Building on this work, a research team followed about 1,000 adults for three years and found that those who used mouthwash at least twice a day were more likely to develop high blood pressure than those who used it less often or not at all. The team concluded that frequent mouthwash use raises the risk of high blood pressure by killing the bacteria that convert nitrate. Which of the following findings, if true, would most weaken the team's conclusion?

    • A.The frequent rinsers had less nitrite in their saliva than the people who rinsed less often
    • B.The trial volunteers' blood pressure fell back to normal within days of stopping the rinse
    • C.The frequent rinsers more often smoked and drank heavily, habits that raise blood pressure
    • D.The people who ate the most leafy vegetables had the lowest blood pressure in the cohort
    Show answerHide answer

    Correct answer: The frequent rinsers more often smoked and drank heavily, habits that raise blood pressure

    The three-year study is observational, so a third factor that differs between groups can explain the link; if frequent rinsers more often smoked and drank heavily, habits that raise blood pressure on their own, those habits rather than the mouthwash could account for the extra cases. Finding less nitrite in frequent rinsers actually fits the proposed mechanism and strengthens the claim. Blood pressure returning to normal after stopping shows the effect is reversible, not that it is absent, and a link between vegetables and lower pressure supports the nitrate pathway rather than weakening it.

  34. Read the passage, then answer the question. Xylitol is a sugar alcohol used to sweeten chewing gum. Unlike sucrose, it cannot be fermented to acid by Streptococcus mutans and related bacteria, and some laboratory studies suggest it may reduce their numbers in plaque. A school district wanted to know whether xylitol gum could reduce tooth decay among its students. At one school, all 200 children in the third and fourth grades chewed xylitol gum three times a day for two years; no other school took part. At the start and end of the study, the school's own dental hygienist, who knew the purpose of the study, examined each child and recorded new cavities. Over the two years, new cavities per child fell by about a third compared with the two years before the study began. During the same two years, the town began adding fluoride to its water supply. The district reported that the gum had cut decay by a third. Which change to the study's design would best rule out the fluoridated water as an explanation for the drop in cavities?

    • A.Doubling the number of children who chewed the xylitol gum during the two years
    • B.Measuring the S. mutans counts in each child's plaque at the start and the end
    • C.Having an examiner who was unaware of the study's purpose record the cavities
    • D.Following a similar group in the same town who chewed gum made without xylitol
    Show answerHide answer

    Correct answer: Following a similar group in the same town who chewed gum made without xylitol

    Every child in the study drank the newly fluoridated water, so the drop in cavities could come from the water, the gum, or both; only a comparison group in the same town, drinking the same water but chewing gum without xylitol, separates the two. An unaware examiner fixes a real flaw, biased counting, but does nothing about the fluoride. Doubling the sample would make the estimate more precise without removing the shared exposure, and plaque bacteria counts would show a possible mechanism, not whether the gum rather than the water reduced decay.

  35. Read the passage, then answer the question. The thyroid gland makes its hormones through a chain of steps that the brain constantly monitors. The hypothalamus releases thyrotropin-releasing hormone (TRH), which prompts the pituitary to secrete thyroid-stimulating hormone (TSH). TSH acts on the thyroid in two ways: it speeds hormone production, and, over a period of weeks, it makes the gland's cells grow and multiply. Inside the gland, the enzyme thyroid peroxidase attaches iodine to a large protein called thyroglobulin, a step without which no thyroxine (T4) can be formed. Thyroxine and its more active relative, T3, then circulate to nearly every tissue, raising the rate at which cells use energy. The loop closes because both hormones act back on the hypothalamus and pituitary, suppressing the release of TRH and TSH. When thyroid hormone levels fall, that suppression weakens and TSH rises; when they climb, TSH falls. In a healthy person this arrangement holds hormone levels steady, but it also explains why the gland itself can change size when something interferes with the chain. Suppose a drug fully blocked thyroid peroxidase in a person whose thyroid was otherwise healthy. Based on the passage, which outcome would be expected after several weeks of treatment?

    • A.A lower TSH level, caused by the fall in thyroxine
    • B.A normal thyroxine level, restored by a rise in TSH
    • C.A smaller gland, since it has less hormone to make
    • D.A larger gland, driven by a sustained rise in TSH
    Show answerHide answer

    Correct answer: A larger gland, driven by a sustained rise in TSH

    With thyroid peroxidase blocked, no thyroxine can be formed, so the brake on TRH and TSH weakens, TSH climbs, and TSH's growth effect produces a larger gland, driven by a sustained rise in TSH. A normal thyroxine level cannot be restored by more TSH, because the passage says no thyroxine can form without the blocked step. TSH moves opposite to thyroxine in this loop, so it rises rather than falls, and a gland under constant TSH stimulation grows rather than shrinks.

  36. Read the passage, then answer the question. Xylitol is a sugar alcohol used to sweeten chewing gum. Unlike table sugar, it cannot be fermented by Streptococcus mutans, the bacterium most closely tied to tooth decay, so it does not feed the acid production that dissolves enamel. Some laboratory studies also report that S. mutans grows more slowly when xylitol is present. Interest in the sweetener rose after a survey of 1,200 schoolchildren in one district found that those who said they chewed xylitol gum at least once a day developed about 30 percent fewer new cavities over two years than those who did not. A local health board has cited the survey as evidence that daily xylitol gum prevents decay and has proposed handing the gum out in schools. Critics note that no child was assigned to chew gum; the children, or their parents, made that choice themselves. Critics add that chewing any gum stimulates saliva, which rinses away food and neutralizes acid. Which finding, if true, would most weaken the health board's conclusion that the xylitol gum itself produced the lower rate of new cavities?

    • A.Daily chewers had about as many cavities as nonchewers when the survey began
    • B.Daily chewers also brushed with fluoride toothpaste more often than nonchewers
    • C.Daily chewers had fewer S. mutans in their saliva than nonchewers had in theirs
    • D.Twice-daily chewers had fewer new cavities than chewers who chewed once each day
    Show answerHide answer

    Correct answer: Daily chewers also brushed with fluoride toothpaste more often than nonchewers

    Because families chose whether to chew, a habit that travels with gum chewing could explain the result, and the finding that daily chewers also brushed with fluoride toothpaste more often than nonchewers supplies exactly that rival cause. The twice-daily finding is a dose-response pattern, which strengthens rather than weakens a causal claim. Equal cavity counts at the start rule out one alternative explanation, and lower S. mutans counts in chewers fit the sweetener's proposed mechanism, so both support the board.

  37. Read the passage, then answer the question. Sickle-cell disease results when a person inherits two copies of a variant hemoglobin gene, one from each parent. The variant protein tends to clump when oxygen levels fall, bending red blood cells into rigid crescents that block small vessels and break apart early. Before modern treatment, most children with the disease died young, usually before they could have children of their own. People who inherit only one copy, a condition called sickle-cell trait, are generally healthy. In the mid-twentieth century, researchers in East Africa noticed that the variant was common in lowland areas where malaria was widespread and rare in highland areas where it was not. Later studies showed that children with sickle-cell trait who catch the malaria parasite are much less likely than other children to develop the severe, often fatal form of the illness. The protection is not complete; carriers can still be infected and can still fall ill. How the variant protects is still debated, though one proposal is that infected cells sickle and are removed by the spleen before the parasite can multiply. Which of the following conclusions is most strongly supported by the passage?

    • A.The variant gene swaps a single amino acid in the beta chain of hemoglobin
    • B.The spleen's removal of sickled cells is why variant carriers survive malaria
    • C.Malaria likely sustains the variant though two copies were often fatal
    • D.Variant carriers who catch malaria are likely to show no symptoms of it
    Show answerHide answer

    Correct answer: Malaria likely sustains the variant though two copies were often fatal

    Two sentences combine here: two copies were usually fatal before reproduction, yet one copy protects against deadly malaria, so the conclusion that malaria likely sustains the variant though two copies were often fatal is the best-supported inference. The spleen explanation is presented only as one proposal in a debate, so stating it as the reason overclaims. The no-symptoms option contradicts the statement that carriers can still fall ill, and the amino-acid fact, though true, appears nowhere in the passage.

  38. Read the passage, then answer the question. When a blood vessel is cut, the body's response is often described by its most visible result, the clot, but the clot is a late arrival. Its framework is fibrin, a meshwork of protein threads that forms when the enzyme thrombin cuts a soluble plasma protein, fibrinogen, into sticky fragments that link together. Thrombin itself is the end product of a cascade of clotting factors, each activating the next, which is set off when blood meets tissue factor, a protein exposed by the injury. Well before any of this, within seconds of the cut, smooth muscle in the vessel wall contracts, narrowing the vessel and slowing the loss of blood. Platelets then stick to collagen fibers exposed in the damaged wall and release chemicals that draw in more platelets, forming a loose plug; the surfaces of these activated platelets also provide sites where the clotting factors assemble. Once fibrin has reinforced the plug, the platelets pull on the threads and the clot shrinks, drawing the wound's edges closer. Days later, as the vessel heals, an enzyme called plasmin dissolves the fibrin. According to the passage, which event occurs immediately before fibrinogen is cut into sticky fragments?

    • A.Clotting factors activate one another until thrombin is made
    • B.Platelets pull on the fibrin threads so that the clot then shrinks
    • C.Smooth muscle in the vessel wall contracts to narrow the vessel
    • D.Platelets gather into a loose plug where clotting factors assemble
    Show answerHide answer

    Correct answer: Clotting factors activate one another until thrombin is made

    Fibrinogen is cut by thrombin, and the clotting factors activate one another until thrombin is made, so that step comes directly before fibrin forms. The platelet plug comes earlier, since its activated platelets provide the surfaces where the cascade assembles. Vessel narrowing is the very first response, within seconds, and clot shrinkage happens only after fibrin has reinforced the plug.

  39. Read the passage, then answer the question. The autonomic nervous system controls internal organs without conscious effort, and its two divisions usually pull in opposite directions. The sympathetic division prepares the body for exertion or emergency: it speeds the heart, widens the airways, and slows digestion. Its fibers leave the spinal cord in the chest and upper abdominal regions and almost at once enter chains of ganglia, clusters of nerve cell bodies lying just beside the spinal column, so the first neuron in each pathway is short and the second is long. The parasympathetic division favors rest and digestion, slowing the heart and stimulating the gut. Its fibers leave from the brainstem and from the lowest part of the spinal cord and travel nearly all the way to the target organ before reaching a ganglion, so its first neuron is long and its second is short. In both divisions, the first neuron releases acetylcholine onto the second. The divisions part ways again at the organ: most sympathetic second neurons release norepinephrine there, while parasympathetic second neurons release acetylcholine. Because many organs receive fibers from both divisions, their activity at any moment reflects the balance between the two. According to the passage, the sympathetic and parasympathetic divisions are alike in

    • A.the part of the nervous system where the fibers of each pathway set out
    • B.the place where the ganglia of each pathway sit relative to its organ
    • C.the chemical that the first neuron of each pathway passes to the second
    • D.the chemical that the second neuron of each pathway releases at its organ
    Show answerHide answer

    Correct answer: the chemical that the first neuron of each pathway passes to the second

    The passage states that in both divisions the first neuron releases acetylcholine onto the second, so they are alike in the chemical that the first neuron of each pathway passes to the second. At the organ they differ, with most sympathetic second neurons releasing norepinephrine. Their fibers also set out from different regions (chest and upper abdomen versus brainstem and lowest cord), and their ganglia sit at opposite ends of the pathway.

  40. Read the passage, then answer the question. Biochemists sort reversible enzyme inhibitors by how they change two measurements. Vmax is the fastest rate an enzyme can reach when substrate is plentiful. Km is the substrate concentration at which the rate is half of Vmax, so a higher Km means the enzyme needs more substrate to work at half its top speed. A competitive inhibitor resembles the substrate and occupies the active site; because enough substrate can crowd it out, it leaves Vmax unchanged but raises Km. A noncompetitive inhibitor binds elsewhere on the enzyme, whether or not substrate is present, and disables it. Extra substrate cannot rescue the disabled molecules, so Vmax falls, while Km stays the same because the enzymes still working bind substrate normally. An uncompetitive inhibitor binds only to an enzyme that already holds substrate, locking the pair together; this lowers Vmax and also lowers Km. Plotting reaction rate against substrate concentration, with and without the inhibitor, is usually enough to tell the three types apart. Without compound X, an enzyme's top rate is 80 units, and a rate of 40 units is reached at 5 mM substrate. With X added, the top rate is 40 units, and a rate of 20 units is reached at 5 mM. Under the passage's scheme, X is best classified as

    • A.competitive, since more substrate is now needed for a rate of 40 units
    • B.competitive, since it slowed the reaction even at only 5 mM substrate
    • C.noncompetitive, since half its new top rate was still reached at 5 mM
    • D.uncompetitive, since both its top rate and its Km went down
    Show answerHide answer

    Correct answer: noncompetitive, since half its new top rate was still reached at 5 mM

    With X, the top rate halves to 40 units, and half of that new top rate (20 units) is still reached at 5 mM, so Km is unchanged and X is noncompetitive, since half its new top rate was still reached at 5 mM. Reading Km off the old 40-unit rate makes Km look higher and points wrongly toward competitive inhibition, which by the passage's definition would leave Vmax unchanged. Uncompetitive inhibition would lower Km too, and slowing the reaction at 5 mM is true of every type, so it classifies nothing.

  41. Read the passage, then answer the question. For more than a century the human appendix was held up as a textbook vestige, a shrunken remnant of a larger gut pouch that once helped our plant-eating ancestors digest tough leaves. Charles Darwin made this case, and the organ's habit of becoming inflamed, sometimes fatally, seemed to show that it served no purpose worth the risk. A growing number of researchers now argue that the appendix earns its keep. The organ is rich in lymphoid tissue, the kind that helps the immune system sample and respond to gut microbes. Its narrow, dead-end shape may let it shelter a film of helpful bacteria that can repopulate the large intestine after a bout of severe diarrhea flushes the gut. A comparison across mammal species found that an appendix has evolved independently many separate times and has rarely been lost once it appeared, a pattern hard to explain if the organ were useless. Removing the appendix remains a safe and common operation, and most people who have one show no obvious ill effects afterward, a point that defenders of the vestige view continue to raise. In the passage, the statement that most people show no obvious ill effects after the appendix is removed functions as

    • A.a fact that critics of the author's view cite and the author admits
    • B.a fact that shows the organ's risks outweigh the benefits it brings
    • C.a fact that supports the author's view that the organ has a purpose
    • D.a fact that explains why the organ was first considered a vestige
    Show answerHide answer

    Correct answer: a fact that critics of the author's view cite and the author admits

    The passage attributes the point to defenders of the vestige view and reports it without disputing it, so it is a fact that critics of the author's view cite and the author admits. It does not support the author, whose evidence is the lymphoid tissue, the bacterial reservoir and the repeated evolution of the organ. The original vestige claim rested on the ancestral gut pouch and the organ's risk of inflammation, not on removal outcomes, and the passage never weighs risks against benefits.

  42. Read the passage, then answer the question. A fever is not simply the body overheating. The hypothalamus, a small region at the base of the brain, normally holds core temperature near 37 °C by comparing signals from temperature sensors with an internal reference value, much as a home thermostat compares room temperature with its setting. During an infection, immune cells release signaling molecules that cause the hypothalamus to produce prostaglandin E2, and this chemical, in effect, turns the dial up. The body now treats its normal temperature as too cold. Blood vessels in the skin narrow, the person feels chilled and may shiver, and heat is conserved until core temperature reaches the new reference value, perhaps 39 °C. When the infection subsides and prostaglandin levels drop, the dial returns to its usual position, and the same mechanisms run in reverse: skin vessels widen and the person sweats, shedding the excess heat. Drugs such as aspirin and ibuprofen reduce fever by blocking prostaglandin production. Heatstroke is different: there the reference value is unchanged, but heat gain overwhelms the body's ability to shed it. In the passage, the phrase "turns the dial up" refers to

    • A.a rise in core body temperature produced by shivering muscles
    • B.a rise in the body's output of prostaglandin E2 in the hypothalamus
    • C.a rise in the setting that core temperature is held to
    • D.a rise in heat gain that overwhelms the body's means of shedding it
    Show answerHide answer

    Correct answer: a rise in the setting that core temperature is held to

    The thermostat comparison makes the dial the internal reference value, so turning it up means a rise in the setting that core temperature is held to. Prostaglandin E2 is what turns the dial, not the dial itself, and shivering is a later response to the new setting. Heat gain that overwhelms cooling describes heatstroke, which the passage contrasts with fever because the reference value stays unchanged.

  43. Read the passage, then answer the question. Nearly every cell in the body keeps time with a molecular clock, but the cells take their cue from a master clock, a small cluster of neurons in the hypothalamus called the suprachiasmatic nucleus. Each morning, light reaching the eyes resets this master clock, and the daily reset keeps the body's roughly daily cycles of temperature, hormone release and sleepiness locked to the 24-hour day. Researchers have asked what happens when that reset is taken away. In studies in which volunteers lived for weeks in rooms with no windows, clocks or other time cues, the cycles did not fade. Free-running, they kept a steady rhythm, but one that no longer matched the day: in most people it averaged slightly longer than 24 hours, about 24.2 hours, so each day the volunteers woke a little later by the outside clock. Many totally blind people, whose eyes cannot pass light signals to the brain, experience the same drift in ordinary life, with spells of insomnia and daytime sleepiness whenever their internal cycle falls out of step with the world. As used in the passage, the term "free-running" describes a cycle that

    • A.shifts at random so that no two days are the same length
    • B.speeds up once the body is released from outside control
    • C.follows whatever schedule of activity the person chooses
    • D.keeps its own period because nothing resets it each day
    Show answerHide answer

    Correct answer: keeps its own period because nothing resets it each day

    The passage builds the meaning from context: with the morning light reset removed, the cycles "kept a steady rhythm" of about 24.2 hours, so a free-running cycle runs on its own built-in period with no daily reset. The idea that it speeds up reverses the evidence, since a period longer than 24 hours made the volunteers wake later each day, which is a slower cycle. The steady rhythm also rules out random day-to-day variation, and nothing in the passage ties the cycle to the person's chosen activities.

  44. Read the passage, then answer the question. Sore throats are among the most common reasons students visit a campus clinic, and in otherwise healthy young adults most are caused by viruses and fade within about a week. Researchers at one university health center wanted to know whether a lozenge containing zinc and honey shortens this illness. They enrolled 220 students who arrived within a day of their first symptoms, a group large enough, by the team's own calculation, to detect even a modest effect. Every student received the lozenges and was told to dissolve one every three hours while awake. Each morning, research nurses who had not been told the purpose of the study scored symptom severity on a standard ten-point scale, and students also reported how their throats felt. By the seventh day, 82 percent of the students said their throats felt normal, and the average nurse-rated score had fallen by more than two-thirds. The team concluded that the lozenge "substantially speeds recovery" and recommended it to the student body. Based on the passage, which weakness in the study most directly undermines the team's conclusion?

    • A.The study gave all students the lozenge, so no untreated group was compared
    • B.The study enrolled only healthy young adults, not older or sicker patients
    • C.The study relied on students' own reports of whether their throats felt normal
    • D.The study never checked that students took a lozenge every three hours awake
    Show answerHide answer

    Correct answer: The study gave all students the lozenge, so no untreated group was compared

    Because the passage says most such sore throats fade within about a week anyway, recovery by day seven proves nothing unless it is compared with students who did not get the lozenge, so the decisive flaw is that the study gave all students the lozenge and compared no untreated group. The self-report criticism is tempting, but the same improvement appeared in scores from nurses who were not told the study's purpose. The narrow sample does not weaken a recommendation aimed at the student body itself, and missed doses would make a benefit harder to show, not create a false one.

  45. Read the passage, then answer the question. The light microscope opened up the cellular world, but it has a hard limit. Because light behaves as a wave, a lens cannot focus it to an infinitely small point; each point of an object is imaged as a tiny blurred disk. When two points lie closer together than about 200 nanometers, roughly half the wavelength of visible light, their disks overlap so much that they merge into one. No adjustment of the focus separates them, and a light microscope therefore cannot resolve structures closer than that, however much the image is magnified; enlarging it further only produces a bigger blur, which microscopists call empty magnification. This is why the ribosomes in a cell, each about 25 nanometers across, appear in a light microscope only as a faint graininess, if at all. Electron microscopes overcame the limit by using beams of electrons, whose wavelengths are thousands of times shorter than those of light. Since the 1990s, techniques known as super-resolution fluorescence microscopy have also found ways around it, by switching neighboring fluorescent molecules on at different moments so that each can be located on its own. As used in the passage, the word "resolve" most nearly means

    • A.enlarge to a larger visible size
    • B.detect as present in the sample
    • C.bring into a sharp, clear focus
    • D.show as distinct, separate items
    Show answerHide answer

    Correct answer: show as distinct, separate items

    The passage defines the limit as two nearby points whose blurred disks merge into one, so to resolve structures is to show them as distinct, separate items. Detecting presence is the most tempting choice, but the passage says ribosomes can show up as a faint graininess, which is detection without resolution. Focusing and enlarging are ruled out directly: no focus adjustment separates the disks, and further magnification only gives empty magnification.

  46. Read the passage, then answer the question. In a small population, the frequency of an allele can change from one generation to the next purely by chance, a process called genetic drift. Imagine a population of ten wildflowers in which half the plants carry an allele for white petals. If, by luck, the white-flowered plants happen to leave more seeds one year, the allele becomes more common; if they leave fewer, it becomes rarer. Over many generations these random swings add up, and eventually one of two things happens: the allele disappears entirely, or it becomes fixed. Once an allele is fixed, drift can no longer alter its frequency, because there is no variation left for chance to act on; only a new mutation, or migrants carrying a different allele, could restore the alternative. Drift operates in large populations too, but far more slowly, because random gains and losses spread across many individuals tend to cancel out. For this reason, small isolated populations often lose genetic variation quickly, even when none of the alleles they lose is harmful. As used in the passage, the word "fixed" most nearly means

    • A.favored by selection, so that it spreads faster than others
    • B.carried by most plants, so that it is the common form
    • C.carried by all plants, so that no alternative remains
    • D.held steady at half the plants, neither rising nor falling
    Show answerHide answer

    Correct answer: carried by all plants, so that no alternative remains

    The passage pairs fixed with the allele disappearing and says that once it is fixed there is no variation left, so only a new mutation or migrants could restore the alternative; the allele is carried by every plant. Carried by most plants is the closest trap, but a majority still leaves the other allele present for drift to act on. Held steady at half misreads drift can no longer alter its frequency as a stable middle level, and favored by selection contradicts a passage about chance in which the lost alleles need not be harmful.

  47. Read the passage, then answer the question. Most enzymes in the human body work best near 37 degrees Celsius, and heating them much above that temperature unfolds their chains and destroys their activity. Bacteria that live in hot springs are a striking exception. Thermus aquaticus, first isolated from a hot spring in Yellowstone National Park, grows at about 70 degrees Celsius, and its DNA polymerase, known as Taq, keeps working after repeated heating to about 95 degrees. That stability made Taq the enzyme of choice for the polymerase chain reaction, or PCR, a laboratory method that copies a stretch of DNA millions of times by cycling the reaction mixture between hot and cooler temperatures; an ordinary polymerase would be destroyed in the first hot step. Even so, Taq is not a perfect copier. It lacks the proofreading activity that allows many other polymerases to remove a wrongly paired nucleotide, so it introduces errors at a higher rate. Laboratories that need highly accurate copies therefore often use polymerases from other heat-loving microbes that do proofread. In the passage, the phrase "Even so" primarily serves to

    • A.reverse the case for Taq as the enzyme of choice for PCR
    • B.qualify the claim that Taq survives repeated heating to 95
    • C.admit a weakness that remains despite the enzyme's merits
    • D.mark an exception to the rule about heat and most enzymes
    Show answerHide answer

    Correct answer: admit a weakness that remains despite the enzyme's merits

    "Even so" grants the praise of Taq's heat stability and its value in PCR, then turns to a shortcoming that still stands, its lack of proofreading, so it serves to admit a weakness that remains despite the enzyme's merits. Marking an exception is tempting, but that job was done earlier by the sentence calling hot-spring bacteria a striking exception to the rule about enzymes and heat. The passage never questions Taq's heat survival, and it does not reverse the case for Taq; only labs that need highly accurate copies switch enzymes.

Language Usage (41)

  1. Identify the sentence that correctly uses subject-verb agreement in a complex context.

    • A.The list of approved sealants were posted on the wall.
    • B.Neither the dentists nor the aide have signed the log.
    • C.A tray of sterile mirrors sits beside the second sink.
    • D.Each of the four operatories need a new suction valve.
    Show answerHide answer

    Correct answer: A tray of sterile mirrors sits beside the second sink.

    Correct answer: A tray of sterile mirrors sits beside the second sink. Explanation: The subject is tray, a singular noun, and the phrase of sterile mirrors between the subject and the verb does not change it, so the singular sits is correct. The list of approved sealants were posted on the wall takes its verb from list, which is singular and requires was posted. Neither the dentists nor the aide have signed the log must agree with the nearer subject aide, which is singular, so has signed is required. Each of the four operatories need a new suction valve is governed by Each, which is singular in every construction, so needs is required.

  2. Choose the sentence that accurately uses a semicolon to connect closely related independent clauses.

    • A.The office ordered new loupes; to replace the old, scratched eyepieces.
    • B.The scaler tip buzzed loudly; therefore, the patient requested a break.
    • C.The child sat quietly; while, the hygienist counted each primary tooth.
    • D.The gums bled slightly; and, the concerned patient noted no discomfort.
    Show answerHide answer

    Correct answer: The scaler tip buzzed loudly; therefore, the patient requested a break.

    Correct answer: The scaler tip buzzed loudly; therefore, the patient requested a break. Explanation: A semicolon joins two clauses that could each stand alone; the scaler tip buzzed loudly and the patient requested a break both can, and therefore is a conjunctive adverb correctly followed by a comma. The office ordered new loupes; to replace the old, scratched eyepieces places an infinitive phrase after the semicolon, and that phrase cannot stand as a sentence. The child sat quietly; while, the hygienist counted each primary tooth opens the second part with a subordinating conjunction, leaving a dependent clause. The gums bled slightly; and, the concerned patient noted no discomfort joins two independent clauses with a coordinating conjunction, which calls for a comma before and, not a semicolon before it and a comma after it.

  3. Identify the sentence that demonstrates the correct use of commas in a list that includes conjunctions.

    • A.Her setup tray holds mirrors, explorers, probes, and sharp scalers.
    • B.The supply cabinet stores bandages, gloves, wax and, paper napkins.
    • C.The team restocks, the gloves, masks, and disposable gowns nightly.
    • D.Our patients brush, floss, and gargle, before each routine checkup.
    Show answerHide answer

    Correct answer: Her setup tray holds mirrors, explorers, probes, and sharp scalers.

    Correct answer: Her setup tray holds mirrors, explorers, probes, and sharp scalers. Explanation: Items in a series are separated by commas, and the last comma goes before the conjunction, never after it, which is what Her setup tray holds mirrors, explorers, probes, and sharp scalers does. The supply cabinet stores bandages, gloves, wax and, paper napkins puts the comma after and, cutting the conjunction off from the item it introduces. The team restocks, the gloves, masks, and disposable gowns nightly inserts a comma between the verb and its object. Our patients brush, floss, and gargle, before each routine checkup adds a comma before a closing phrase that attaches directly to those verbs.

  4. Which sentence correctly uses a relative clause to provide additional information?

    • A.The dentist, that trained abroad, now leads our weekly case reviews.
    • B.This new mouthwash, which it reduces plaque, tastes much too bitter.
    • C.The digital sensor, who broke last Friday, sits inside the cupboard.
    • D.Our autoclave, which runs each night, holds two full cassette trays.
    Show answerHide answer

    Correct answer: Our autoclave, which runs each night, holds two full cassette trays.

    Correct answer: Our autoclave, which runs each night, holds two full cassette trays. Explanation: A non-restrictive relative clause adds information the sentence does not need in order to identify its subject, uses which for a thing, and sits inside a pair of commas, which is what Our autoclave, which runs each night, holds two full cassette trays does. The dentist, that trained abroad, now leads our weekly case reviews uses that, which cannot introduce a non-restrictive clause, and who is the pronoun a person calls for. This new mouthwash, which it reduces plaque, tastes much too bitter repeats the subject with it after the relative pronoun has already supplied one. The digital sensor, who broke last Friday, sits inside the cupboard applies who to an object.

  5. Select the sentence that correctly employs an appositive phrase to add detail.

    • A.The senior hygienist, she trained in Boston, joins the clinic today.
    • B.The lab technician, and a trained ceramist, will finish the veneers.
    • C.The newest staff hire, a seasoned periodontist, starts in late June.
    • D.The oral surgeon, who a retired paramedic, arrives here next Monday.
    Show answerHide answer

    Correct answer: The newest staff hire, a seasoned periodontist, starts in late June.

    Correct answer: The newest staff hire, a seasoned periodontist, starts in late June. Explanation: An appositive is a noun phrase that renames the noun beside it, carries no verb of its own, and is set off by commas, so a seasoned periodontist renaming the hire is the correct construction. The senior hygienist, she trained in Boston, joins the clinic today inserts a full clause with its own subject and verb, which makes a comma splice rather than an appositive. The lab technician, and a trained ceramist, will finish the veneers adds and, which turns the phrase into a second subject. The oral surgeon, who a retired paramedic, arrives here next Monday opens with a relative pronoun and then supplies no verb for it.

  6. Identify the sentence that correctly uses the passive voice for emphasis.

    • A.The sharp instruments was sorted by the new sterile tech.
    • B.The recall reminder was mailed by our front office staff.
    • C.The instrument trays got broke down by the weekend staff.
    • D.The x-ray sensor been wiped by the assistant last Monday.
    Show answerHide answer

    Correct answer: The recall reminder was mailed by our front office staff.

    Correct answer: The recall reminder was mailed by our front office staff. Explanation: The passive is a form of be plus a past participle, and was mailed puts the weight on the action while the agent follows in a by phrase, which is what The recall reminder was mailed by our front office staff does. The sharp instruments was sorted by the new sterile tech pairs a plural subject with the singular was. The instrument trays got broke down by the weekend staff uses a past tense form where the participle broken is required. The x-ray sensor been wiped by the assistant last Monday drops the auxiliary that been must have.

  7. Choose the sentence that accurately uses conditional sentences to discuss hypothetical situations.

    • A.If the sealant cracked, the tooth would need a restoration.
    • B.If the patient flosses daily, the gums would have improved.
    • C.If the curette had slipped, the tissue will have blistered.
    • D.If she would have flossed, her teeth stayed much healthier.
    Show answerHide answer

    Correct answer: If the sealant cracked, the tooth would need a restoration.

    Correct answer: If the sealant cracked, the tooth would need a restoration. Explanation: An unreal present condition takes a past tense verb in the if clause and would plus a base verb in the result, which is exactly the pattern in If the sealant cracked, the tooth would need a restoration. If the patient flosses daily, the gums would have improved attaches a past unreal result to a present real condition. If the curette had slipped, the tissue will have blistered pairs a past perfect condition with will have, where would have is required. If she would have flossed, her teeth stayed much healthier puts would inside the if clause and then gives a simple past result.

  8. Which sentence correctly uses the subjunctive mood to express a wish or hypothetical situation?

    • A.She wishes she was born with much stronger tooth enamel.
    • B.He wishes he studied harder before the state board exam.
    • C.The dentist insists that she brushes twice each day now.
    • D.I would reorder supplies if I were the senior hygienist.
    Show answerHide answer

    Correct answer: I would reorder supplies if I were the senior hygienist.

    Correct answer: I would reorder supplies if I were the senior hygienist. Explanation: A hypothetical contrary to fact takes the past subjunctive were with every subject, so if I were the senior hygienist is correct. She wishes she was born with much stronger tooth enamel states a wish and therefore needs were born. He wishes he studied harder before the state board exam is a regret about the past and needs had studied. The dentist insists that she brushes twice each day now follows a verb of insistence, where the mandative subjunctive calls for the base form brush.

  9. Identify the sentence that correctly employs modifiers to clarify meaning.

    • A.Rinsing the sink, the mouthwash spilled across the white floor.
    • B.The dentist warned the patients after lunch to floss carefully.
    • C.The assistant handed the mirror carefully to the nervous child.
    • D.She almost polished each tooth within the lower right quadrant.
    Show answerHide answer

    Correct answer: The assistant handed the mirror carefully to the nervous child.

    Correct answer: The assistant handed the mirror carefully to the nervous child. Explanation: The adverb carefully sits beside the verb it modifies, so The assistant handed the mirror carefully to the nervous child has one reading only. Rinsing the sink, the mouthwash spilled across the white floor attaches the opening participle to mouthwash, which cannot rinse anything. The dentist warned the patients after lunch to floss carefully strands after lunch between two verbs, so nothing in the sentence settles whether the warning or the flossing happens then. She almost polished each tooth within the lower right quadrant places almost before polished, which says the polishing barely began rather than that most teeth were finished.

  10. Select the sentence that demonstrates the correct use of an infinitive phrase.

    • A.The purpose of this project is to reducing gum disease.
    • B.The practice hopes to open a second office next spring.
    • C.To find a good dentist, it requires plenty of patience.
    • D.She looks forward to meet the new front office manager.
    Show answerHide answer

    Correct answer: The practice hopes to open a second office next spring.

    Correct answer: The practice hopes to open a second office next spring. Explanation: An infinitive is to plus the base form of a verb, and to open works as the object of hopes, so The practice hopes to open a second office next spring is correct. The purpose of this project is to reducing gum disease follows to with an -ing form instead of the base verb. To find a good dentist, it requires plenty of patience leaves the opening infinitive phrase with nothing to modify and props the sentence up with an empty it. She looks forward to meet the new front office manager treats the to of the phrasal verb look forward to as an infinitive marker, where a gerund is required.

  11. Which sentence accurately uses a dangling modifier and needs correction?

    • A.Adjusting the operatory lights, the senior assistant discovered hidden calculus.
    • B.Reviewing the recent radiographs, the approximal caries escaped early detection.
    • C.Charting the pocket depths, the attentive hygienist recorded marginal recession.
    • D.Polishing the mandibular crowns, the diligent student removed stubborn staining.
    Show answerHide answer

    Correct answer: Reviewing the recent radiographs, the approximal caries escaped early detection.

    Reviewing the recent radiographs, the approximal caries escaped early detection is the sentence that needs correction. An introductory participial phrase has to describe the subject that follows the comma, and the subject here is caries, which cannot review anything; the person who did the reviewing is never named, which is what makes the modifier dangle. Adjusting the operatory lights, the senior assistant discovered hidden calculus is sound, because the assistant is the one adjusting the lights. Charting the pocket depths, the attentive hygienist recorded marginal recession attaches correctly for the same reason, since the hygienist does the charting. Polishing the mandibular crowns, the diligent student removed stubborn staining is also correct, because the student performs both the polishing and the removing.

  12. Choose the sentence that demonstrates incorrect use of a conjunction and needs correction.

    • A.The assistant neither completed the wrapping nor sealed the sterile pouches.
    • B.The student neither reviewed the charting nor measured the buccal recession.
    • C.The clerk neither processed the billing nor scanned the insurance referrals.
    • D.The hygienist neither polished the margins nor scaling the posterior molars.
    Show answerHide answer

    Correct answer: The hygienist neither polished the margins nor scaling the posterior molars.

    The correlative pair neither ... nor has to join elements of the same grammatical form, and The hygienist neither polished the margins nor scaling the posterior molars pairs a past-tense verb with a gerund, so the conjunction links mismatched structures and the sentence needs correction to nor scaled the posterior molars. The assistant neither completed the wrapping nor sealed the sterile pouches is correct, because both halves are past-tense verb phrases. The student neither reviewed the charting nor measured the buccal recession balances reviewed against measured in the same way. The clerk neither processed the billing nor scanned the insurance referrals also joins two matching predicates, so its conjunction is used properly.

  13. Identify the sentence that correctly employs the use of an Oxford comma for clarity in a series.

    • A.The hygienist debrided the quadrant, recorded the bleeding, and polished the amalgams.
    • B.The assistant wiped the counters, restocked the bibs, and sterilizing the instruments.
    • C.The dentist checked the crowns, reviewed the films, and bitewing interpretation notes.
    • D.The student documented the crowding, described the attachment, and the chart remained.
    Show answerHide answer

    Correct answer: The hygienist debrided the quadrant, recorded the bleeding, and polished the amalgams.

    The Oxford comma is the comma placed before the coordinating conjunction in a series of three or more parallel items, and only The hygienist debrided the quadrant, recorded the bleeding, and polished the amalgams contains such a series: three past-tense verb phrases, with the serial comma in front of the last one. The assistant wiped the counters, restocked the bibs, and sterilizing the instruments ends in a gerund phrase rather than a matching verb phrase, so there is no parallel series for the comma to clarify. The dentist checked the crowns, reviewed the films, and bitewing interpretation notes fails the same way, closing with a noun phrase instead of a predicate. The student documented the crowding, described the attachment, and the chart remained ends with a separate independent clause, which makes that comma a clause separator rather than a serial comma inside a list.

  14. Which sentence demonstrates the correct use of a colon to introduce a list?

    • A.The new morning huddle briefly reviews: scheduling, conflicts, referrals, and emergencies.
    • B.The afternoon sterilization cycle finishes with: washing, drying, wrapping, and packaging.
    • C.The recall appointment covers several tasks: scaling, polishing, charting, and varnishing.
    • D.The surgical cassette waiting for extractions: forceps, elevators, hemostats, and sutures.
    Show answerHide answer

    Correct answer: The recall appointment covers several tasks: scaling, polishing, charting, and varnishing.

    A colon introduces a list only when the words in front of it form a complete independent clause, and The recall appointment covers several tasks is exactly that, so The recall appointment covers several tasks: scaling, polishing, charting, and varnishing is punctuated correctly. The new morning huddle briefly reviews: scheduling, conflicts, referrals, and emergencies drops the colon between the verb and its own objects, cutting a verb off from the complements it requires. The afternoon sterilization cycle finishes with: washing, drying, wrapping, and packaging places the colon after a preposition, leaving that preposition stranded without an object. The surgical cassette waiting for extractions: forceps, elevators, hemostats, and sutures has no finite verb before the colon at all, so what precedes it is a fragment rather than a clause.

  15. Select the sentence that accurately uses a nonrestrictive clause to add information.

    • A.The oral rinse that contains chlorhexidine carries a printed prescription label.
    • B.The adhesive which bonds to etched enamel requires continual moisture isolation.
    • C.The instrument, that reaches deep pockets, belongs inside the sterile cassettes.
    • D.The sterilizer, which cycles unattended overnight, needs a validated spore test.
    Show answerHide answer

    Correct answer: The sterilizer, which cycles unattended overnight, needs a validated spore test.

    A nonrestrictive clause adds information the sentence does not need in order to identify its subject; it is introduced by which and fenced with commas, and both conditions hold in The sterilizer, which cycles unattended overnight, needs a validated spore test. The oral rinse that contains chlorhexidine carries a printed prescription label uses that with no commas, which defines which rinse is meant and is therefore restrictive. The adhesive which bonds to etched enamel requires continual moisture isolation also narrows its noun instead of adding to it, and it carries no commas, so the clause is essential rather than parenthetical. The instrument, that reaches deep pockets, belongs inside the sterile cassettes punctuates its clause as nonrestrictive but heads it with that, a pronoun that cannot introduce a set-off clause.

  16. Identify the sentence that correctly uses a hyphen in a compound adjective.

    • A.The practice hired a well-trained hygienist before the evening recall sessions.
    • B.The trainee opened a newly-sterilized cassette before the second morning visit.
    • C.The dentist ordered a highly-polished handpiece from the local dental supplier.
    • D.The student filed a poorly-scanned radiograph inside the wrong patient folders.
    Show answerHide answer

    Correct answer: The practice hired a well-trained hygienist before the evening recall sessions.

    A compound adjective takes a hyphen when two words work together as a single modifier in front of a noun, which is what well-trained does before hygienist in The practice hired a well-trained hygienist before the evening recall sessions. The trainee opened a newly-sterilized cassette before the second morning visit hyphenates after an adverb ending in -ly, and such an adverb already shows that it modifies the word after it, so the hyphen is wrong there. The dentist ordered a highly-polished handpiece from the local dental supplier repeats that error with highly. The student filed a poorly-scanned radiograph inside the wrong patient folders does the same with poorly, so each of those three should drop the hyphen entirely.

  17. Choose the sentence that correctly avoids a split infinitive.

    • A.The clinician hopes to quickly finish after the bridge preparation begins.
    • B.The office plans to gradually reopen after the operatory repairs conclude.
    • C.The patient attempts to rinse thoroughly after the fluoride varnish dries.
    • D.The student wants to correctly respond after the clinical instructor asks.
    Show answerHide answer

    Correct answer: The patient attempts to rinse thoroughly after the fluoride varnish dries.

    An infinitive is split when a modifier is dropped between to and its verb, so the sentence that avoids the construction is the one that keeps the pair intact and puts the adverb after the verb: The patient attempts to rinse thoroughly after the fluoride varnish dries. The clinician hopes to quickly finish after the bridge preparation begins inserts quickly between to and finish. The office plans to gradually reopen after the operatory repairs conclude inserts gradually between to and reopen. The student wants to correctly respond after the clinical instructor asks inserts correctly between to and respond, so all three split the infinitive rather than avoiding it.

  18. Identify the sentence that correctly uses a possessive pronoun.

    • A.The owner decided its unfair after the insurance company refused coverage.
    • B.The practice revised its handbook after the annual state inspection ended.
    • C.The hygienist realized its unusual after the second sealant cracked early.
    • D.The assistant reported its overdue after the compressor alarm rang loudly.
    Show answerHide answer

    Correct answer: The practice revised its handbook after the annual state inspection ended.

    Its is the possessive form and takes no apostrophe, and in The practice revised its handbook after the annual state inspection ended it shows that the handbook belongs to the practice, which is the possessive use the sentence needs. The owner decided its unfair after the insurance company refused coverage needs the contraction it is, because nothing is being possessed there. The hygienist realized its unusual after the second sealant cracked early needs it is for the same reason. The assistant reported its overdue after the compressor alarm rang loudly also calls for it is, so those three put a possessive where a contraction belongs.

  19. Select the sentence that accurately employs ellipsis to indicate an omission.

    • A.The frightened child whispered, "The scaler...feels strange against my teeth."
    • B.The elderly patient complained, "The drilling...bothers me during each visit."
    • C.The dental assistant hesitated, "The sensor...shifted while the child turned."
    • D.The printed manual states, "The sealant...shields molars against early decay."
    Show answerHide answer

    Correct answer: The printed manual states, "The sealant...shields molars against early decay."

    Ellipsis points stand for words removed from quoted material, and that is their function in the sentence in which the printed manual is quoted: the marks replace wording cut out of a written source while the quotation continues to read as one statement. The sentence in which the frightened child whispers uses the marks to show a speaker faltering mid-sentence, and nothing has been cut from any source. The sentence in which the elderly patient complains records the same kind of spoken pause rather than a deletion. The sentence in which the dental assistant hesitates also marks hesitation in speech, so none of those three signals that material was left out.

  20. Identify the sentence that correctly uses quotation marks for titles of short works.

    • A.She quoted the article "Pediatric Fluoride Varnish Application Guidelines" during her lecture.
    • B.She praised the textbook "Clinical Periodontology Treatment Planning Manual" during her class.
    • C.She consulted the journal "Modern Dental Materials Quarterly Reviews" during her presentation.
    • D.She screened the documentary "Silent Epidemic Threatening Young Children" during her training.
    Show answerHide answer

    Correct answer: She quoted the article "Pediatric Fluoride Varnish Application Guidelines" during her lecture.

    Quotation marks belong on the titles of short works that appear inside a larger publication, which is why the article title is punctuated correctly in the sentence about quoting during her lecture. The sentence about the treatment planning manual encloses the title of a whole textbook, and a complete book takes italics instead. The sentence about the quarterly review encloses the name of an entire journal, another complete publication that is italicised rather than quoted. The sentence about the documentary encloses the title of a full-length film, a standalone work that also takes italics, so the marks are misapplied in all three.

  21. Choose the sentence that correctly uses a comma to set off a tag question.

    • A.The autoclave, finished its cycle before the morning huddle didn't it?
    • B.The clear sealant hardening quickly under the bright light, didn't it?
    • C.The flowable bonding resin cured under the operatory light, didn't it?
    • D.The patient rinsed, before the student applied the varnish didn't she?
    Show answerHide answer

    Correct answer: The flowable bonding resin cured under the operatory light, didn't it?

    A tag question is a short reversed question added to a complete statement, and the comma between them is what sets the tag off. The flowable bonding resin cured under the operatory light, didn't it? does that correctly: cured is a finite verb, so the words before the comma form a statement, and the comma isolates the tag. The autoclave, finished its cycle before the morning huddle didn't it? puts its only comma directly after the subject, which severs a subject from its verb and leaves the tag unpunctuated. The clear sealant hardening quickly under the bright light, didn't it? uses the participle hardening rather than a finite verb, so there is no statement in front of the comma for a tag to attach to. The patient rinsed, before the student applied the varnish didn't she? sets the comma after the opening verb instead of before the tag, so that tag also runs on unmarked.

  22. Identify the sentence that correctly uses "who" or "whom" in a question.

    • A.Whom did the assistant assume scheduled the emergency extraction visits?
    • B.Whom did the committee appoint despite the repeated calendar objections?
    • C.Whom did the instructors believe misplaced the sterilization logs today?
    • D.Whom did the coordinator think submitted the duplicate insurance claims?
    Show answerHide answer

    Correct answer: Whom did the committee appoint despite the repeated calendar objections?

    Whom is the object form, so it is right only when the questioned word receives the action. In Whom did the committee appoint despite the repeated calendar objections? the questioned word is the direct object of appoint, since the committee appoints someone, so the object form is required. Whom did the assistant assume scheduled the emergency extraction visits? asks about the one who did the scheduling, which makes the word the subject of scheduled and calls for who. Whom did the instructors believe misplaced the sterilization logs today? asks who misplaced the logs, again a subject. Whom did the coordinator think submitted the duplicate insurance claims? asks who submitted them, so each of those three needs who in place of whom.

  23. Which sentence correctly uses a complex sentence to describe a condition and its outcome?

    • A.If the patient flosses regularly, a reduced index appears before the recall.
    • B.If the sealant cracks early, a lengthy repair appointment before the recall.
    • C.If the varnish dries slowly, a thick patchy coating across the restorations.
    • D.If the scaler vibrates loudly, a possible bearing fracture inside the motor.
    Show answerHide answer

    Correct answer: If the patient flosses regularly, a reduced index appears before the recall.

    A complex sentence pairs a dependent clause with an independent one, and only If the patient flosses regularly, a reduced index appears before the recall does that: the opening clause states the condition, and a reduced index appears before the recall is a full clause with its own subject and verb stating the outcome. If the sealant cracks early, a lengthy repair appointment before the recall ends in a noun phrase with no verb, so the condition has no outcome clause to attach to. If the varnish dries slowly, a thick patchy coating across the restorations closes with another verbless fragment. If the scaler vibrates loudly, a possible bearing fracture inside the motor does the same, leaving three sentence fragments rather than complex sentences.

  24. Identify the sentence that correctly demonstrates the use of a predicate adjective.

    • A.The unusually swollen tissue was clearly bleeding after the probing appointment.
    • B.The freshly polished enamel was sharply reflecting the operatory overhead light.
    • C.The carefully charted pocket depths were slowly exceeding the acceptable ranges.
    • D.The inflamed periodontal tissue was noticeably firmer after the initial scaling.
    Show answerHide answer

    Correct answer: The inflamed periodontal tissue was noticeably firmer after the initial scaling.

    A predicate adjective follows a linking verb and describes the subject, which is what firmer does after was in The inflamed periodontal tissue was noticeably firmer after the initial scaling. In The unusually swollen tissue was clearly bleeding after the probing appointment, was is an auxiliary rather than a linking verb, since was bleeding is a progressive verb form and the only adjectives sit in front of the noun. The freshly polished enamel was sharply reflecting the operatory overhead light is built the same way, with a progressive verb that takes an object. The carefully charted pocket depths were slowly exceeding the acceptable ranges also uses a progressive verb with an object, so none of those three places an adjective in the predicate.

  25. Choose the sentence that accurately uses a restrictive clause to define a specific element.

    • A.The dental floss, which glides between contacts, arrives in waxed varieties.
    • B.The prophy paste that contains fine pumice removes extrinsic surface stains.
    • C.The topical ointment, that numbs soft tissues, works within several minutes.
    • D.The scaler insert which reaches deep calculus needs gentle sterile cleaning.
    Show answerHide answer

    Correct answer: The prophy paste that contains fine pumice removes extrinsic surface stains.

    A restrictive clause identifies which one is meant, is essential to the sentence, and is written with that and no commas; The prophy paste that contains fine pumice removes extrinsic surface stains satisfies all three, because the clause is what narrows the paste to the kind containing pumice. The dental floss, which glides between contacts, arrives in waxed varieties encloses its clause in commas, marking the information as an aside rather than a defining detail. The topical ointment, that numbs soft tissues, works within several minutes also uses commas, and it heads the clause with that, which cannot introduce a set-off clause. The scaler insert which reaches deep calculus needs gentle sterile cleaning omits the commas but introduces a defining clause with which, the pronoun standard usage reserves for nonrestrictive clauses.

  26. Identify the sentence that correctly uses an absolute phrase.

    • A.Her stomach growled loudly, the assistant scurried through the instrument trays.
    • B.Her pager vibrated loudly, the receptionist moved toward the sterilization area.
    • C.Her gloves securely fastened, the hygienist reclined the padded operatory chair.
    • D.Her shoulders ached badly, the student repositioned the rolling operatory stool.
    Show answerHide answer

    Correct answer: Her gloves securely fastened, the hygienist reclined the padded operatory chair.

    An absolute phrase is a noun plus a participle that modifies the whole sentence rather than any single word, and Her gloves securely fastened is exactly that: fastened is a participle, not a finite verb, so the phrase cannot stand alone and attaches to the main clause. Her stomach growled loudly, the assistant scurried through the instrument trays uses growled, a finite past-tense verb, which makes the words before the comma a complete clause and the sentence a comma splice. Her pager vibrated loudly, the receptionist moved toward the sterilization area joins two independent clauses with only a comma in the same way. Her shoulders ached badly, the student repositioned the rolling operatory stool uses the finite verb ached, so each of those three needs a semicolon or a conjunction rather than an absolute phrase.

  27. Which sentence correctly uses a gerund phrase as the subject?

    • A.Bleeding gums signal inflammation from the reddened marginal papillae.
    • B.Erupting molars displace premolars during the mixed primary dentition.
    • C.Aching incisors indicate lesions beneath the existing amalgam margins.
    • D.Polishing restorations removes stain from the visible enamel surfaces.
    Show answerHide answer

    Correct answer: Polishing restorations removes stain from the visible enamel surfaces.

    A gerund phrase used as a subject is an -ing form working as a noun together with its own object, and Polishing restorations does that; the singular verb removes confirms that the whole phrase, not a plural noun, is the subject. In Bleeding gums signal inflammation from the reddened marginal papillae the -ing word is a participial adjective describing gums, so the subject is the plain noun and no gerund phrase is present. Erupting molars displace premolars during the mixed primary dentition is built the same way, with the -ing word modifying molars. Aching incisors indicate lesions beneath the existing amalgam margins also uses its -ing word adjectivally, so all three have an ordinary noun phrase as the subject.

  28. Select the sentence that correctly uses an infinitive phrase to express purpose.

    • A.The assistant returned early to restock the sterilization supply cabinets.
    • B.The receptionist decided quickly to reschedule the busy afternoon columns.
    • C.The technician forgot completely to calibrate the panoramic imaging units.
    • D.The student refused firmly to duplicate the blurred radiographic exposure.
    Show answerHide answer

    Correct answer: The assistant returned early to restock the sterilization supply cabinets.

    An infinitive expresses purpose when it answers why the action happened, and returning early in order to restock the cabinets is that relationship; the phrase in The assistant returned early to restock the sterilization supply cabinets could be replaced by in order to restock without changing the meaning. In The receptionist decided quickly to reschedule the busy afternoon columns the infinitive completes decided and names what was decided, not the reason for deciding. In The technician forgot completely to calibrate the panoramic imaging units the infinitive completes forgot and names the thing forgotten. In The student refused firmly to duplicate the blurred radiographic exposure it completes refused and names what was refused, so none of those three states a purpose.

  29. Identify the sentence that demonstrates the correct use of a participle phrase for description.

    • A.Sharpening the curette carefully, the cassette stored the instruments.
    • B.Explaining the procedure gently, the hygienist reassured the children.
    • C.Sterilizing the handpiece quickly, the cabinet remained totally empty.
    • D.Charting the attachment quickly, the probes scratched the restoration.
    Show answerHide answer

    Correct answer: Explaining the procedure gently, the hygienist reassured the children.

    A participial phrase describes the noun that follows it, and in Explaining the procedure gently, the hygienist reassured the children the hygienist both explains and reassures, so the phrase modifies the right subject. In Sharpening the curette carefully, the cassette stored the instruments the noun after the comma is cassette, and a cassette cannot sharpen an instrument, so the phrase dangles. In Sterilizing the handpiece quickly, the cabinet remained totally empty the subject is cabinet, which cannot sterilize anything. In Charting the attachment quickly, the probes scratched the restoration the subject is probes, which cannot chart, so all three attach the description to a noun that could not have performed the action.

  30. Choose the sentence that employs a correlative conjunction correctly.

    • A.Fluoride not only strengthens enamel but also improved acid defense.
    • B.Scaling not only removes calculus but also smoother dental surfaces.
    • C.Sealants not only protect fissures but also reduce replacement cost.
    • D.Varnish not only covers dentin but also reduced sensitivity reports.
    Show answerHide answer

    Correct answer: Sealants not only protect fissures but also reduce replacement cost.

    The correlative pair not only ... but also must be followed by matching grammatical structures, and Sealants not only protect fissures but also reduce replacement cost supplies a verb phrase on each side. Fluoride not only strengthens enamel but also improved acid defense follows a present-tense verb phrase with a mismatched element, so the two halves no longer balance. Scaling not only removes calculus but also smoother dental surfaces follows a verb phrase with a noun phrase that contains no verb. Varnish not only covers dentin but also reduced sensitivity reports does the same, so each of those three breaks the parallelism the correlative requires.

  31. Which sentence correctly uses a modal auxiliary to express necessity?

    • A.The sharps must be discarded inside locking containers, since regulations demand logs.
    • B.The autoclave must be running unusually short cycles, since indicators changed colors.
    • C.The patient must be skipping frequent flossing sessions, since heavier plaque appears.
    • D.The compressor must be leaking beneath heavy cabinets, since pressure drops overnight.
    Show answerHide answer

    Correct answer: The sharps must be discarded inside locking containers, since regulations demand logs.

    Must expresses necessity when it states an obligation the subject has to meet, and The sharps must be discarded inside locking containers, since regulations demand logs does that: the disposal is required, and the clause about regulations names the source of the requirement. The autoclave must be running unusually short cycles, since indicators changed colors uses must to draw a conclusion from evidence, inferring a fault rather than imposing a duty. The patient must be skipping frequent flossing sessions, since heavier plaque appears infers a habit from what the clinician can see. The compressor must be leaking beneath heavy cabinets, since pressure drops overnight infers a leak from the falling pressure, so in those three must carries the sense of the evidence shows rather than this is required.

  32. Identify the sentence that accurately uses a prepositional phrase to indicate location.

    • A.The insurance statements circulate in the seventh week of the semester.
    • B.The treatment discussion proceeds in the opening minutes of the visits.
    • C.The bonding technique improves in the closing months of the internship.
    • D.The replacement handpieces rest in the second drawer of the sterilizer.
    Show answerHide answer

    Correct answer: The replacement handpieces rest in the second drawer of the sterilizer.

    A prepositional phrase shows location when its object names a place, and in the second drawer of the sterilizer is where the handpieces physically sit. The insurance statements circulate in the seventh week of the semester puts week after the preposition, which fixes a point in time rather than a place. The treatment discussion proceeds in the opening minutes of the visits puts minutes after the preposition, another measure of time. The bonding technique improves in the closing months of the internship puts months after the preposition, so each of those three answers when rather than where.

  33. Select the sentence that correctly uses a determiner in a specific context.

    • A.The receptionist scheduled an one-hour recall for the anxious young child.
    • B.The hygienists selected a interdental brush for the wide molar embrasures.
    • C.The dentists ordered an ultrasonic scaler for the busy surgical operatory.
    • D.The assistant opened a instrument cassette for the busy afternoon clinics.
    Show answerHide answer

    Correct answer: The dentists ordered an ultrasonic scaler for the busy surgical operatory.

    The indefinite article is chosen by the sound that begins the next word, not by its spelling, and ultrasonic opens with a vowel sound, so an ultrasonic scaler is correct. The receptionist scheduled an one-hour recall for the anxious young child pairs an with one-hour, which begins with a consonant w sound and therefore takes a. The hygienists selected a interdental brush for the wide molar embrasures pairs a with interdental, which begins with a vowel sound and needs an. The assistant opened a instrument cassette for the busy afternoon clinics pairs a with instrument, another word beginning with a vowel sound, so it also requires an.

  34. Which sentence correctly uses a quantifier with countable nouns?

    • A.Much hygienists complete fluoride training before the summer break begins.
    • B.Many hygienists renew clinical licenses before the annual state deadlines.
    • C.Many equipment requires annual repair before the yearly safety inspection.
    • D.Much sealants safeguard the occlusal fissures from early carious cavities.
    Show answerHide answer

    Correct answer: Many hygienists renew clinical licenses before the annual state deadlines.

    Many quantifies things that can be counted one by one, and hygienists is a countable plural, so Many hygienists renew clinical licenses before the annual state deadlines pairs the quantifier with the right kind of noun. Much hygienists complete fluoride training before the summer break begins puts much in front of a countable plural, and much belongs only with uncountable nouns. Many equipment requires annual repair before the yearly safety inspection reverses the error, putting many in front of equipment, which is uncountable and takes much. Much sealants safeguard the occlusal fissures from early carious cavities uses much with the countable plural sealants, so each of those three mismatches the quantifier to its noun.

  35. Identify the sentence that correctly uses a conjunction to connect an independent and a dependent clause.

    • A.Although the patient brushes nightly, a visible film persists across the arches.
    • B.Although the sealant hardened quickly, a faint yellow coating across the enamel.
    • C.Although the appointment ran late, a lengthy unusual delay inside the reception.
    • D.Although the scaler vibrated loudly, a steady coolant stream inside the turbine.
    Show answerHide answer

    Correct answer: Although the patient brushes nightly, a visible film persists across the arches.

    A subordinating conjunction joins a dependent clause to an independent one, and Although the patient brushes nightly, a visible film persists across the arches supplies both: the opening clause cannot stand alone, while a visible film persists across the arches is a complete clause with its own subject and verb. Although the sealant hardened quickly, a faint yellow coating across the enamel follows the dependent clause with a noun phrase that has no verb, so there is no independent clause for the conjunction to connect. Although the appointment ran late, a lengthy unusual delay inside the reception ends in another verbless fragment. Although the scaler vibrated loudly, a steady coolant stream inside the turbine does the same, leaving the subordinate clause attached to nothing.

  36. Identify the sentence that accurately uses complex prepositions to indicate time relationships.

    • A.Before the appointment ended, he noted the bleeding in his chart.
    • B.In spite of the delay, she polished the largest quadrant quickly.
    • C.In advance of the surgery, she reviewed his full medical history.
    • D.By means of the mirror, she inspected behind both lower incisors.
    Show answerHide answer

    Correct answer: In advance of the surgery, she reviewed his full medical history.

    Correct answer: In advance of the surgery, she reviewed his full medical history. Explanation: "In advance of" is a complex preposition, a fixed multi-word unit that works as a single preposition, and it places one event earlier in time than another, which is what the question asks for. "Before the appointment ended" opens with a subordinating conjunction and is followed by its own subject and verb, so it is an adverbial clause rather than a prepositional phrase. "In spite of" and "By means of" are genuine complex prepositions, but they express concession and means; neither one locates an event in time.

  37. Choose the sentence that correctly employs subjunctive mood to express a hypothetical situation or wish.

    • A.If the hygienist was on call, he would take the impression now.
    • B.She wishes she was a little better at flossing after each meal.
    • C.If the clinic opens at seven, the office can see more patients.
    • D.If he were a dentist, he would recommend a checkup each spring.
    Show answerHide answer

    Correct answer: If he were a dentist, he would recommend a checkup each spring.

    Correct answer: If he were a dentist, he would recommend a checkup each spring. Explanation: The past subjunctive uses "were" for every person and marks a situation contrary to fact, and he is not a dentist, so this sentence carries the mood the question asks about. "If the hygienist was on call" uses the indicative "was", which reports a real past possibility instead of an imagined one. "She wishes she was a little better" also calls for "were" after a verb of wishing, so it misses the subjunctive too. "If the clinic opens at seven" is an open conditional in the present indicative describing something that can actually happen.

  38. Identify the sentence that demonstrates the correct use of inverted syntax for emphasis.

    • A.Rarely do patients replace a toothbrush before the bristles fray.
    • B.Often patients delay their checkup until the gums start bleeding.
    • C.Quickly the plaque returns between the crowded lower front teeth.
    • D.Yesterday the dentist photographed a hairline crack in her molar.
    Show answerHide answer

    Correct answer: Rarely do patients replace a toothbrush before the bristles fray.

    Correct answer: Rarely do patients replace a toothbrush before the bristles fray. Explanation: When a limiting adverb such as "rarely" is fronted, English requires subject-auxiliary inversion, and the auxiliary "do" moves ahead of the subject "patients". That reordering is the inverted syntax the question asks for. The other three sentences also begin with an adverb, but each keeps ordinary subject-verb order, since "patients delay", "the plaque returns" and "the dentist photographed" all place the subject first, so no inversion takes place and no emphasis is created by word order.

  39. Which sentence correctly uses an adverbial clause to indicate cause?

    • A.When the visit finally ended, she booked a second cleaning today.
    • B.Because she flossed each night, her gums healed within six weeks.
    • C.Although the swelling worsened, he refused to try a milder rinse.
    • D.If the sealant chips again, the practice will replace it quickly.
    Show answerHide answer

    Correct answer: Because she flossed each night, her gums healed within six weeks.

    Correct answer: Because she flossed each night, her gums healed within six weeks. Explanation: "Because she flossed each night" is a subordinate adverbial clause introduced by a causal subordinator, and it states the reason the gums healed. The other three are adverbial clauses as well, which is why they look alike, but they answer different questions: "When the visit finally ended" fixes a time, "Although the swelling worsened" concedes a contrast, and "If the sealant chips again" sets a condition. None of the three supplies a cause.

  40. Select the sentence that accurately employs ellipsis for dramatic effect.

    • A.The clinic opens at eight... and closes at five each afternoon.
    • B.The consent form... the signature of a parent and today's date.
    • C.The dentist read the report twice... then set it quietly aside.
    • D.The label says to rinse for thirty seconds... twice each night.
    Show answerHide answer

    Correct answer: The dentist read the report twice... then set it quietly aside.

    Correct answer: The dentist read the report twice... then set it quietly aside. Explanation: The three dots hold the sentence open at its most tense moment and make the reader wait for what the dentist does next, and that suspended pause is the dramatic use of ellipsis. In "The clinic opens at eight... and closes at five each afternoon" the dots interrupt two routine facts that need no pause. "The consent form... the signature of a parent and today's date" puts the dots where the verb should be, leaving a fragment rather than an effect. "The label says to rinse for thirty seconds... twice each night" uses them to show words left out of a set of directions, which is omission, not drama.

  41. Which sentence contains a nonstandard expression that should be replaced in formal academic writing?

    • A.The solvent, being highly inflammable, was stored well away from the burner.
    • B.The samples, irregardless of storage temperature, degraded within one week.
    • C.The results, inasmuch as the sample was small, should be read with caution.
    • D.The cultures, notwithstanding the brief power outage, grew at the usual rate.
    Show answerHide answer

    Correct answer: The samples, irregardless of storage temperature, degraded within one week.

    Irregardless is labeled nonstandard by major dictionaries, so the sentence The samples, irregardless of storage temperature, degraded within one week should use regardless. Inflammable is the most tempting choice because it looks like a negative of flammable, but it is a standard word that means the same thing as flammable. Notwithstanding and inasmuch as are formal but fully standard connectives.

Quantitative Reasoning (53)

  1. A researcher uses a solution with a 15\% concentration of a certain substance. If she needs 2 liters of a 45\% concentration, how much of the 15\% solution should she use if she plans to evaporate the water to increase the concentration to the desired level?

    • A.6 liters
    • B.3 liters
    • C.4 liters
    • D.5 liters
    Show answerHide answer

    Correct answer: 6 liters

    Correct answer: 6 liters. Explanation: Evaporation removes water only, so the amount of dissolved substance never changes. The finished 2 liters at 45\% holds 2×0.45=0.92 \times 0.45 = 0.9 liters of substance, and 0.9 liters is 15\% of 0.9÷0.15=60.9 \div 0.15 = 6 liters. Starting with 3 liters would supply only 0.45 liters of substance, 4 liters would supply 0.6 liters and 5 liters would supply 0.75 liters, so only 6 liters carries the 0.9 liters the final solution needs.

  2. In a sequence, the nth term is given by the formula 3n2−2n+13n^2 - 2n + 1. What is the 5th term?

    • A.76
    • B.66
    • C.86
    • D.96
    Show answerHide answer

    Correct answer: 66

    Correct answer: 66. Explanation: Substituting n=5n = 5 into 3n2−2n+13n^2 - 2n + 1 gives 3(25)−10+1=75−10+1=663(25) - 10 + 1 = 75 - 10 + 1 = 66. 76 drops the −2n-2n term, 86 adds 2n2n instead of subtracting it, and 96 adds 4n4n rather than subtracting 2n2n.

  3. If the odds against an event are 5 to 3, what is the probability that the event will occur?

    • A.38\frac{3}{8}
    • B.58\frac{5}{8}
    • C.35\frac{3}{5}
    • D.53\frac{5}{3}
    Show answerHide answer

    Correct answer: 38\frac{3}{8}

    Correct answer: 38\frac{3}{8}. Explanation: Odds against compare unfavorable outcomes with favorable ones, so 5 to 3 means 5 unfavorable parts and 3 favorable parts among 8 parts in all, and the probability the event occurs is 38\frac{3}{8}. 58\frac{5}{8} is the probability that the event does not occur. 35\frac{3}{5} is the odds in favor written as a fraction and 53\frac{5}{3} is the odds against written as a fraction; neither is a probability, and 53\frac{5}{3} is greater than 1, which no probability can be.

  4. A set of data has a mean of 50 and a standard deviation of 5. If all values in the set are increased by 10, what will be the new mean and standard deviation?

    • A.Mean: 60, standard deviation: 15
    • B.Mean: 60, standard deviation: 5
    • C.Mean: 50, standard deviation: 15
    • D.Mean: 50, standard deviation: 5
    Show answerHide answer

    Correct answer: Mean: 60, standard deviation: 5

    Correct answer: Mean: 60, standard deviation: 5. Explanation: Adding the same constant to every value slides the whole distribution 10 units up the scale, so the mean moves from 50 to 60. The distances between the values are untouched, so the spread stays exactly as it was and the standard deviation remains 5. Leaving the mean at 50 ignores the shift, and raising the standard deviation to 15 treats a shift as though it had stretched the data apart.

  5. A rectangle's length is three times its width. If the perimeter is 64 cm, what are the rectangle's dimensions?

    • A.Length: 24 cm, Width: 8 cm
    • B.Length: 15 cm, Width: 5 cm
    • C.Length: 18 cm, Width: 6 cm
    • D.Length: 21 cm, Width: 7 cm
    Show answerHide answer

    Correct answer: Length: 24 cm, Width: 8 cm

    Correct answer: Length: 24 cm, Width: 8 cm. Explanation: With width ww and length 3w3w, the perimeter is 2(3w)+2w=8w2(3w) + 2w = 8w. Setting 8w=648w = 64 gives w=8w = 8 and 3w=243w = 24. Every option keeps the 3-to-1 shape, so the perimeter is what separates them: 15 by 5 gives 40 cm, 18 by 6 gives 48 cm and 21 by 7 gives 56 cm.

  6. A car travels 150 miles in 2.5 hours. What is its average speed in miles per hour?

    • A.70 mph
    • B.60 mph
    • C.80 mph
    • D.90 mph
    Show answerHide answer

    Correct answer: 60 mph

    Correct answer: 60 mph. Explanation: Average speed is total distance divided by total time, so 150÷2.5=60150 \div 2.5 = 60 miles per hour. In 2.5 hours a car at 70 mph would cover 175 miles, a car at 80 mph would cover 200 miles and a car at 90 mph would cover 225 miles, so none of those speeds matches the 150 miles given.

  7. A sequence is defined as an=3n+2na_n = 3^n + 2^n. What is a4a_4?

    • A.73
    • B.97
    • C.81
    • D.89
    Show answerHide answer

    Correct answer: 97

    Correct answer: 97. Explanation: Substituting n=4n = 4 gives a4=34+24=81+16=97a_4 = 3^4 + 2^4 = 81 + 16 = 97. 81 is 343^4 with the second term dropped, 89 adds 232^3 instead of 242^4, and 73 subtracts 232^3 rather than adding 242^4.

  8. If 3x−7<2(x+4)3x - 7 < 2(x + 4), what is the range of possible values for xx?

    • A.x>15x > 15
    • B.x>11x > 11
    • C.x<15x < 15
    • D.x<11x < 11
    Show answerHide answer

    Correct answer: x<15x < 15

    Correct answer: x<15x < 15. Explanation: Distributing on the right gives 3x−7<2x+83x - 7 < 2x + 8; subtracting 2x2x leaves x−7<8x - 7 < 8, and adding 7 to both sides gives x<15x < 15. Nothing here is multiplied or divided by a negative number, so the inequality never flips to x>15x > 15 or x>11x > 11. The bound 11 appears only if the 2 is multiplied by xx but not by the 4 inside the parentheses.

  9. What is the coefficient of x3x^3 in the expansion of (2x−1)4(2x - 1)^4?

    • A.−32-32
    • B.−64-64
    • C.−48-48
    • D.−16-16
    Show answerHide answer

    Correct answer: −32-32

    Correct answer: −32-32. Explanation: By the binomial theorem the x3x^3 term of (2x−1)4(2x - 1)^4 is (43)(2x)3(−1)1=4×8x3×(−1)=−32x3\binom{4}{3}(2x)^3(-1)^1 = 4 \times 8x^3 \times (-1) = -32x^3, so the coefficient is −32-32. −64-64 uses 242^4 in place of 232^3, −48-48 uses (42)=6\binom{4}{2} = 6 in place of (43)=4\binom{4}{3} = 4, and −16-16 keeps 242^4 but leaves the binomial coefficient out altogether.

  10. A rectangle's length is twice its width, and its area is 128128 square cm. What is the perimeter of the rectangle?

    • A.32 cm
    • B.40 cm
    • C.48 cm
    • D.56 cm
    Show answerHide answer

    Correct answer: 48 cm

    Correct answer: 48 cm. Explanation: With width ww and length 2w2w, the area is w×2w=2w2=128w \times 2w = 2w^2 = 128, so w2=64w^2 = 64, w=8w = 8 and the length is 16. The perimeter is 2(16+8)=482(16 + 8) = 48 cm. The other perimeters belong to different rectangles of the same 2-to-1 shape: 32 cm to a 10.67 by 5.33 rectangle, 40 cm to 13.33 by 6.67 and 56 cm to 18.67 by 9.33, and none of those has an area of 128 square cm.

  11. In how many ways can 5 books be arranged on a shelf if two of the books must stay together?

    • A.24
    • B.72
    • C.96
    • D.48
    Show answerHide answer

    Correct answer: 48

    Correct answer: 48. Explanation: Treat the two books that must stay together as one unit. That unit and the other 3 books make 4 items, which can be ordered in 4!=244! = 24 ways, and the paired books can be arranged inside their unit in 2!=22! = 2 ways, so the total is 24×2=4824 \times 2 = 48. 24 counts the orderings but forgets the internal order of the pair, while 72 and 96 multiply that count by 3 or by 4 instead of by 2.

  12. A tank is filled by Pipe A in 3 hours and by Pipe B in 6 hours. When both pipes are opened together, how long will it take to fill the tank?

    • A.2.0 hours
    • B.2.5 hours
    • C.3.0 hours
    • D.3.5 hours
    Show answerHide answer

    Correct answer: 2.0 hours

    Correct answer: 2.0 hours. Explanation: Pipe A fills 13\frac{1}{3} of the tank each hour and Pipe B fills 16\frac{1}{6}, so together they fill 13+16=12\frac{1}{3} + \frac{1}{6} = \frac{1}{2} of the tank each hour, and half a tank per hour fills it in 2.0 hours. 2.5 hours implies a combined rate of 25\frac{2}{5} of a tank per hour, 3.0 hours is simply Pipe A working on its own, and 3.5 hours is slower than Pipe A manages alone, which cannot happen once a second pipe is helping.

  13. If 5x=1255^x = 125 and 5y=1/255^y = 1/25, what is the value of x+yx + y?

    • A.0
    • B.1
    • C.2
    • D.3
    Show answerHide answer

    Correct answer: 1

    Correct answer: 1. Explanation: 125=53125 = 5^3 gives x=3x = 3, and 125=5−2\frac{1}{25} = 5^{-2} gives y=−2y = -2, so x+y=3+(−2)=1x + y = 3 + (-2) = 1. 0 would follow from reading 125\frac{1}{25} as 5−35^{-3}, 2 from reading it as 5−15^{-1}, and 3 from treating the negative exponent as 505^0 and adding nothing to xx.

  14. What is the smallest positive integer value of nn for which 2n>1,0002^n > 1,000?

    • A.9
    • B.11
    • C.10
    • D.12
    Show answerHide answer

    Correct answer: 10

    Correct answer: 10. Explanation: 29=5122^9 = 512, which is below 1,000, while 210=1,0242^{10} = 1{,}024, the first power of 2 above 1,000. 9 falls short at 512, and 11 and 12 give 2,048 and 4,096, which clear 1,000 but are larger than the smallest exponent that does.

  15. If x3−6x2+11x−6=0x^3 - 6x^2 + 11x - 6 = 0, what are the sum and product of its roots?

    • A.Sum = +6, Product = +6
    • B.Sum = +6, Product = -6
    • C.Sum = -6, Product = +6
    • D.Sum = -6, Product = -6
    Show answerHide answer

    Correct answer: Sum = +6, Product = +6

    Correct answer: Sum = +6, Product = +6. Explanation: For a monic cubic x3+bx2+cx+d=0x^3 + bx^2 + cx + d = 0, Vieta's formulas give the sum of the roots as −b-b and the product as −d-d. Here b=−6b = -6 and d=−6d = -6, so the sum is −(−6)=+6-(-6) = +6 and the product is −(−6)=+6-(-6) = +6; the roots are 1, 2 and 3, which add to 6 and multiply to 6. Reading the product as +d+d instead of −d-d produces a product of -6, and reading the sum as +b+b instead of −b-b produces a sum of -6; the option carrying both sign errors at once is wrong twice over.

  16. A set contains all integers xx such that 2<x2<502 < x^2 < 50. How many elements are in the set?

    • A.10
    • B.11
    • C.12
    • D.13
    Show answerHide answer

    Correct answer: 12

    Correct answer: 12. Explanation: x2>2x^2 > 2 forces ∣x∣≥2|x| \ge 2 because 22=42^2 = 4 already exceeds 2, and x2<50x^2 < 50 forces ∣x∣≤7|x| \le 7 because 82=648^2 = 64 is too large. The set is therefore ±2,±3,±4,±5,±6,±7\pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 7, which is 12 integers. A count of 10 drops the pair ±2\pm 2 by wrongly requiring x2>4x^2 > 4. Counts of 11 and 13 are impossible in principle: every solution arrives with its negative, so the total must be even.

  17. If the interquartile range of a data set is 15 and the range is 30, what is the minimum possible number of elements in the set?

    • A.4
    • B.5
    • C.6
    • D.7
    Show answerHide answer

    Correct answer: 5

    Correct answer: 5. Explanation: A range of 30 is twice the interquartile range of 15, so the smallest and largest values must sit outside the quartile pair rather than on it. That calls for five distinct ordered positions - minimum, first quartile, median, third quartile and maximum - and five values is the smallest set that supplies all five. Four values leave no member outside the quartile pair, so the range could not exceed the interquartile range. Sets of 6 and of 7 values can also meet both conditions, but the question asks for the minimum, and 5 already achieves it.

  18. A survey conducted on a sample of 1000 people found that 60\% prefer tea over coffee. If the margin of error is 4\%, what is the confidence interval for the population proportion who prefer tea?

    • A.58\% to 62\%
    • B.56\% to 64\%
    • C.60\% to 64\%
    • D.56\% to 60\%
    Show answerHide answer

    Correct answer: 56\% to 64\%

    Correct answer: 56\% to 64\%. Explanation: A confidence interval is the sample proportion plus and minus the margin of error, so 60\% with a margin of 4\% gives 60 - 4 = 56\% at the low end and 60 + 4 = 64\% at the high end. The interval 58\% to 62\% applies only half the stated margin. The interval 60\% to 64\% adds the margin above the estimate but never subtracts it below, and 56\% to 60\% subtracts it below but never adds it above; an interval built from a two-sided margin has to move in both directions.

  19. If a fair die is rolled twice, what is the probability that the sum of the two rolls is 9?

    • A.236\frac{2}{36}
    • B.336\frac{3}{36}
    • C.436\frac{4}{36}
    • D.536\frac{5}{36}
    Show answerHide answer

    Correct answer: 436\frac{4}{36}

    Correct answer: 436\frac{4}{36}. Explanation: Two rolls of a fair die give 6×6=366 \times 6 = 36 equally likely ordered outcomes. Exactly four of them total 9: (3,6), (4,5), (5,4) and (6,3), so the probability is 436\frac{4}{36}. The count 2 belongs to a total of 11, which has only (5,6) and (6,5). The count 3 belongs to a total of 10, which has (4,6), (5,5) and (6,4). The count 5 belongs to a total of 8, which has (2,6), (3,5), (4,4), (5,3) and (6,2).

  20. A line intersects the xx-axis at (4,0)(4,0) and the yy-axis at (0,2)(0,2). What is the area of the triangle formed by the line and the coordinate axes?

    • A.2
    • B.4
    • C.6
    • D.8
    Show answerHide answer

    Correct answer: 4

    Correct answer: 4. Explanation: The intercepts (4,0) and (0,2) put the right angle at the origin, so the triangle has legs of 4 along the xx-axis and 2 along the yy-axis, giving an area of 12×4×2=4\frac{1}{2} \times 4 \times 2 = 4. The value 8 is the product of the two intercepts with the factor of one half left out. The value 6 is their sum rather than half their product, and 2 is simply the yy-intercept restated.

  21. When interpreting a complex chart that tracks the progression of gum disease in patients over time, which of the following abilities is MOST important for understanding the chart's data?

    • A.Converting the plotted units to a different scale
    • B.Grouping the patients by the practice they attend
    • C.Relating each plotted value to the earlier points
    • D.Deciding what other chart would display the trend
    Show answerHide answer

    Correct answer: Relating each plotted value to the earlier points

    Correct answer: Relating each plotted value to the earlier points. Explanation: A chart of disease progression carries its meaning in the movement from one reading to the next, so understanding it means reading each plotted value against the values that came before it. Converting the plotted units to a different scale restates the same numbers in other terms and leaves the trend exactly where it was. Grouping the patients by the practice they attend partitions the sample by site, which says nothing about how any patient changed over time. Deciding what other chart would display the trend is a presentation choice made after the data are already understood, so it cannot be the means of understanding them.

  22. When interpreting a complex chart detailing the pH levels in the mouth after consuming various foods, which skill is MOST essential?

    • A.Recalling each food's acid level without the chart
    • B.Ranking the sampled foods by their calorie content
    • C.Reading the values straight off each plotted curve
    • D.Naming the acids released inside each sampled food
    Show answerHide answer

    Correct answer: Reading the values straight off each plotted curve

    Correct answer: Reading the values straight off each plotted curve. Explanation: The chart holds the answer in the shape and height of its curves, so making sense of it depends on extracting values from those plotted lines at the points that matter. Recalling each food's acid level without the chart substitutes memory for the display, which defeats the purpose of interpreting a chart at all. Ranking the sampled foods by their calorie content orders them on a quantity the chart does not plot. Naming the acids released inside each sampled food supplies chemistry that lies behind the curves but does not tell you what any curve reaches or when.

  23. When interpreting a chart that compares the fluoride release rate of different dental materials, which aspect is MOST crucial for understanding the long-term efficacy of the materials?

    • A.The units the chart uses to report the released fluoride
    • B.The count of materials the chart lists within its legend
    • C.The medium the samples rest inside for the fluoride test
    • D.The number of days the chart displays along the baseline
    Show answerHide answer

    Correct answer: The number of days the chart displays along the baseline

    Correct answer: The number of days the chart displays along the baseline. Long term behaviour can only be read from a long record, because most materials release a large burst in the first hours and then settle, so the period covered by the plot decides whether sustained release is visible at all. The units the chart uses to report the released fluoride change the scale of the numbers but not the period they cover. The count of materials the chart lists within its legend sets how many curves are drawn. The medium the samples rest inside for the fluoride test is a condition held constant so that the curves can be compared.

  24. A dental hygiene clinic has 250 milliliters of a 4 percent antiseptic solution. To prepare a 1 percent rinse, water is added without changing the amount of antiseptic. How many milliliters of water must be added?

    • A.250 milliliters
    • B.500 milliliters
    • C.1,000 milliliters
    • D.750 milliliters
    Show answerHide answer

    Correct answer: 750 milliliters

    The answer is 750 milliliters. Because the amount of antiseptic itself does not change, concentration times volume before equals concentration times volume after: 4 percent of 250 milliliters equals 1 percent of the final volume, so the final volume must be 1,000 milliliters. The water added is that final volume minus the 250 milliliters already in the bottle, which is 750 milliliters. The 1,000 milliliters figure is the total volume at the end rather than the water added; adding only 250 milliliters would leave a 2 percent rinse, and adding 500 milliliters would leave it above 1 percent.

  25. Instruments in a sterilization tray are sorted into scalers and probes in a ratio of 3 to 5. If the tray holds 64 instruments total, how many are probes?

    • A.24
    • B.32
    • C.40
    • D.48
    Show answerHide answer

    Correct answer: 40

    The answer is 40 probes. The ratio 3 to 5 has 3 plus 5, or 8 equal parts, and 64 instruments divided by 8 parts gives 8 instruments per part. Probes make up the 5-part share, so 5 times 8 is 40. The value 24 is the scaler count, the 3-part share; 32 would be half of the tray; and 48 would be six parts rather than five.

  26. A student's first five quiz scores have a mean of 82. After a sixth quiz, the mean of all six scores drops to 80. What score did the student earn on the sixth quiz?

    • A.64
    • B.70
    • C.76
    • D.82
    Show answerHide answer

    Correct answer: 70

    The answer is 70. Five quizzes averaging 82 total 5 times 82, or 410 points, and six quizzes averaging 80 must total 6 times 80, or 480 points, so the sixth quiz contributed 480 minus 410, which is 70. The value 82 is the old average, the score that would have held the mean at 82 instead of pulling it down to 80; 76 and 64 come from adjusting that old average by hand rather than comparing the two totals, which is the only route to the missing score.

  27. The numbers of patients seen by a hygienist over seven days were 12, 7, 9, 15, 7, 20, and 11. What is the median number of patients seen per day?

    • A.11
    • B.9
    • C.13
    • D.15
    Show answerHide answer

    Correct answer: 11

    The answer is 11. Ordering the seven counts from least to greatest gives 7, 7, 9, 11, 12, 15, 20, and the fourth value, the one with three counts on either side, is 11. The value 15 is the middle entry of the list as it was written down, before sorting, which is the most common error; 9 is one place too early in the sorted list; and 13 is near the halfway point between the smallest and largest counts, which is the range midpoint rather than the median.

  28. A jar contains 4 blue and 6 red toothbrushes. If two toothbrushes are drawn at random without replacement, what is the probability that both are blue?

    • A.3 over 25
    • B.4 over 25
    • C.1 over 15
    • D.2 over 15
    Show answerHide answer

    Correct answer: 2 over 15

    The answer is 2 over 15. The first draw is blue with probability 4 over 10, and with that toothbrush gone 3 of the remaining 9 are blue, so the second draw is blue with probability 3 over 9; multiplying gives 12 over 90, which reduces to 2 over 15. The value 4 over 25 assumes the first toothbrush is replaced, 3 over 25 keeps the denominator at 10 for the second draw, and 1 over 15 divides the 6 favorable pairs by 90 ordered draws instead of by the 45 unordered pairs.

  29. For which values of x is the inequality 5 minus 2x greater than or equal to 11 true?

    • A.x is no less than negative 8
    • B.x is no more than negative 3
    • C.x is no less than negative 3
    • D.x is no more than negative 8
    Show answerHide answer

    Correct answer: x is no more than negative 3

    Subtracting 5 from both sides leaves negative 2x greater than or equal to 6, and dividing by negative 2 reverses the direction of the inequality, so the solution is x no more than negative 3. Keeping the direction unchanged after dividing by a negative number is the standard slip, and it produces x no less than negative 3. The boundary of negative 8 comes from adding 5 to 11 instead of subtracting it, so both statements built on negative 8 rest on that arithmetic error.

  30. What is the sum of all solutions to the equation absolute value of (2x minus 5) equals 9?

    • A.9
    • B.5
    • C.2
    • D.7
    Show answerHide answer

    Correct answer: 5

    The equation splits into two branches: 2x minus 5 equals 9 gives x equals 7, and 2x minus 5 equals negative 9 gives x equals negative 2, so the sum of the solutions is 7 plus negative 2, which is 5. A total of 7 keeps only the positive branch, a total of 2 keeps only the size of the negative branch, and a total of 9 comes from adding the two solutions after dropping the minus sign on negative 2.

  31. Simplify the expression (2 to the 3rd power times 2 to the 5th power) divided by 2 squared. What is the result?

    • A.2 to the 8th power
    • B.2 to the 3rd power
    • C.2 to the 6th power
    • D.2 to the 4th power
    Show answerHide answer

    Correct answer: 2 to the 6th power

    Multiplying powers of the same base adds the exponents, so the numerator is 2 to the 8th power, and dividing by 2 squared subtracts 2 from that exponent, leaving 2 to the 6th power, which equals 64. Stopping after the addition and never applying the denominator leaves 2 to the 8th power. Dividing the exponent 8 by 2 rather than subtracting 2 leaves 2 to the 4th power. Cancelling the denominator into 2 to the 5th power while forgetting the other factor of the numerator leaves 2 to the 3rd power.

  32. A dental supply item priced at $200 is first marked up by 20 percent, then the new price is discounted by 15 percent. What is the final price?

    • A.$240
    • B.$170
    • C.$276
    • D.$204
    Show answerHide answer

    Correct answer: $204

    The 20 percent markup raises 200 dollars to 240 dollars, and 15 percent of 240 dollars is 36 dollars, so the final price is 204 dollars. Stopping after the markup and never applying the discount leaves 240 dollars. Adding 15 percent to 240 dollars instead of taking it away gives 276 dollars. Taking 15 percent off the original 200 dollars while ignoring the markup leaves 170 dollars, since each percent change applies to the price in force at that step rather than to the starting price.

  33. A clinic's appointment log shows that 3 cleanings together took 75 minutes, and each cleaning takes the same amount of time. Based on this rate, how long should 8 cleanings take?

    • A.200 minutes
    • B.120 minutes
    • C.240 minutes
    • D.160 minutes
    Show answerHide answer

    Correct answer: 200 minutes

    Seventy-five minutes for 3 cleanings is a unit rate of 25 minutes per cleaning, and 25 times 8 gives 200 minutes. Each of the other totals assumes a different rate: 15 minutes per cleaning gives 120 minutes, 20 minutes per cleaning gives 160 minutes, and 30 minutes per cleaning gives 240 minutes, and none of those three rates fits 3 cleanings in 75 minutes.

  34. Evaluate (3.2 × 10^-4)(5 × 10^6) ÷ (8 × 10^-3) and express the result in scientific notation.

    • A.2 × 10^4
    • B.2 × 10^7
    • C.2 × 10^-1
    • D.2 × 10^5
    Show answerHide answer

    Correct answer: 2 × 10^5

    The numerator is 16 × 10^2, or 1.6 × 10^3, and dividing by 8 × 10^-3 gives 0.2 × 10^6, which normalizes to 2 × 10^5. Adding the -3 exponent instead of subtracting it gives 10^0 and the value 2 × 10^-1. Rewriting 0.2 × 10^6 by moving the exponent the wrong way gives 2 × 10^7, and forgetting to raise the exponent when 16 becomes 1.6 gives 2 × 10^4.

  35. In a large dental group, the ratio of hygienists to assistants is 3 to 4, and the ratio of assistants to front-desk staff is 6 to 5. If the group employs 90 hygienists, how many front-desk staff does it employ?

    • A.150
    • B.100
    • C.81
    • D.144
    Show answerHide answer

    Correct answer: 100

    Scaling both ratios so the shared term matches gives 9 : 12 : 10, so hygienists to front-desk staff is 9 to 10 and 90 hygienists means 100 front-desk staff. Chaining the ratios as 3 : 4 : 5 without matching the assistant term gives 150. Using the second ratio upside down gives 5 to 8 and 144, and flipping the final 9 to 10 ratio gives 81.

  36. Each of the following quadratic equations has two distinct real solutions EXCEPT:

    • A.3x^2 + 7x + 4 = 0
    • B.5x^2 + 9x + 4 = 0
    • C.4x^2 - 9x + 5 = 0
    • D.2x^2 - 5x + 4 = 0
    Show answerHide answer

    Correct answer: 2x^2 - 5x + 4 = 0

    The discriminant b^2 - 4ac decides the count of real roots. For 2x^2 - 5x + 4 = 0 it is 25 - 32 = -7, which is negative, so there are no real solutions. The other three each have a discriminant of exactly 1 (49 - 48, 81 - 80 and 81 - 80), which is small but positive, so each has two distinct real solutions.

  37. Young's rule estimates a child's dose C from the adult dose A and the child's age a in years: C = A × a / (a + 12). Solved for the age a, which expression is correct?

    • A.12C / (C - A)
    • B.12A / (C - A)
    • C.12A / (A + C)
    • D.12C / (A - C)
    Show answerHide answer

    Correct answer: 12C / (A - C)

    Multiplying both sides by (a + 12) gives Ca + 12C = Aa, so 12C = Aa - Ca = a(A - C), and a = 12C / (A - C). Collecting the a terms on the wrong side without changing signs gives 12C / (C - A), which would make every age negative because the child dose is smaller than the adult dose. The two forms with 12A come from mixing up which dose is multiplied by 12 when clearing the fraction.

  38. A clinic recorded 200 patients. Of the 60 smokers, 36 had gingivitis; of the 140 nonsmokers, 42 had gingivitis. If a patient with gingivitis is chosen at random, what is the probability, to the nearest whole percent, that the patient is a smoker?

    • A.46 percent
    • B.30 percent
    • C.18 percent
    • D.60 percent
    Show answerHide answer

    Correct answer: 46 percent

    The condition is having gingivitis, so the denominator is all 78 gingivitis patients (36 + 42), and 36 of them smoke: 36/78 is about 46 percent. Dividing 36 by the 60 smokers gives 60 percent, which answers the reverse question, the chance a smoker has gingivitis. Dividing 36 by all 200 patients gives 18 percent, the joint probability, and 60 of 200 gives 30 percent, the overall share of smokers.

  39. A table shows the percent of a clinic's child patients with untreated caries: 48 percent in 2023, 40 percent in 2024, and 36 percent in 2025. By what percent did this rate decrease from 2023 to 2025?

    • A.25 percent
    • B.about 27 percent
    • C.12 percent
    • D.about 33 percent
    Show answerHide answer

    Correct answer: 25 percent

    Percent change is the change divided by the starting value: (48 - 36) / 48 = 12/48 = 25 percent. The 12 is the drop in percentage points, not the percent change. Dividing by the ending value, 12/36, gives about 33 percent, and adding the two yearly percent changes (about 16.7 and 10) gives about 27 percent, which does not equal the change over the whole period.

  40. A supply table lists four chlorhexidine rinse bottles: 240 mL for $4.20, 473 mL for $9.46, 1,000 mL for $18.50, and 1.89 L for $36.00. Which bottle has the lowest cost per milliliter?

    • A.The 473 mL bottle at $9.46
    • B.The 1,000 mL bottle at $18.50
    • C.The 240 mL bottle at $4.20
    • D.The 1.89 L bottle at $36.00
    Show answerHide answer

    Correct answer: The 240 mL bottle at $4.20

    Dividing price by volume gives about $0.0175 per mL for the 240 mL bottle, $0.0200 for the 473 mL bottle, $0.0185 for the 1,000 mL bottle and about $0.0190 for the 1.89 L (1,890 mL) bottle, so the 240 mL bottle at $4.20 is cheapest per mL. The 1,000 mL bottle is the most tempting choice because larger sizes are usually assumed to be the better value, but it costs a tenth of a cent more per mL. The 1.89 L bottle must first be converted to 1,890 mL before comparing.

  41. A clinic's yearly patient survey reports the share of patients who say they floss daily: 2023, 16 percent; 2024, 20 percent; 2025, 24 percent. By what percent did the share of daily flossers increase from 2023 to 2025?

    • A.33 percent
    • B.25 percent
    • C.50 percent
    • D.8 percent
    Show answerHide answer

    Correct answer: 50 percent

    Correct answer: 50 percent. Percent change is the change divided by the starting value: the share rose 8 points, from 16 to 24, and 8 divided by 16 is 0.50, or 50 percent. The 8 percent figure is the percentage-point difference, not the percent change, and 33 percent divides the 8-point rise by the ending value of 24 instead of the starting value of 16.

  42. A hygienist needs 200 mL of a 15 percent solution but has only a 10 percent solution and a 30 percent solution on hand. To the nearest mL, how many mL of the 30 percent solution should be used in the mixture?

    • A.67 mL
    • B.100 mL
    • C.150 mL
    • D.50 mL
    Show answerHide answer

    Correct answer: 50 mL

    Correct answer: 50 mL. If x mL of the 30 percent solution is used, then 0.30x + 0.10(200 - x) = 0.15(200) = 30, so 0.20x = 10 and x = 50 mL, mixed with 150 mL of the 10 percent solution. The 150 mL figure is the amount of the weaker solution, which comes from swapping the two parts of the 5-to-15 ratio, and 67 mL treats that 1-to-3 ratio as one-third of the total instead of one-fourth.

  43. Restocking a clinic's supply room takes Assistant A 6 hours working alone, Assistant B 12 hours alone, and Assistant C 4 hours alone. A and B start together at 9:00 AM, and C joins them at 10:00 AM. Working at these steady rates, at what time do they finish?

    • A.12:00 PM
    • B.1:00 PM
    • C.11:30 AM
    • D.11:00 AM
    Show answerHide answer

    Correct answer: 11:30 AM

    Correct answer: 11:30 AM. In the first hour A and B finish 1/6 + 1/12 = 1/4 of the job; after that all three work at 1/6 + 1/12 + 1/4 = 1/2 job per hour, so the remaining 3/4 takes 1.5 hours, ending at 11:30 AM. The 12:00 PM answer adds the 2 hours all three would need for the whole job to the first hour, ignoring the quarter already done, and 11:00 AM assumes C was there from 9:00.

  44. The price of a case of nitrile gloves rises 25 percent in March and then another 20 percent in June. In September, the clinic negotiates a 30 percent discount off the June price. Compared with the price before March, the September price is how much higher?

    • A.20 percent higher
    • B.15 percent higher
    • C.5 percent higher
    • D.1.5 percent higher
    Show answerHide answer

    Correct answer: 5 percent higher

    Correct answer: 5 percent higher. Successive percent changes multiply: 1.25 times 1.20 is 1.50, and 1.50 times 0.70 is 1.05, a net rise of 5 percent. The 15 percent answer simply adds 25 + 20 - 30, which ignores that each change applies to a different base, and 20 percent subtracts 30 points from the compounded 50 percent rise instead of taking 30 percent of the higher price.

  45. A clinic's continuing-education budget was cut by 20 percent one year and then increased by 20 percent the next year. The budget is now $5,760. What was the budget before the cut?

    • A.$5,990.40
    • B.$6,000.00
    • C.$5,760.00
    • D.$5,529.60
    Show answerHide answer

    Correct answer: $6,000.00

    Correct answer: $6,000.00. The two changes multiply to 0.80 times 1.20 = 0.96, so the original budget is 5,760 divided by 0.96, which is $6,000. The $5,760.00 answer assumes a 20 percent cut and a 20 percent raise cancel, and $5,990.40 adds 4 percent of the current budget back, but the 4 percent loss was taken from the larger original amount.

  46. A medication order calls for 1.5 mg per kilogram of body weight. The drug is supplied as 25 mg per mL, and the patient weighs 110 pounds. Using 1 kg = 2.2 lb, how many mL should be drawn up?

    • A.14.5 mL
    • B.3.0 mL
    • C.6.6 mL
    • D.0.3 mL
    Show answerHide answer

    Correct answer: 3.0 mL

    Correct answer: 3.0 mL. The patient weighs 110 / 2.2 = 50 kg, so the dose is 1.5 times 50 = 75 mg, and 75 mg divided by 25 mg per mL is 3.0 mL. The 6.6 mL answer skips the conversion and treats 110 pounds as 110 kg, and 14.5 mL multiplies by 2.2 instead of dividing, which converts in the wrong direction.

  47. A rectangular instrument tray measures 10 inches by 6 inches. Using 1 inch = 2.54 centimeters, what is the tray's area in square centimeters, to the nearest whole number?

    • A.387 square centimeters
    • B.152 square centimeters
    • C.305 square centimeters
    • D.24 square centimeters
    Show answerHide answer

    Correct answer: 387 square centimeters

    Correct answer: 387 square centimeters. Convert each side first: 10 inches is 25.4 cm and 6 inches is 15.24 cm, so the area is 25.4 times 15.24, about 387 square centimeters; equivalently, 60 square inches times 2.54 squared (6.4516). The 152 answer multiplies the area by 2.54 only once, a linear factor applied to a squared unit, and 305 multiplies by 2 times 2.54 instead of 2.54 squared.

  48. Three sections took the same dental terminology quiz. Section 1 had 18 students with a mean of 84, Section 2 had 12 students with a mean of 74, and Section 3 had 10 students. The mean for all 40 students was 79. What was the mean score of Section 3?

    • A.78
    • B.82
    • C.79
    • D.76
    Show answerHide answer

    Correct answer: 76

    Correct answer: 76. The 40 students scored 40 times 79 = 3,160 points in total, Sections 1 and 2 account for 18 times 84 + 12 times 74 = 2,400, so Section 3 scored 760 points, a mean of 76. The 79 answer treats the three section means as equally weighted, and 82 attaches each mean to the other section's size.

  49. A hygienist deposits $4,000 in an account that pays 5 percent annual interest, compounded semiannually. No other deposits or withdrawals are made. How much interest has the account earned after 3 years, to the nearest cent?

    • A.$638.77
    • B.$600.00
    • C.$307.56
    • D.$630.50
    Show answerHide answer

    Correct answer: $638.77

    Correct answer: $638.77. Semiannual compounding applies 2.5 percent per period for 6 periods: 4,000 times 1.025 to the 6th power is about $4,638.77, so the interest is $638.77. The $630.50 answer compounds once a year (4,000 times 1.05 cubed minus 4,000), and $600.00 is simple interest with no compounding at all.

  50. A line graph shows the cell count of a yeast culture, in thousands of cells per milliliter, measured every 2 hours: 200 at hour 0, 480 at hour 2, 1,100 at hour 4, 1,750 at hour 6, and 2,000 at hour 8. Between which two consecutive readings was the percent increase in the cell count greatest?

    • A.From hour 4 to hour 6
    • B.From hour 2 to hour 4
    • C.From hour 0 to hour 2
    • D.From hour 6 to hour 8
    Show answerHide answer

    Correct answer: From hour 0 to hour 2

    Percent increase is the change divided by the starting value: 280/200 = 140 percent from hour 0 to hour 2, 620/480 = about 129 percent from hour 2 to hour 4, 650/1,100 = about 59 percent from hour 4 to hour 6, and 250/1,750 = about 14 percent from hour 6 to hour 8. So the greatest percent increase is from hour 0 to hour 2. The interval from hour 4 to hour 6 has the largest absolute increase (650), which is the steepest segment on the graph but not the largest percent change.

  51. A table lists applicants and admissions for three dental hygiene programs: Program A, 80 applicants and 36 admitted; Program B, 150 applicants and 60 admitted; Program C, 50 applicants and 24 admitted. Which statement is NOT supported by the table?

    • A.Program A admitted a larger share of its applicants than Program C did.
    • B.Program B rejected more applicants than Programs A and C did combined.
    • C.Program B admitted a smaller share of its applicants than Program A did.
    • D.Program C rejected fewer of its own applicants than Program A did.
    Show answerHide answer

    Correct answer: Program A admitted a larger share of its applicants than Program C did.

    Admission rates are 36/80 = 45 percent for A, 60/150 = 40 percent for B and 24/50 = 48 percent for C, so the claim that Program A admitted a larger share of its applicants than Program C did is false; A admitted more people (36 versus 24) but a smaller percentage. B's 40 percent is below A's 45 percent, B rejected 90 against 44 + 26 = 70 for A and C combined, and C rejected 26 against A's 44, so the other statements all hold.

  52. A lab table shows two shifts last month: the day shift processed 240 samples with a mean processing time of 18 minutes, and the night shift processed 160 samples with a mean of 23 minutes. Next month the night shift is expected to process 260 samples while the day shift stays at 240, and both shifts keep the same means. What is the projected mean processing time for all samples next month?

    • A.20.6 minutes
    • B.20.0 minutes
    • C.20.4 minutes
    • D.20.5 minutes
    Show answerHide answer

    Correct answer: 20.6 minutes

    Weight each mean by next month's sample counts: (240 x 18 + 260 x 23) / 500 = (4,320 + 5,980) / 500 = 10,300 / 500 = 20.6 minutes. Averaging 18 and 23 without weights gives 20.5, attaching each count to the wrong shift's mean gives 20.4, and 20.0 is last month's combined mean, which ignores the projected change in the night shift's volume.

  53. A science museum sold 420 tickets in one day and collected $3,960. Adult tickets cost $12.00 and student tickets cost $7.50. How many student tickets were sold?

    • A.108
    • B.240
    • C.180
    • D.210
    Show answerHide answer

    Correct answer: 240

    Let a be adult tickets, so students = 420 - a and 12a + 7.5(420 - a) = 3,960. Then 4.5a + 3,150 = 3,960, so a = 180 and the number of student tickets is 240; check: 180 x $12 + 240 x $7.50 = $2,160 + $1,800 = $3,960. Stopping at 180 answers for adult tickets instead of student tickets, and 210 assumes an even split.

Perceptual Ability (57)

  1. In a perceptual ability test, which of the following skills is MOST important when determining the relationship between two-dimensional patterns that can be folded into three-dimensional objects?

    • A.Folding a flat pattern into a solid object mentally
    • B.Recalling a flat pattern printed in an earlier item
    • C.Judging a solid shape's mass from its faint outline
    • D.Matching a flat pattern to a printed template sheet
    Show answerHide answer

    Correct answer: Folding a flat pattern into a solid object mentally

    Correct answer: Folding a flat pattern into a solid object mentally. Explanation: Relating a two-dimensional net to the three-dimensional object it produces is a mental folding task: the candidate has to carry each edge and face of the flat figure through the fold and see where it lands on the finished solid. Recalling a flat pattern printed in an earlier item retrieves a picture already seen and says nothing about how that picture behaves when it is folded. Judging a solid shape's mass from its faint outline estimates a physical property rather than a geometric correspondence, and mass is not shown anywhere in a folding item. Matching a flat pattern to a printed template sheet compares one flat figure with another flat figure, so the second dimension is never left behind.

  2. A solid cube measuring 3 units on each edge is built from 27 small unit cubes. The entire outer surface of the large cube is painted, and then it is taken apart into the 27 unit cubes. How many of the small cubes have paint on exactly two of their faces?

    • A.24
    • B.12
    • C.26
    • D.18
    Show answerHide answer

    Correct answer: 12

    The small cubes with exactly two painted faces are the ones lying along an edge of the large cube but not at a corner, and a cube has 12 edges with one such middle cube on each, so the count is 12. Counting 4 edge cubes on each of the 6 painted faces reaches 24 because every edge cube is then counted twice. Adding the 6 face-centre cubes, which carry a single painted face, to the 12 edge cubes gives 18. Every small cube except the hidden centre one takes some paint, which is 26, but most of those carry one or three painted faces rather than two.

  3. A square sheet of paper is folded exactly in half from left to right, and then the resulting rectangle is folded exactly in half from top to bottom, producing a small square that is one quarter of the original area. A single hole is punched through all the layers near the center of this small folded square. When the paper is completely unfolded back to the original square, how many holes appear?

    • A.2
    • B.8
    • C.4
    • D.1
    Show answerHide answer

    Correct answer: 4

    Each fold doubles the number of layers, so two folds take the sheet from 1 layer to 2 and then to 4, and one punch through 4 layers leaves 4 holes, one in each quadrant of the unfolded square. A single hole would mean the sheet was punched flat, 2 holes would follow from one fold only, and 8 holes would need a third fold that the description does not include.

  4. Four angles must be ranked from smallest to largest. Angle W is described as a sharp, narrow wedge only slightly open. Angle X is a right angle. Angle Y is obtuse, opening just past a right angle. Angle Z is nearly a straight line, almost fully opened. Which ordering lists the angles from smallest opening to largest opening?

    • A.W, Y, X, Z
    • B.Z, Y, X, W
    • C.W, X, Y, Z
    • D.X, W, Y, Z
    Show answerHide answer

    Correct answer: W, X, Y, Z

    The described openings widen in the order sharp wedge, right angle, obtuse angle, nearly straight angle, which is the sequence W, X, Y, Z. The sequence Z, Y, X, W lists the same four angles from widest to narrowest, the reverse of what is asked. Putting X ahead of W ranks a 90 degree angle below an angle described as only slightly open, and putting Y ahead of X ranks an opening just past 90 degrees below 90 degrees itself.

  5. A solid object is a cylinder with a hemispherical dome on its top, like a capsule that is flat on the bottom. An aperture must exactly match a true outline of this object as seen from one direction so the object can pass through. Which opening exactly matches one of this object's true silhouettes?

    • A.a rectangle with a notched top edge
    • B.a rectangle with a slanted top edge
    • C.a rectangle with a pointed top edge
    • D.a rectangle with a rounded top edge
    Show answerHide answer

    Correct answer: a rectangle with a rounded top edge

    Seen from the side, the flat-bottomed cylinder shows straight parallel sides and the hemispherical dome adds a semicircular cap, so the true outline is a rectangle with a rounded top edge. A pointed top edge is the profile of a cone set on the cylinder, a slanted top edge belongs to a cylinder cut off at an angle, and a notched top edge belongs to a cylinder with a groove cut across its top; none of those three shapes appears in any view of this solid.

  6. A view-recognition task gives the top view and the front view of a solid and asks what the object is. The top view is a solid circle, and the front view is a solid square (taller than it is wide is not specified; it is a true square). Which single solid object is consistent with both of these views?

    • A.a cylinder standing on a flat base
    • B.a cone rising from a circular base
    • C.a sphere resting on a smooth table
    • D.a cube standing flat on its bottom
    Show answerHide answer

    Correct answer: a cylinder standing on a flat base

    Only the cylinder matches both views: looking straight down its axis gives a circle, and looking at it from the front gives a rectangle that is a true square when its height equals its diameter, which is the cylinder standing on a flat base described here. A cone rising from a circular base also reads as a circle from above, but from the front it shows a triangle rather than a square. A sphere reads as a circle from every direction, so its front view could never be a square. A cube gives a square from the front but a square, not a circle, from above.

  7. A view-recognition task provides three orthographic views of an object: the front view is a square, the top view is a square, and the right-side view is also a square, with no internal lines or notches shown in any view. What single solid is represented?

    • A.a cylinder with a curved side wall
    • B.a pyramid with a broad square base
    • C.a block with two long narrow sides
    • D.a cube with six equal square faces
    Show answerHide answer

    Correct answer: a cube with six equal square faces

    Three identical square views with no internal lines mean every dimension is equal and every face is flat, which describes a cube with six equal square faces. A cylinder shows a circle in one of the three views because of its curved wall. A pyramid on a square base shows a triangle from the front and from the side even though its view from above is a square. A block with two long narrow sides shows a rectangle rather than a square in at least one of the three views.

  8. A staircase shape is built from unit cubes in three rows. The bottom row has 4 cubes in a line, the second row has 3 cubes stacked directly on the leftmost 3 bottom cubes, and the top row has 2 cubes stacked directly on the leftmost 2 of the second row. How many unit cubes were used to build this stepped structure?

    • A.6
    • B.9
    • C.8
    • D.7
    Show answerHide answer

    Correct answer: 9

    The three rows hold 4, 3 and 2 cubes, and 4 plus 3 plus 2 is 9. Counting only the bottom two rows gives 7, reading the top row as a single cube gives 8, and reading the rows as 3, 2 and 1 gives 6, and none of those counts matches the stacking described.

  9. In a cube-counting figure, unit cubes are stacked and then the whole assembly is painted on every exposed surface, including any faces facing down toward the table, except where cubes touch each other. A single unit cube is fully surrounded on all six faces by other cubes in the stack. How many of its faces are painted?

    • A.2
    • B.6
    • C.0
    • D.4
    Show answerHide answer

    Correct answer: 0

    A unit cube enclosed by neighbours on all six sides has no exposed surface, so paint never reaches it and the number of painted faces is 0. A cube left with its four side faces exposed would show 4, a cube exposed on two opposite sides would show 2, and a cube standing clear of the stack would show 6, but the cube described here touches another cube on every face.

  10. A square sheet is folded in half along its vertical centerline, then the doubled sheet is folded in half again along its vertical centerline, giving a tall narrow rectangle of four layers. A hole is punched once through all four layers. After the paper is fully unfolded, how are the holes arranged across the original square?

    • A.four holes lying in one straight row
    • B.four holes forming a big square grid
    • C.two holes sitting one over the other
    • D.one hole showing at the sheet center
    Show answerHide answer

    Correct answer: four holes lying in one straight row

    Both folds run along vertical lines, so unfolding spreads the single punch sideways only and leaves four holes at the same height in one straight row. A big square grid of four holes would need one vertical fold and one horizontal fold. Two holes one over the other would follow from a single horizontal fold, and one hole at the sheet center would mean the paper was punched while flat.

  11. A 3D form-development task describes a flat pattern (net) that, when folded, should form a closed cube. The net consists of six squares: a vertical column of four squares, with one extra square attached to the right side of the second square from the top and another extra square attached to the left side of that same second square. When this net is folded, does it form a complete cube, and why?

    • A.Yes, but a single square face stays clear
    • B.No, two of the squares would overlap once
    • C.No, the column of four cannot bend around
    • D.Yes, the six squares cover each face once
    Show answerHide answer

    Correct answer: Yes, the six squares cover each face once

    The vertical column of four squares bends round to make the four side faces, and the two flaps attached to opposite sides of one square fold up to become the top and the bottom, so the six squares cover each face once. No face is left uncovered, because the two flaps supply exactly the two faces the column does not reach. The flaps sit on opposite sides of a single square, so they land on different faces instead of doubling onto one, so no two squares overlap. A column of four is exactly the length needed to bend round and close the ring of side faces.

  12. Under the aperture rules the object may be turned any way before it starts, then must pass straight through without twisting, and the opening is the exact outside outline of the object seen from one direction. A solid rectangular block is 8 cm long, 4 cm wide and 2 cm tall. A groove 2 cm wide and 1 cm deep is cut across its top face at the middle of its length, running the full 4 cm width. Which opening can the block pass through?

    • A.An 8 by 2 cm outline with a 4 by 1 cm notch at the middle of a long side
    • B.An 8 by 2 cm outline with a 2 by 1 cm notch at the middle of a long side
    • C.A 4 by 2 cm outline with a 1 by 1 cm notch at the middle of a long side
    • D.A 4 by 2 cm outline with a 2 by 1 cm notch at the middle of a long side
    Show answerHide answer

    Correct answer: An 8 by 2 cm outline with a 2 by 1 cm notch at the middle of a long side

    Correct answer: An 8 by 2 cm outline with a 2 by 1 cm notch at the middle of a long side. Looking along the width, straight down the groove, the groove shows as a 2 by 1 cm notch in the middle of the 8 by 2 cm side outline. Looking along the length instead, the full-height material at the two ends hides the groove, so that outline is a plain 4 by 2 cm rectangle and any notched 4 by 2 opening would block those ends. A 4 cm wide notch is twice the groove's width and would catch the block's top shoulders.

  13. Under the aperture rules the object may be turned any way before it starts, then must pass straight through without twisting, and the opening is the exact outside outline of the object seen from one direction. Two solid square bars, each 2 cm by 2 cm in cross section, are joined at a right angle to form an L lying flat. Measured to the outer corner, one leg is 6 cm long and the other is 4 cm long. Which opening can the L pass through?

    • A.A rectangle 3 cm long and 2 cm wide
    • B.A rectangle 4 cm long and 2 cm wide
    • C.A rectangle 2 cm long and 2 cm wide
    • D.An L with 6 and 4 cm legs, 1 cm wide
    Show answerHide answer

    Correct answer: A rectangle 4 cm long and 2 cm wide

    Correct answer: A rectangle 4 cm long and 2 cm wide. Looking straight down the 6 cm leg, that leg hides behind the 4 cm leg, which shows as a 4 by 2 cm rectangle. The 2 by 2 cm opening is tempting because it matches a bar's cross section, but the other leg would hit the edge, and the object cannot turn once it starts. A 3 by 2 cm rectangle measures the leg only to the bar's centerline, and a 1 cm thick L is too thin for 2 cm bars.

  14. A rectangular block is 6 units wide, 3 units tall, and 3 units deep. A round hole 1 unit across is drilled into the center of its left face and runs 2 units into the block, stopping well short of the right face. In the standard top, front, and end views, how does this hole appear in the end view?

    • A.As a dashed circle drawn at the center of the view
    • B.As two dashed lines that run across the whole view
    • C.As a solid circle drawn at the center of the view
    • D.As no lines, because the hole ends inside the block
    Show answerHide answer

    Correct answer: As a dashed circle drawn at the center of the view

    The end view looks at the right face, and the hole points straight along that line of sight, so it projects as a circle; because solid material lies between the right face and the hole, that circle is drawn dashed. A solid circle would be correct only if the hole opened on the right face, which is the result of treating the end view as the left side. A hidden feature is drawn wherever it projects, however far inside the block it stops, so the view is not left blank.

  15. An object is made of three rectangular blocks set side by side from left to right, each running the full 2-unit depth. In the front view the left block is 1 unit tall, the middle block 3 units tall, and the right block 2 units tall. The top view is a rectangle divided by two solid vertical lines at the block boundaries. Which describes the end view?

    • A.A rectangle with a solid line at height 1 and a solid line at height 2
    • B.A rectangle with a solid line at height 2 and a dashed line at height 1
    • C.A rectangle with a solid line at height 1 and a dashed line at height 2
    • D.A rectangle with a dashed line at height 1 and a dashed line at height 2
    Show answerHide answer

    Correct answer: A rectangle with a solid line at height 2 and a dashed line at height 1

    Seen from the right, the 2-unit right block is nearest, so its top edge at height 2 is visible against the taller middle block and is drawn solid, while the left block's top edge at height 1 sits behind the right block and is drawn dashed. Solid at height 1 with dashed at height 2 is the view from the left side, where the short block is nearest. Drawing both lines solid ignores that the right block hides the edge at height 1.

  16. A block is 4 units wide, 4 units tall, and 6 units deep. The front view shows a solid circle 2 units across at the center of the front face. The top view shows two dashed lines that run from the front edge 3 units toward the back, joined by a short dashed line across their ends. Which describes the two long lines the hole produces in the end view?

    • A.Two dashed lines that start at the right edge and stop halfway across
    • B.Two dashed lines that start at the left edge and stop halfway across
    • C.Two dashed lines that run the full distance from one edge to the other
    • D.Two solid lines that start at the right edge and stop halfway across
    Show answerHide answer

    Correct answer: Two dashed lines that start at the left edge and stop halfway across

    The hole opens on the front face and stops 3 units into a 6-unit depth, and in the end view the front of the object is on the left, so its two hidden lines start at the left edge and stop halfway across. Starting them from the right edge puts the hole's opening at the back, which is the mirror error of reading the end view as if the front were on its right. Lines running edge to edge would describe a hole that goes all the way through, which the closed end in the top view rules out.

  17. An object is 4 units wide and 3 units deep. Its front view is a four-sided outline whose left side is 4 units tall, whose right side is 2 units tall, and whose top is one straight slanted line joining them. Its top view is a plain rectangle with no lines inside. Which describes the end view?

    • A.A rectangle with a dashed horizontal line 2 units above its base
    • B.A rectangle with a solid horizontal line 2 units above its base
    • C.A rectangle with a solid diagonal line running corner to corner
    • D.A rectangle with a dashed diagonal line running corner to corner
    Show answerHide answer

    Correct answer: A rectangle with a solid horizontal line 2 units above its base

    The slanted top is a sloped surface seen edge-on in the front view; from the right it is seen as an area rising behind the 2-unit right face, so the end view is a 4-unit-tall rectangle split by the edge where the right face meets the slope. That edge faces the viewer, so it is solid. A dashed line would be right only if the tall side were on the right, hiding the low edge. A diagonal line is wrong because a slope appears as a slanted line only in the view where it is seen edge-on.

  18. A block is 6 units wide, 4 units tall, and 3 units deep. A channel 2 units wide and 1 unit deep is cut into the center of the top face and runs from the front face to the back face. The front view shows this channel as a notch in the top edge, and the top view shows two solid vertical lines 2 units apart. Which describes the end view?

    • A.A rectangle crossed by two dashed vertical lines spaced 2 units apart
    • B.A rectangle crossed by a solid horizontal line 1 unit below its top
    • C.A rectangle crossed by a dashed horizontal line 1 unit below its top
    • D.A rectangle crossed by two solid vertical lines spaced 2 units apart
    Show answerHide answer

    Correct answer: A rectangle crossed by a dashed horizontal line 1 unit below its top

    From the right, the channel runs straight across the line of sight, so its floor is seen edge-on as a horizontal line 1 unit below the top, and the full-height material to the right of the channel hides it, making it dashed. A solid line would mean the viewer could see the floor, but the right portion of the block blocks it. The channel walls face left and right, parallel to the end view, so they appear as areas rather than as vertical lines.

  19. An object is 4 units wide, 4 units tall, and 3 units deep. Its front view is an outline made of a 1-unit-wide post on the left, rising the full 4 units, topped by a 1-unit-thick shelf spanning the full width, with open space under the shelf to the right of the post. Its end view is a rectangle with a solid horizontal line 1 unit below its top. Which describes the top view?

    • A.A rectangle with a solid vertical line 1 unit from its right edge
    • B.A rectangle with a solid vertical line 1 unit from its left edge
    • C.A rectangle with a dashed vertical line 1 unit from its left edge
    • D.A rectangle with a solid horizontal line 1 unit from its bottom edge
    Show answerHide answer

    Correct answer: A rectangle with a dashed vertical line 1 unit from its left edge

    From above, the shelf covers the whole object, so the only interior feature is the right face of the post, which lies under the shelf 1 unit from the left and is drawn dashed. A solid line at that spot would mean the post's edge could be seen from above, but the shelf sits on top of it. A line 1 unit from the right edge mirrors the post to the wrong side, and a horizontal line copies the end view's shelf edge onto the wrong axis.

  20. Three blocks sit side by side from left to right. The left block is 2 units tall and the full 2-unit depth, the middle block is 4 units tall and the full depth, and the right block is 2 units tall but only fills the front half of the depth. Ignoring the outline and the short vertical edge of the right block, how is the horizontal line at a height of 2 units drawn in the end view?

    • A.Dashed along the left half and solid along the right half
    • B.Solid along the left half and solid along the right half
    • C.Solid along the left half and dashed along the right half
    • D.Solid along the left half and absent from the right half
    Show answerHide answer

    Correct answer: Solid along the left half and dashed along the right half

    In the end view the front is on the left, so the right block's visible top edge covers the front half at height 2 and is solid there, and a solid line wins over the left block's hidden edge lying behind it. Over the back half the right block is missing, so the left block's top edge is seen only through the middle block and shows as dashed. Solid on both halves forgets that the middle block hides the back half, and dashed-then-solid is the mirror image you get by putting the front on the right.

  21. A block is 6 units wide, 3 units tall, and 5 units deep. A groove 1 unit square in cross-section is cut into the bottom face and runs left to right across the full width, starting 1 unit behind the front face. The front view shows a dashed horizontal line 1 unit above the base, and the top view shows two dashed horizontal lines. Which describes the end view?

    • A.An outline with a 1-unit notch in its base starting 1 unit from its left end
    • B.A full rectangle with a dashed 1-unit square on its base 1 unit from its right end
    • C.An outline with a 1-unit notch in its base starting 1 unit from its right end
    • D.A full rectangle with a dashed 1-unit square on its base 1 unit from its left end
    Show answerHide answer

    Correct answer: An outline with a 1-unit notch in its base starting 1 unit from its left end

    The groove runs out through the right face, so the end view looks straight into its open end and shows it as a notch cut into the bottom of the outline. Because the groove is 1 unit behind the front and the front is on the left of the end view, the notch starts 1 unit from the left end. A dashed square would apply to a groove that stopped inside the block, so it never reached the right face.

  22. A block is 6 units wide, 4 units tall, and 5 units deep, with a round hole 1 unit across drilled straight down through it. In the top view the hole is a solid circle whose edges lie 1 unit and 2 units below the top edge of the view, and the front view shows two dashed vertical lines running the full height. Which describes the end view?

    • A.Two dashed vertical lines, 3 and 4 units from the left edge
    • B.Two dashed vertical lines, 1 and 2 units from the left edge
    • C.Two solid vertical lines, 1 and 2 units from the left edge
    • D.Two solid vertical lines, 3 and 4 units from the left edge
    Show answerHide answer

    Correct answer: Two dashed vertical lines, 3 and 4 units from the left edge

    The top edge of the top view is the back, so the hole sits 1 to 2 units from the back, which is 3 to 4 units from the front, and in the end view the front is on the left. The hole is enclosed by material on its right side, so its sides are dashed at 3 and 4 units from the left edge. Lines at 1 and 2 units come from carrying the top-view distances across without turning the view, which flips front and back.

  23. Each of four angles is defined by the compass bearings of its two arms, measured clockwise from north, and each angle is the smaller opening between its arms. Angle 1 has arms at 15° and 98°, each 2 cm long. Angle 2 has arms at 341° and 66°, each 6 cm long. Angle 3 has arms at 200° and 284°, each 3 cm long. Angle 4 has arms at 110° and 196°, each 1 cm long. Which ordering ranks the angles from smallest to largest?

    • A.1, 4, 3, 2
    • B.1, 3, 2, 4
    • C.4, 1, 3, 2
    • D.1, 3, 4, 2
    Show answerHide answer

    Correct answer: 1, 3, 2, 4

    The openings are 83° (98 minus 15), 85° (19° up to north plus 66° past it), 84° (284 minus 200) and 86° (196 minus 110), so the order is 1, 3, 2, 4. Angle 2 crosses north, and treating its bearings as 275° apart, or miscounting the wrap, pushes it to the end of the list. Ranking by arm length or by which way the angle points is the perceptual trap the subtest is built on, because neither changes an angle's size.

  24. Four angles are each drawn against a horizontal or vertical arm. For P, one arm points right along the horizontal and the other is tilted 1° from vertical toward that arm. For Q, one arm points right along the horizontal and the other is tilted 2° from vertical away from that arm; Q's arms are drawn three times as long as the rest. For R, one arm points straight up and the other points right, tilted 2° above horizontal. For S, one arm points straight up and the other points right, tilted 1° below horizontal. Which ordering ranks the angles from smallest to largest?

    • A.R, S, P, Q
    • B.Q, P, S, R
    • C.R, P, S, Q
    • D.Q, S, P, R
    Show answerHide answer

    Correct answer: R, P, S, Q

    Work from 90° each time: P is 90 minus 1, or 89°; Q is 90 plus 2, or 92°; R is 90 minus 2, or 88°, because its slanted arm rises toward the vertical one; S is 90 plus 1, or 91°, because its arm drops away from the vertical one. That gives R, P, S, Q. The ordering R, S, P, Q comes from reversing the two 1° tilts, and Q's long arms have no bearing on its size.

  25. An accurate analog clock is read at four times: 12:16, 4:38, 6:16 and 9:32. At each time, the angle is the smaller opening between the hour hand and the minute hand, and the hour hand is drawn much shorter than the minute hand. Which ordering ranks these four angles from smallest to largest?

    • A.4:38, 12:16, 6:16, 9:32
    • B.4:38, 6:16, 12:16, 9:32
    • C.12:16, 4:38, 6:16, 9:32
    • D.9:32, 6:16, 12:16, 4:38
    Show answerHide answer

    Correct answer: 12:16, 4:38, 6:16, 9:32

    The minute hand moves 6° per minute and the hour hand 0.5° per minute, so the openings are 88° at 12:16, 89° at 4:38, 92° at 6:16 and 94° at 9:32. Ordering 9:32, 6:16, 12:16, 4:38 comes from leaving the hour hand fixed on its hour mark, which gives 78°, 84°, 96° and 108°. Moving the hour hand 1° per minute, or rounding it to the nearest hour mark, produces the other two orderings. The shorter hour hand changes nothing, because arm length never affects an angle.

  26. A square sheet 8 inches on a side is folded by bringing its right edge over to the left so that the crease runs top to bottom 5 inches from the left edge, which lays a 3-inch-wide flap on top. The sheet is then folded in half by bringing its top edge down onto its bottom edge. One hole is punched 1 inch from the left edge and a second 3.5 inches from the left edge, each through every layer at that spot. How many holes are in the sheet once it is fully unfolded?

    • A.8
    • B.5
    • C.6
    • D.4
    Show answerHide answer

    Correct answer: 6

    The flap covers the strip from 2 to 5 inches, so after the first fold the sheet is two layers thick there and one layer from 0 to 2 inches; the second fold doubles both, giving 4 layers at 3.5 inches and 2 layers at 1 inch. One punch makes one hole per layer, so 4 plus 2 gives 6. The answer 8 assumes both punches go through four layers, but the uneven first fold left the strip near the left edge single before the half fold.

  27. A square sheet is folded along the diagonal from its top-left corner to its bottom-right corner by lifting the bottom-left corner onto the top-right corner. The triangle that results is folded in half by bringing its top-left corner onto its bottom-right corner. One hole is punched through all layers close to the folded triangle's sharp corner that sits at the sheet's original top-right corner. Where are the holes once the sheet is fully unfolded?

    • A.One hole near each of the four corners of the unfolded square sheet
    • B.Two holes near the top-left corner and two near the bottom-right corner
    • C.One hole near the midpoint of each of the four edges of the sheet
    • D.Two holes by the top-right corner and two by the bottom-left corner
    Show answerHide answer

    Correct answer: Two holes by the top-right corner and two by the bottom-left corner

    The second crease lies along the other diagonal, so undoing it mirrors the hole across that diagonal, leaving two holes side by side at the top-right corner. Undoing the first fold mirrors both across the top-left to bottom-right diagonal, which carries them to the bottom-left corner, so the holes are two by the top-right corner and two by the bottom-left corner. One hole at each corner is the tempting picture, but a point at the end of a fold line stays at that same corner when it is mirrored across the line.

  28. A square sheet is ruled into a 4-by-4 grid of cells, with rows 1 to 4 running top to bottom and columns 1 to 4 left to right. It is folded by laying the right half over the left half, then by laying the top half down over the bottom half, so the folded square covers rows 3 and 4 of columns 1 and 2. That small square is then folded along its diagonal by lifting its bottom-left corner onto its top-right corner. One hole is punched through every layer in the cell at row 3, column 2. Which cells hold holes once the sheet is fully unfolded?

    • A.Every cell in the two middle columns of the grid
    • B.Every cell in the two middle rows of the grid
    • C.The four cells forming the central block of the grid
    • D.Every cell on the two diagonals of the grid
    Show answerHide answer

    Correct answer: Every cell on the two diagonals of the grid

    Undoing the diagonal fold adds row 4, column 1; undoing the top-over-bottom fold mirrors those to row 2, column 2 and row 1, column 1; undoing the first fold mirrors all four into columns 3 and 4, giving 8 holes on the two diagonals of the grid. Every cell in the two middle columns is what you get by treating the diagonal fold as a bottom-onto-top book fold. The central block of four is what remains if the diagonal fold is forgotten.

  29. A figure of 12 identical cubes is cemented together on a table. Seen from directly above, it covers a 3-by-3 square of positions, and the number of cubes stacked at each position is: back row, left to right, 3, 2, 1; middle row 2, 1, 1; front row 1, 1, 0, so the front-right position is empty. Every cube rests on the table or on another cube. The figure is painted on all exposed faces except the bottom faces resting on the table. How many cubes have exactly three painted faces?

    • A.5
    • B.4
    • C.3
    • D.1
    Show answerHide answer

    Correct answer: 4

    The back-right cube, the middle-right cube, the front-left cube and the front-middle cube each show a top and two open sides, so 4 cubes have exactly three painted faces. The answer 5 comes from treating the raised cubes in the back-left and back-middle stacks as covered wherever any neighbor stands, but a side is exposed wherever the neighboring stack is shorter, which gives the top back-left cube five painted faces, not three. Counting the empty front-right spot as filled drops the count to 3, and painting the table-side bottoms shifts nearly every cube up a category, leaving 1.

  30. A flat pattern of six squares is drawn on a grid. The top row has squares A and B side by side, with A on the left. The second row has square C directly below B and square D to the right of C. The third row has square E directly below D and square F to the right of E. The pattern is folded along every shared edge to form a cube. Which square ends up on the face opposite square A?

    • A.Square D
    • B.Square F
    • C.Square E
    • D.Square C
    Show answerHide answer

    Correct answer: Square D

    Treat C as the bottom face: B folds up as the back wall, D folds up as the right wall, and A, hinged on B's left edge, swings down to become the left wall, directly opposite D. E then becomes the front and F the top. Square C is the tempting answer from the skip-one rule, but that rule holds only for three squares in a straight line, and A, B and C turn a corner, so C shares an edge with A on the cube.

  31. A flat pattern of six equal squares folds into a cube. The top row has two squares, labeled 1 and 2 from left to right. A middle row of three squares, labeled 3, 4, and 5 from left to right, sits below it so that square 3 is directly under square 2. Square 6 is directly under square 5. When the pattern is folded into a cube, which square ends up opposite square 1?

    • A.Square 6
    • B.Square 4
    • C.Square 5
    • D.Square 3
    Show answerHide answer

    Correct answer: Square 4

    Correct answer: Square 4. Squares 1, 2, 3, and 4 form a Z-shaped zigzag, and the two end squares of that zigzag always land on opposite faces. If square 4 is the front, square 3 becomes the left face, square 2 folds over to the top, and square 1 folds down to the back. Square 6 is tempting because it is the farthest from square 1 on the flat pattern, but it folds under square 5 to become the bottom, which is opposite square 2.

  32. A cube pattern is a vertical column of four squares, labeled 1 to 4 from top to bottom. Square 5 is attached to the left edge of square 2, and square 6 is attached to the right edge of square 2. The cube is folded with square 2 as the front face. On square 4 an arrow points straight down the page, toward the edge of square 4 that touches no other square. After folding, which face does the arrow point toward?

    • A.The top face, square 1
    • B.The bottom face, square 3
    • C.The right face, square 6
    • D.The left face, square 5
    Show answerHide answer

    Correct answer: The top face, square 1

    Correct answer: The top face, square 1. With square 2 at the front, square 1 folds back to form the top, square 3 folds back to form the bottom, and square 4 swings up from the back edge of the bottom to become the back face. The free bottom edge of square 4 therefore ends at the top of the cube, where it meets the free top edge of square 1, so a downward arrow now points up. The bottom face is the tempting answer because the arrow points down on the flat page, but square 4's attached edge, not its free edge, touches square 3.

  33. Each pattern below is made of six equal squares in two horizontal rows. The leftmost square of the lower row sits directly beneath the named square of the upper row, counting from the left. Which pattern folds into a closed cube?

    • A.Upper row of 3, lower row of 3, under the upper row's 3rd square
    • B.Upper row of 2, lower row of 4, under the upper row's 1st square
    • C.Upper row of 3, lower row of 3, under the upper row's 2nd square
    • D.Upper row of 2, lower row of 4, under the upper row's 2nd square
    Show answerHide answer

    Correct answer: Upper row of 3, lower row of 3, under the upper row's 3rd square

    Correct answer: Upper row of 3, lower row of 3, under the upper row's 3rd square. That is the staircase pattern in which the rows overlap by one square, and it folds with each row wrapping three faces around a shared corner. Starting the lower row under the 2nd square, or under the 1st square of a two-square row, creates a two-by-two block, and four squares meeting at a point can never fold onto a cube. The two-square row over the 2nd square is the subtle trap: the square above the row of 4 becomes the top face, and the square beside it folds down onto a side face that the row of 4 already covers, so the bottom stays open.

  34. A flat pattern has five identical rectangles joined side by side in a row. A regular pentagon is attached to the top edge of the second rectangle, and another regular pentagon is attached to the bottom edge of the fourth rectangle. When the pattern is folded into a closed solid, how many edges and vertices does the solid have?

    • A.14 edges and 9 vertices
    • B.15 edges and 10 vertices
    • C.10 edges and 10 vertices
    • D.10 edges and 6 vertices
    Show answerHide answer

    Correct answer: 15 edges and 10 vertices

    Correct answer: 15 edges and 10 vertices. The pattern folds into a pentagonal prism: each pentagon contributes 5 edges and 5 vertices, and 5 vertical edges join the two pentagons, giving 5 + 5 + 5 = 15 edges and 10 vertices. Ten edges and ten vertices counts only one pentagon's ring of edges plus the vertical ones. Ten edges and six vertices describes a pentagonal pyramid, and 14 edges with 9 vertices satisfies Euler's formula for 7 faces but does not match the actual corners of this solid.

  35. A flat pattern has a small square in the center. Four identical isosceles trapezoids are attached to it, each by its shorter parallel side, one on each side of the square. A larger square is attached to the longer parallel side of one trapezoid. When the pattern is folded closed, which solid does it form?

    • A.A pyramid on a square base
    • B.A box with two square ends
    • C.A prism with trapezoid ends
    • D.A truncated square pyramid
    Show answerHide answer

    Correct answer: A truncated square pyramid

    Correct answer: A truncated square pyramid. The four trapezoids lean inward from the large square to the small one, which is the shape of a square pyramid with its tip cut off parallel to the base. A prism with trapezoid ends is tempting because the pattern is full of trapezoids, but such a prism has only two trapezoid faces and four rectangles, not four trapezoids. A pyramid on a square base would need triangles meeting at a point, and a box needs rectangles, not trapezoids, around its square ends.

  36. A cube pattern is a vertical column of four squares, labeled 1 to 4 from top to bottom. Square 5 is attached to the left edge of square 1, and square 6 is attached to the right edge of square 4. After the pattern is folded into a cube, which three squares meet at a single corner?

    • A.Squares 1, 3, and 5
    • B.Squares 3, 5, and 6
    • C.Squares 1, 4, and 5
    • D.Squares 1, 3, and 6
    Show answerHide answer

    Correct answer: Squares 1, 4, and 5

    Correct answer: Squares 1, 4, and 5. With square 2 as the front, square 1 is the top, square 4 is the back, and square 5 folds down from the top to the left side, so these three faces meet at the top-back-left corner. Squares 1 and 3 are separated by one square in the column, which makes them opposite faces, so no corner can contain both. Squares 5 and 6 are also opposite, as the left and right faces.

  37. A pattern for a closed triangular prism has three identical rectangles joined side by side along their long edges. An equilateral triangle is attached to the top of the left rectangle, and another is attached to the bottom of the right rectangle. After folding, how are the left and right rectangles related?

    • A.They share an edge and meet at a 60-degree angle
    • B.They share an edge and meet at a 120-degree angle
    • C.They lie parallel on opposite sides of the solid
    • D.They share an edge and meet at a 90-degree angle
    Show answerHide answer

    Correct answer: They share an edge and meet at a 60-degree angle

    Correct answer: They share an edge and meet at a 60-degree angle. In a triangular prism the three rectangles wrap around the triangle, so each rectangle borders the other two, and the angle between any two of them equals an interior angle of the equilateral triangle, 60 degrees. Treating the outer rectangles as parallel applies the cube rule that alternate squares are opposite, which fails here because the prism has only three side faces. The 90-degree angle is the cube habit, and 120 degrees is the exterior angle of the triangle rather than its interior angle.

  38. Aperture rules: the object may be turned any way before it enters, must then pass straight through without twisting, and the opening must exactly match its outside outline seen straight on from the top, front or end (or from the opposite side). A solid cube 4 cm on each edge has a solid cylinder 2 cm across and 3 cm long fixed to the center of one face, sticking straight out from it. Which opening can the object pass through?

    • A.A 4 cm square with a round-ended tab 3 cm wide and 2 cm long centered on one side
    • B.A 4 cm square with a round-ended tab 2 cm wide and 3 cm long centered on one side
    • C.A 4 cm square with a flat-ended tab 2 cm wide and 3 cm long centered on one side
    • D.A 4 cm square with a flat-ended tab 3 cm wide and 2 cm long centered on one side
    Show answerHide answer

    Correct answer: A 4 cm square with a flat-ended tab 2 cm wide and 3 cm long centered on one side

    Seen from the side, the cylinder shows as a rectangle as wide as its 2 cm diameter and as long as its 3 cm length, so the outline is the square with a flat-ended 2 by 3 cm tab. A cylinder only looks round when viewed along its axis, and from that direction it is hidden inside the 4 cm square, so a round-ended tab never appears. The 3 cm wide, 2 cm long tab swaps the diameter and the length.

  39. Third-angle layout: the top view sits above the front view, so the bottom edge of the top view is the object's front; the end view sits to the right of the front view, so its left edge is the object's front. A block is 6 units wide, 5 units deep and 4 units tall. Its top view is a 6 by 5 rectangle containing a solid 2 by 2 square whose sides are 2 and 4 units from the left edge and whose bottom side is 1 unit above the bottom edge. Its front view is a 6 by 4 rectangle with dashed vertical lines 2 and 4 units from the left, running from the top down to 1 unit above the base and joined there by a dashed line. Inside its plain 5 by 4 outline, which describes the end view?

    • A.Dashed lines 2 and 4 units from the left edge, from the top to 1 unit above the base, joined there
    • B.Dashed lines 1 and 3 units from the left edge, from the top to 1 unit above the base, joined there
    • C.Dashed lines 1 and 3 units from the left edge, running the full height, with nothing joining them
    • D.Dashed lines 2 and 4 units from the left edge, running the full height, with nothing joining them
    Show answerHide answer

    Correct answer: Dashed lines 1 and 3 units from the left edge, from the top to 1 unit above the base, joined there

    The views describe a pocket 2 units square cut 3 units down into the top, starting 1 unit behind the front, so in the end view its sides fall 1 and 3 units from the front (left) edge and stop at its floor 1 unit above the base, drawn dashed because they are inside the block. Lines at 2 and 4 units measure the depth from the back, or copy the front view's left-to-right positions into a view whose width is the object's depth. Full-height lines would mean a hole through the bottom, but the front view shows the pocket's floor.

  40. Views follow the standard layout: the top view sits above the front view, and the end view sits to the right of the front view and shows the object as seen from the right. Solid lines are visible edges and dashed lines are hidden edges. A block is 4 units wide, 3 units tall and 4 units deep. Its front view is a 4-by-3 rectangle with a solid horizontal line 1 unit above its base. Its top view is a 4-by-4 square with a solid horizontal line halfway between its top and bottom edges. Which describes the end view?

    • A.An L-shaped outline, 3 units tall on its left half and 1 unit tall on its right half
    • B.An L-shaped outline, 1 unit tall on its left half and 3 units tall on its right half
    • C.A 4-by-3 rectangle with a solid vertical line drawn halfway across the width of the view
    • D.A 4-by-3 rectangle with a solid horizontal line drawn 1 unit above the base of the view
    Show answerHide answer

    Correct answer: An L-shaped outline, 1 unit tall on its left half and 3 units tall on its right half

    The solid line at height 1 in the front view is the top of a low front half, and the top-view line marks where it steps up to the 3-unit back half. In the end view the front of the object lies on the left, next to the front view, so the profile is 1 unit tall on the left and 3 units tall on the right. Putting the tall half on the left reads the end view as if it were seen from the left side, and a plain rectangle with a line ignores that the step changes the outline itself.

  41. Views follow the standard layout: the top view sits above the front view, and the end view sits to the right of the front view and shows the object as seen from the right. Solid lines are visible edges and dashed lines are hidden edges. A flat slab is 4 units wide, 4 units deep and 1 unit tall. A 1-unit cube sits on top of the slab at its back-right corner. In the top view and in the end view, where does the small cube appear?

    • A.Top view: the bottom-right corner; end view: a raised bump at the left end
    • B.Top view: the bottom-right corner; end view: a raised bump at the right end
    • C.Top view: the top-right corner; end view: a raised bump at the right end
    • D.Top view: the top-right corner; end view: a raised bump at the left end
    Show answerHide answer

    Correct answer: Top view: the top-right corner; end view: a raised bump at the right end

    The top view is drawn above the front view, so its bottom edge is the object's front and its top edge is the back, which puts a back-right cube in the top-right corner. The end view is drawn to the right of the front view, so its left edge is the front and its right edge is the back, which puts the bump at the right end. The most tempting error treats the end view as if the front were on its right, which moves the bump to the left end even when the top view is read correctly.

  42. Each angle is formed by two arms whose directions are given as quadrant bearings (N 12° E means 12° east of due north), and each angle is the smaller opening between its arms. Angle P: arms at N 12° E and S 33° E, each 1 cm long. Angle Q: arms at N 47° W and N 86° E, each 4 cm long. Angle R: arms at S 10° W and N 34° W, each 2 cm long. Angle S: arms at N 4° W and S 42° W, each 3 cm long. Which ordering ranks the angles from smallest to largest?

    • A.R, P, S, Q
    • B.Q, S, R, P
    • C.Q, S, P, R
    • D.P, R, S, Q
    Show answerHide answer

    Correct answer: Q, S, P, R

    Arms on opposite sides of north (Q) add their offsets, 47 plus 86, giving 133°. Arms on the same side but split between north and south subtract both offsets from 180°: P is 180 minus 45, or 135°; R is 180 minus 44, or 136°; S is 180 minus 46, or 134°. That gives Q, S, P, R. Applying the add and subtract rules the wrong way round gives 45°, 47°, 44° and 46°, which reverses the order, and arm length never changes an angle's size.

  43. Four angles are described by how they relate to other angles. Angle A: the reflex angle on its outside measures 316°. Angle B: placed beside a 134° angle, it completes a straight line. Angle C: placed beside a 47° angle, it completes a right angle. Angle D: it is the smaller of the angles formed where two straight lines cross, and the larger one there is 135°. Which ordering ranks the angles from smallest to largest?

    • A.D, B, C, A
    • B.C, D, B, A
    • C.A, D, B, C
    • D.C, A, D, B
    Show answerHide answer

    Correct answer: C, A, D, B

    A full turn is 360°, so A is 360 minus 316, or 44°. A straight line is 180°, so B is 46° and D, the partner of 135° at a crossing, is 45°. A right angle is 90°, so C is 43°. That gives C, A, D, B. Subtracting 47 from 180 instead of 90 makes C 133° and pushes it last, and subtracting A's reflex angle from 180 instead of 360 makes A 136° and pushes it last.

  44. Each angle is formed by two arms from one vertex, and each arm is described by its tilt from the horizontal. Angle W: one arm points right, tilted 20° up, and the other points left, tilted 25° up. Angle X: both arms point right, one tilted 41° down and the other 5° up. Angle Y: both arms point left, one tilted 31° up and the other 76° up. Angle Z: one arm points left, tilted 48° down, and the other points right, tilted 4° up. Which ordering ranks the angles from smallest to largest?

    • A.X, Y, Z, W
    • B.Y, X, Z, W
    • C.Y, X, W, Z
    • D.X, Y, W, Z
    Show answerHide answer

    Correct answer: Y, X, W, Z

    When both arms point the same way, their tilts add if one is above and one below the horizontal and subtract if both are on the same side of it: X is 41 plus 5, or 46°, and Y is 76 minus 31, or 45°. W opens over the top, so it is 180 minus 20 minus 25, or 135°. Z's left arm drops below the horizontal while its right arm rises, so it is 180 minus 48 plus 4, or 136°. That gives Y, X, W, Z. Subtracting X's tilts gives 36°, and treating Z like W gives 128°, which produce the other three orderings.

  45. A protractor has two scales. The outer scale reads 0 at the right and increases counterclockwise to 180, and at any mark the inner scale reads 180 minus the outer value. For each angle, the vertex is at the protractor's center, one arm crosses the outer scale at the value given and the other arm crosses the inner scale at the value given. A: outer 20, inner 115. B: outer 30, inner 104. C: outer 100, inner 36. D: outer 12, inner 121. Which ordering ranks the angles from smallest to largest?

    • A.D, B, A, C
    • B.C, B, A, D
    • C.C, A, B, D
    • D.A, C, B, D
    Show answerHide answer

    Correct answer: C, A, B, D

    Convert each inner reading to the outer scale before subtracting: A's 115 is outer 65, so A is 45°; B's 104 is outer 76, so B is 46°; C's 36 is outer 144, so C is 44°; D's 121 is outer 59, so D is 47°. That gives C, A, B, D. Subtracting the two printed numbers directly gives 95°, 74°, 64° and 109°, and adding them gives the supplements 135°, 134°, 136° and 133°.

  46. Each angle starts with both arms pointing due east. One arm is then turned counterclockwise by the amount given, and the angle is the smaller opening between the two arms. A: turned 224°, arms 5 cm long. B: turned 135°, arms 2 cm long. C: turned 227°, arms 4 cm long. D: turned 134°, arms 1 cm long. Which ordering ranks the angles from smallest to largest?

    • A.D, B, C, A
    • B.A, C, D, B
    • C.D, B, A, C
    • D.C, D, B, A
    Show answerHide answer

    Correct answer: C, D, B, A

    A turn past 180° leaves a smaller opening of 360 minus the turn, so A is 136° and C is 133°, while B and D stay at 135° and 134°. That gives C, D, B, A. Ranking by the size of the turn puts C last instead of first, and subtracting 180 from the large turns makes A and C acute at 44° and 47°. Arm length has no effect on angle size.

  47. Four angles must be ranked from smallest to largest, where each angle is the smaller opening between its two arms. Angle P has arms pointing along compass bearings 352° and 38°, and each arm is 6 cm long. Angle Q is formed by the hour hand and the minute hand of an accurate clock at 4:30, and each arm is 1 cm long. Angle R is an angle whose larger, reflex opening measures 316°, and each arm is 4 cm long. Angle S forms a straight line together with an adjacent 133° angle, and each arm is 2 cm long. Which ordering ranks the angles from smallest to largest?

    • A.P, R, Q, S
    • B.R, Q, P, S
    • C.R, P, S, Q
    • D.Q, S, R, P
    Show answerHide answer

    Correct answer: R, Q, P, S

    R is 360° minus 316°, or 44°; Q is 45°, because at 4:30 the hour hand has moved halfway from the 4 to the 5 (135° from 12) while the minute hand is on the 6 (180°); P is 8° plus 38°, or 46°, measured across north; and S is 180° minus 133°, or 47°. That gives R, Q, P, S. Placing the hour hand exactly on the 4 makes Q 60° and pushes it to the end, and arm length plays no part in an angle's size.

  48. A square sheet is ruled into a 4-by-4 grid of cells, with rows 1 to 4 running top to bottom and columns 1 to 4 left to right. Column 1 is folded over onto column 2 along the line between them, and then row 4 is folded up onto row 3 along the line between them. Holes are punched through every layer at three cells of the folded sheet: row 3 column 2, row 2 column 2, and row 1 column 4. How many holes are in the sheet once it is fully unfolded?

    • A.5
    • B.6
    • C.4
    • D.7
    Show answerHide answer

    Correct answer: 7

    The folds are off-center, so layer counts differ by cell. Row 3 column 2 has both flaps on it (column 1 and row 4), so it holds four layers and gives holes at rows 3 and 4 of columns 1 and 2; row 2 column 2 has only the column-1 flap, giving two holes; row 1 column 4 is a single layer, giving one hole, for seven in all. Answering six treats the folded sheet as a uniform two layers everywhere, which ignores that the flaps cover only some cells.

  49. A square sheet is folded in half by laying its right half over its left half, then folded in half again by laying its top half down over its bottom half, leaving a small square in the sheet's original bottom-left quarter. A round punch is centered exactly on the small square's top-right corner, the one point where both folded edges meet, and it cuts through every layer. What does the sheet show once it is fully unfolded?

    • A.One round hole at the center of the sheet
    • B.A quarter-round notch cut from every corner
    • C.Four round holes set evenly around the center
    • D.Two round holes on the vertical center line
    Show answerHide answer

    Correct answer: One round hole at the center of the sheet

    The small square's top-right corner lies on both creases at once, and when the sheet is opened it is the sheet's center. The punch cuts a quarter circle from each of the four layers there, and the four quarters open out into one full round hole at the center. Four separate holes around the center would need a punch clear of both creases; notches at the corners come from punching the small square's free bottom-left corner, where the sheet's four original corners lie.

  50. Seventeen identical cubes are cemented together on a table. The footprint has a back, a middle and a front row, each with four positions numbered 1 to 4 from left to right. Layer 1, resting on the table, fills every position except back position 4. Layer 2 holds five cubes in a plus shape, on back 2, middle 1, middle 2, middle 3 and front 2. Layer 3 is a single cube on middle 2. Every exposed face of the figure is painted, including the back and the sides, except the bottom faces resting on the table. How many cubes have exactly four painted faces?

    • A.Five
    • B.Nine
    • C.Three
    • D.Four
    Show answerHide answer

    Correct answer: Four

    Each of the four layer 2 cubes forming the arms of the plus has its top and three sides exposed, with only the side touching the center tower and its bottom covered, so each has four painted faces. The layer 3 cube on top has five painted faces, its top and all four sides, so it does not belong in this count. Three misses the back arm hidden behind the tower, and nine comes from painting the bottoms of the corner cubes on the table.

  51. A flat pattern of six equal squares folds into a cube. The top row holds squares 1, 2 and 3 from left to right. The bottom row holds squares 4, 5 and 6 from left to right, placed so that square 4 sits directly below square 3. After folding, which list gives all three pairs of opposite faces?

    • A.1 and 5, 2 and 4, 3 and 6
    • B.1 and 6, 2 and 4, 3 and 5
    • C.1 and 4, 2 and 6, 3 and 5
    • D.1 and 3, 2 and 5, 4 and 6
    Show answerHide answer

    Correct answer: 1 and 3, 2 and 5, 4 and 6

    Two squares in a straight line with one square between them always end up opposite, so 1 and 3 form a pair and 4 and 6 form a pair. That leaves 2 and 5 as the last pair, so the answer is 1 and 3, 2 and 5, 4 and 6. The lists that pair 2 with 4 are tempting because the two squares look diagonally apart, but square 4 is already opposite square 6.

  52. A flat pattern for a cube has a horizontal row of four squares, labeled A, B, C and D from left to right. Square E is attached to the top edge of square B, and square F is attached to the bottom edge of square D. When the pattern is folded into a cube, which edge does the top edge of square D meet?

    • A.The bottom edge of square F
    • B.The top edge of square E
    • C.The right edge of square E
    • D.The left edge of square E
    Show answerHide answer

    Correct answer: The top edge of square E

    The row of four rolls into a ring of side faces, and E folds over as a lid on top of B. The edge of E farthest from B lies along the face opposite B, which is D, so the top edge of D meets the top edge of square E. The right edge of square E is the tempting choice, but that edge meets the top of C, the square beside B, not D.

  53. A cube pattern has a top row of three squares, labeled 1, 2 and 3 from left to right. A column of three squares hangs from the bottom edge of square 2, labeled 4, 5 and 6 from top to bottom. The lower-left corner of square 6 is shaded. After folding, the shaded corner is shared by square 6 and which two other squares?

    • A.Squares 1 and 2
    • B.Squares 1 and 5
    • C.Squares 3 and 5
    • D.Squares 2 and 3
    Show answerHide answer

    Correct answer: Squares 1 and 2

    Squares 2, 4, 5 and 6 roll into a ring, so the free bottom edge of square 6 closes against the top edge of square 2, and squares 1 and 3 become the left and right caps. The lower-left corner of square 6 sits on its bottom edge (touching 2) and its left edge (touching 1), so it is shared with squares 1 and 2. Squares 1 and 5 would be right for the upper-left corner, which is where a candidate lands who forgets that the bottom of 6 wraps back to square 2.

  54. A pattern for a square pyramid starts with square base PQRS, whose corners are labeled in order around the square. Identical isosceles triangles are attached by their bases to sides PQ, QR and RS. A fourth identical triangle is then attached along the edge named, by its base if on the square and by a slanted edge if on a triangle. Which attachment does NOT let the pattern fold into a closed square pyramid?

    • A.Along the slanted edge of the PQ triangle that runs from corner P
    • B.Along the slanted edge of the QR triangle that runs from corner R
    • C.Along the open side SP of the square, the edge that runs to corner P
    • D.Along the slanted edge of the RS triangle that runs from corner S
    Show answerHide answer

    Correct answer: Along the slanted edge of the QR triangle that runs from corner R

    The missing face is the one over side SP, and it must meet the base along SP and meet its neighbors along the slanted edges rising from P and S. Attaching along the slanted edge of the QR triangle that runs from corner R places the fourth triangle on the face over RS, which is already filled, so it overlaps and SP stays open. The slanted edges from P and from S are both edges of the missing face, so triangles hung there fold neatly into place.

  55. A pattern for a hexagonal prism has six identical rectangles joined side by side in a row, labeled A to F from left to right. A regular hexagon is attached to the top edge of rectangle A, and a second regular hexagon is attached to the bottom edge of rectangle D. After folding, the edge of the top hexagon that is parallel to its attached edge meets the top edge of which rectangle?

    • A.Rectangle F
    • B.Rectangle C
    • C.Rectangle D
    • D.Rectangle E
    Show answerHide answer

    Correct answer: Rectangle D

    Going around the top hexagon, its six edges meet the tops of rectangles A, B, C, D, E and F in order, so the edge parallel to A's edge is three steps away and meets rectangle D. The hexagon on the bottom of D does not block this, because it covers D's bottom edge, not its top. Rectangle F is tempting because it sits at the far end of the row, but once the row closes into a ring F is next to A.

  56. Four identical equilateral triangles are joined edge to edge in a straight strip, labeled 1 to 4 from left to right. Triangles 1 and 3 point up with a horizontal bottom edge, and triangles 2 and 4 point down with a horizontal top edge. The strip folds into a regular tetrahedron. Which edge does the horizontal edge of triangle 1 meet?

    • A.The horizontal edge of triangle 2
    • B.The horizontal edge of triangle 3
    • C.The horizontal edge of triangle 4
    • D.The free slanted edge of triangle 4
    Show answerHide answer

    Correct answer: The horizontal edge of triangle 3

    In a regular tetrahedron triangle 1 must meet triangle 3, and the only free edge of triangle 3 is its horizontal bottom edge, so the horizontal edge of triangle 1 meets the horizontal edge of triangle 3. The free slanted edge of triangle 4 is the tempting wrap-around answer, but it closes against the left slanted edge of triangle 1. The horizontal edges of triangles 2 and 4 meet each other.

  57. A flat pattern has seven pieces: three squares, three pentagons that are squares with one corner clipped off, and one small equilateral triangle whose sides match the clipped edges. It folds into a cube with one corner sliced off. How many edges and vertices does the folded solid have?

    • A.15 edges and 11 vertices
    • B.15 edges and 10 vertices
    • C.12 edges and 7 vertices
    • D.12 edges and 11 vertices
    Show answerHide answer

    Correct answer: 15 edges and 10 vertices

    The cut removes one of the cube's 8 corners and creates 3 new ones, giving 10 vertices, and it adds the triangle's 3 edges to the cube's 12, giving 15 edges. The check is Euler's rule, faces minus edges plus vertices equals 2: 7 minus 15 plus 10 is 2. The answer of 15 edges and 11 vertices forgets that the original corner is gone, and 12 edges and 7 vertices forgets the new edges and corners the cut creates.

Biology (36)

  1. In mammalian cells, which component is primarily responsible for the detoxification of drugs and poisons?

    • A.Golgi apparatus compartments
    • B.Mitochondrial inner membrane
    • C.Lysosomal digestive vesicles
    • D.Smooth endoplasmic reticulum
    Show answerHide answer

    Correct answer: Smooth endoplasmic reticulum

    The smooth endoplasmic reticulum carries the cytochrome P450 enzyme systems that oxidize drugs and lipophilic poisons into more water-soluble products for excretion, and it proliferates in hepatocytes on repeated exposure. Lysosomal digestive vesicles hydrolyze macromolecules and worn organelles at acid pH. Golgi apparatus compartments modify and sort proteins for delivery. Mitochondrial inner membrane houses the electron transport chain for ATP production; none of the three performs drug oxidation.

  2. During which phase of the cell cycle does DNA replication occur?

    • A.The S phase of each cycle
    • B.The M phase of this cycle
    • C.The G1 phase of the cycle
    • D.The G2 phase of one cycle
    Show answerHide answer

    Correct answer: The S phase of each cycle

    Chromosomal DNA is copied during the S phase of each cycle, the synthesis interval of interphase, so that each daughter cell receives a complete set. The G1 phase of the cycle is the growth interval that precedes copying. The G2 phase of one cycle is when the cell checks the copied DNA and prepares the machinery for division. The M phase of this cycle is when the duplicated chromosomes are separated, not when they are duplicated.

  3. Which of the following enzymes is responsible for unwinding the DNA double helix during replication?

    • A.Double-stranded DNA ligase
    • B.Bidirectional DNA helicase
    • C.Replicative DNA polymerase
    • D.Circular DNA topoisomerase
    Show answerHide answer

    Correct answer: Bidirectional DNA helicase

    A bidirectional DNA helicase is the enzyme that separates the two strands of the double helix at the fork, using ATP to break the hydrogen bonds between paired bases. Replicative DNA polymerase extends a primed strand but cannot open duplex DNA on its own. Double-stranded DNA ligase seals the phosphodiester backbone between adjacent fragments. Circular DNA topoisomerase relieves the torsional strain that builds ahead of the fork by cutting and rejoining strands, which is not the same as separating them.

  4. What role do microtubules play during mitosis?

    • A.Contractile ring constriction with myosin
    • B.Chromatin condensation into compact coils
    • C.Nuclear envelope reformation at telophase
    • D.Chromosome movement toward opposite poles
    Show answerHide answer

    Correct answer: Chromosome movement toward opposite poles

    Microtubules build the mitotic spindle, attach at the kinetochores, and produce chromosome movement toward opposite poles as the fibers shorten. Chromatin condensation into compact coils is driven by condensin complexes rather than by spindle fibers. Nuclear envelope reformation at telophase is carried out by lamins and membrane vesicles. Contractile ring constriction with myosin is an actomyosin event of cytokinesis and does not depend on microtubules.

  5. Which of the following processes is an example of a catabolic reaction?

    • A.Glycolysis inside the cytoplasm
    • B.Gluconeogenesis within the cell
    • C.Glycogenesis across the myocyte
    • D.Lipogenesis inside fatty tissue
    Show answerHide answer

    Correct answer: Glycolysis inside the cytoplasm

    Glycolysis inside the cytoplasm breaks glucose down to pyruvate and releases energy captured as ATP and NADH, which is what defines a catabolic reaction. Gluconeogenesis within the cell builds glucose from smaller precursors and consumes energy. Glycogenesis across the myocyte assembles glucose units into stored glycogen. Lipogenesis inside fatty tissue assembles fatty acids and triglycerides; all three are anabolic syntheses that cost energy rather than release it.

  6. In the context of membrane transport, what is the primary function of a uniporter?

    • A.Pulls two solutes along matched routes
    • B.Transfers one solute down its gradient
    • C.Drives one solute against its gradient
    • D.Swaps two solutes along reverse routes
    Show answerHide answer

    Correct answer: Transfers one solute down its gradient

    A uniporter transfers one solute down its gradient, carrying a single species in the direction its own electrochemical gradient favors, so no metabolic energy is spent and the process is facilitated diffusion. Swaps two solutes along reverse routes describes an antiporter. Pulls two solutes along matched routes describes a symporter. Drives one solute against its gradient describes a primary active transporter, which must consume ATP to work.

  7. Which of the following molecules acts as a second messenger in signal transduction pathways?

    • A.Serine-specific protein kinase
    • B.Transmembrane adenylyl cyclase
    • C.Cyclic adenosine monophosphate
    • D.Bloodborne epinephrine hormone
    Show answerHide answer

    Correct answer: Cyclic adenosine monophosphate

    Cyclic adenosine monophosphate is the classical second messenger: it is generated inside the cell once a first messenger binds its receptor, and it relays that signal to intracellular targets. Transmembrane adenylyl cyclase is the enzyme that produces it and is not itself the message. Bloodborne epinephrine hormone is a first messenger that acts at the cell surface and never enters the cytosol. Serine-specific protein kinase is the downstream effector that the messenger switches on.

  8. In the lac operon model of gene regulation in E. coli, what triggers the expression of lactose-metabolizing enzymes?

    • A.Lactose removes the repressor from the operator
    • B.Tryptophan activates the promoter of the operon
    • C.The repressor protein fastens onto the promoter
    • D.Glucose raises the repressor count inside cells
    Show answerHide answer

    Correct answer: Lactose removes the repressor from the operator

    Lactose removes the repressor from the operator: converted to allolactose, it binds the repressor and changes its shape so the protein releases the operator, letting RNA polymerase transcribe the structural genes. Glucose raises the repressor count inside cells is false, since glucose acts through catabolite repression and lowers cyclic AMP rather than making more repressor. Tryptophan activates the promoter of the operon belongs to a separate operon and has no role here. The repressor protein fastens onto the promoter misplaces it, because the repressor binds the operator.

  9. Which of the following best describes the role of antioxidants in cellular processes?

    • A.Peptide synthesis inside the ribosomes
    • B.Electron donation to unstable radicals
    • C.Oxygen transport across cell membranes
    • D.Phosphate transfer to adenosine groups
    Show answerHide answer

    Correct answer: Electron donation to unstable radicals

    Antioxidants work by electron donation to unstable radicals, quenching the radical without themselves becoming reactive, which is how they prevent oxidative injury to lipids, proteins and DNA. Oxygen transport across cell membranes is the carrier function of hemoglobin and myoglobin. Phosphate transfer to adenosine groups describes the kinase reactions of energy metabolism. Peptide synthesis inside the ribosomes is translation; none of the three quenches a radical.

  10. In the human body, which type of cell is primarily involved in the process of antibody production?

    • A.T lymphocytes of each cortical lobule
    • B.Natural killer cells of the periphery
    • C.B lymphocytes of each germinal center
    • D.Dendritic cells of each cortical zone
    Show answerHide answer

    Correct answer: B lymphocytes of each germinal center

    B lymphocytes of each germinal center recognize antigen, undergo affinity maturation and differentiate into plasma cells that secrete antibody. T lymphocytes of each cortical lobule help and regulate that response and kill infected cells, but they secrete no immunoglobulin. Natural killer cells of the periphery lyse targets without antigen-specific receptors. Dendritic cells of each cortical zone present antigen to lymphocytes; all three shape the response without producing antibody.

  11. Which cellular structure is primarily responsible for the synthesis of proteins destined for secretion?

    • A.Golgi apparatus cis-face compartment
    • B.Nucleolar fibrillar center component
    • C.Smooth endoplasmic reticulum network
    • D.Rough endoplasmic reticulum cisterna
    Show answerHide answer

    Correct answer: Rough endoplasmic reticulum cisterna

    Ribosomes studding the rough endoplasmic reticulum cisterna translate their proteins directly into its lumen, which is the entry point of the secretory pathway. Smooth endoplasmic reticulum network handles lipid synthesis, calcium storage and detoxification and carries no ribosomes. Golgi apparatus cis-face compartment receives, modifies and sorts proteins that have already been made. Nucleolar fibrillar center component is where ribosomal RNA is transcribed and ribosomal subunits are assembled.

  12. In the context of gene expression, what is the role of a promoter?

    • A.Binding platform for RNA polymerase
    • B.Starting signal for DNA replication
    • C.Release trigger for RNA transcripts
    • D.Attachment signal for poly(A) tails
    Show answerHide answer

    Correct answer: Binding platform for RNA polymerase

    Correct answer: Binding platform for RNA polymerase. Explanation: A promoter is the stretch of DNA just upstream of a gene where RNA polymerase and its general transcription factors dock, which is how transcription is started at the right place on the right gene. A starting signal for DNA replication describes an origin of replication, a site used by the replication machinery rather than by RNA polymerase. A release trigger for RNA transcripts describes a terminator, which acts at the far end of a gene once the transcript is already finished. An attachment signal for poly(A) tails is the polyadenylation site, a processing instruction read after the transcript exists.

  13. What is the main function of the enzyme telomerase?

    • A.Seals the small breaks between fragments
    • B.Adds repeated units onto chromosome ends
    • C.Splits the paired strands before copying
    • D.Trims the introns from young transcripts
    Show answerHide answer

    Correct answer: Adds repeated units onto chromosome ends

    Correct answer: Adds repeated units onto chromosome ends. Explanation: Telomerase carries its own short RNA template and uses it to add repeated DNA sequence to the telomeres at the ends of chromosomes, offsetting the loss that occurs each round of replication. Sealing the small breaks between fragments is the work of DNA ligase, which joins Okazaki fragments on the lagging strand. Splitting the paired strands before copying is done by helicase at the replication fork. Trimming the introns from young transcripts is spliceosome activity on pre-mRNA and never touches chromosome ends.

  14. Which of the following best describes the function of microRNAs (miRNAs) in gene regulation?

    • A.Transfers amino acids toward working ribosomes
    • B.Assembles catalytic cores inside new ribosomes
    • C.Sends matching messages toward rapid breakdown
    • D.Governs intron removal inside the spliceosomes
    Show answerHide answer

    Correct answer: Sends matching messages toward rapid breakdown

    Correct answer: Sends matching messages toward rapid breakdown. Explanation: A microRNA is a short non-coding RNA that base-pairs with complementary sequence in a target messenger RNA and, through the RISC complex, marks that message for degradation or blocks its translation, so less protein is made from it. Transferring amino acids toward working ribosomes describes transfer RNA. Assembling catalytic cores inside new ribosomes describes ribosomal RNA, which builds the peptidyl transferase site. Governing intron removal inside the spliceosomes describes the small nuclear RNAs. Each of those is a genuine RNA job, but none of them belongs to a microRNA.

  15. During which process do sister chromatids separate to opposite poles of the cell?

    • A.Prophase
    • B.Metaphase
    • C.Telophase
    • D.Anaphase
    Show answerHide answer

    Correct answer: Anaphase

    Correct answer: Anaphase. Explanation: Sister chromatids stay joined at the centromere until the spindle checkpoint is satisfied; cohesin is then cleaved and the chromatids are drawn to opposite poles, and that stage is anaphase. Prophase is when chromosomes condense and the spindle starts to form, before anything separates. Metaphase is when the chromosomes are aligned on the equator, still joined together. Telophase comes after the separation, when nuclear envelopes reform around the two separated sets.

  16. What is the primary role of the sodium-potassium pump in neuronal cells?

    • A.Keeps the resting membrane potential steady
    • B.Springs open quickly during neural impulses
    • C.Breaks apart transmitter inside the synapse
    • D.Discharges vesicles into the synaptic cleft
    Show answerHide answer

    Correct answer: Keeps the resting membrane potential steady

    Correct answer: Keeps the resting membrane potential steady. Explanation: The sodium-potassium pump exports three sodium ions and imports two potassium ions per cycle at the cost of one ATP, holding the ion gradients that set the negative resting potential of the neuron. Springing open quickly during neural impulses describes voltage-gated ion channels, which are separate proteins that react to depolarization. Breaking apart transmitter inside the synapse describes degrading enzymes such as acetylcholinesterase. Discharging vesicles into the synaptic cleft is exocytosis performed by the vesicle fusion machinery, not by the pump.

  17. Which of the following is a characteristic feature of apoptosis?

    • A.The cell swells before its membrane ruptures
    • B.The cell shrinks and its chromatin condenses
    • C.The cell spills enzymes and inflames tissues
    • D.The chromosome's DNA breaks at random points
    Show answerHide answer

    Correct answer: The cell shrinks and its chromatin condenses

    Correct answer: The cell shrinks and its chromatin condenses. Explanation: Apoptosis is an orderly, energy-requiring death in which the cell shrinks, chromatin clumps against the nuclear membrane, DNA is cut cleanly between nucleosomes, and the remains are sealed into membrane-bound fragments that neighboring cells clear quietly. The cell swelling before its membrane ruptures is necrosis, the opposite of the shrinkage seen here. The cell spilling enzymes and inflaming tissues is also necrosis, because apoptosis keeps the contents enclosed so that no inflammation follows. The chromosome's DNA breaking at random points produces the smear characteristic of necrosis, whereas apoptotic cleavage is regular and internucleosomal.

  18. In the Calvin cycle of photosynthesis, what molecule acts as the initial carbon acceptor?

    • A.Fructose bisphosphate
    • B.Sedoheptulose bisphosphate
    • C.Ribulose bisphosphate
    • D.Erythrose phosphate
    Show answerHide answer

    Correct answer: Ribulose bisphosphate

    Correct answer: Ribulose bisphosphate. Explanation: In the Calvin cycle the enzyme RuBisCO attaches incoming carbon dioxide to ribulose bisphosphate, the five-carbon acceptor, and the unstable six-carbon product splits at once into two molecules of 3-phosphoglycerate. Fructose bisphosphate and sedoheptulose bisphosphate are real intermediates of the cycle, but they belong to the later regeneration phase that rebuilds the acceptor. Erythrose phosphate is likewise a regeneration-phase sugar. None of the three ever receives the incoming carbon dioxide.

  19. What is the primary function of chaperone proteins in the cell?

    • A.Nucleotide excision
    • B.Vesicle trafficking
    • C.Lysosomal digestion
    • D.Polypeptide folding
    Show answerHide answer

    Correct answer: Polypeptide folding

    Correct answer: Polypeptide folding. Explanation: Chaperones bind the exposed hydrophobic patches of newly made or heat-stressed chains and give them a protected setting in which to reach their native three-dimensional shape, and they can also refold or hand off chains that have gone wrong. Nucleotide excision is a DNA repair pathway carried out by repair enzymes. Vesicle trafficking depends on coat proteins, motor proteins and SNAREs. Lysosomal digestion is performed by acid hydrolases inside the lysosome.

  20. In eukaryotic cells, where does the Krebs cycle (Citric Acid Cycle) occur?

    • A.Mitochondrial matrix
    • B.Cytoplasmic interior
    • C.Chloroplast envelope
    • D.Peroxisomal interior
    Show answerHide answer

    Correct answer: Mitochondrial matrix

    Correct answer: Mitochondrial matrix. Explanation: In eukaryotic cells the citric acid cycle enzymes sit in the fluid matrix enclosed by the inner mitochondrial membrane, and that is where acetyl-CoA is oxidized to carbon dioxide while NADH and FADH2 are generated for the electron transport chain. The cytoplasmic interior is where glycolysis runs, upstream of the cycle. The chloroplast envelope belongs to a plant organelle devoted to photosynthesis. The peroxisomal interior handles fatty-acid oxidation and the breakdown of hydrogen peroxide.

  21. Which type of bond is primarily responsible for the secondary structure of proteins?

    • A.Covalent bonds
    • B.Hydrogen bonds
    • C.Cysteine links
    • D.Ionic contacts
    Show answerHide answer

    Correct answer: Hydrogen bonds

    Correct answer: Hydrogen bonds. Explanation: Alpha helices and beta pleated sheets are held in shape by hydrogen bonds between the carbonyl oxygen of one backbone unit and the amide hydrogen of another, which is why secondary structure is a property of the backbone rather than the side chains. Covalent bonds link the amino acids into the chain itself, and that is primary structure. Cysteine links are disulfide bridges that stabilize tertiary and quaternary structure. Ionic contacts between charged side chains also act at the tertiary level.

  22. In genetics, what is the significance of Mendel's law of independent assortment?

    • A.Paired alleles part as the gametes are formed
    • B.Linked genes on one chromosome travel in step
    • C.Genes for two traits are passed on separately
    • D.One allele hides the effect of another allele
    Show answerHide answer

    Correct answer: Genes for two traits are passed on separately

    Correct answer: Genes for two traits are passed on separately. Explanation: Independent assortment states that the alleles of one gene enter a gamete without regard to the alleles of another gene, because homologous pairs line up at the metaphase plate in random orientations, and this is a large source of genetic variation. Paired alleles parting as the gametes are formed is the law of segregation, Mendel's other rule. Linked genes on one chromosome travelling in step is the exception to independent assortment rather than a statement of it. One allele hiding the effect of another allele is dominance, which concerns a single gene.

  23. Which enzyme is responsible for relieving the supercoiling tension in DNA ahead of the replication fork?

    • A.Endonuclease
    • B.Recombinase
    • C.Telomerase
    • D.Topoisomerase
    Show answerHide answer

    Correct answer: Topoisomerase

    Correct answer: Topoisomerase. Explanation: As the replication fork opens the helix ahead of it becomes overwound, and topoisomerase relieves that torsional strain by cutting one or both strands, allowing rotation, and then resealing the break. Endonuclease cuts within a strand during repair and restriction, but it neither reseals the cut nor manages supercoiling. Recombinase exchanges segments between DNA molecules. Telomerase extends the repeats at chromosome ends and takes no part at the fork.

  24. In a eukaryotic cell, which organelle is primarily involved in the synthesis and processing of lipids and steroids?

    • A.Smooth endoplasmic reticulum
    • B.Lysosomal hydrolase vesicles
    • C.Peroxisomal oxidase granules
    • D.Vacuolar storage compartment
    Show answerHide answer

    Correct answer: Smooth endoplasmic reticulum

    Correct answer: Smooth endoplasmic reticulum. Explanation: The smooth endoplasmic reticulum carries no ribosomes on its surface and holds the enzymes for phospholipid and steroid synthesis, along with drug detoxification and calcium ion storage. Lysosomal hydrolase vesicles break macromolecules down rather than build lipids. Peroxisomal oxidase granules oxidize very long chain fatty acids and dispose of hydrogen peroxide. The vacuolar storage compartment holds water, ions and waste, mainly in plant cells.

  25. What is the primary outcome of meiosis I in germ cells?

    • A.Four haploid cells with single chromatids
    • B.Two haploid cells with doubled chromatids
    • C.Two diploid cells with paired chromosomes
    • D.Four diploid cells with copied chromatids
    Show answerHide answer

    Correct answer: Two haploid cells with doubled chromatids

    Correct answer: Two haploid cells with doubled chromatids. Explanation: Meiosis I separates the homologous chromosomes, so the chromosome number is halved and two cells result, and each chromosome in those cells still consists of two sister chromatids that meiosis II will later pull apart. Four haploid cells with single chromatids is the product of the whole of meiosis, after the second division. Two diploid cells with paired chromosomes is what mitosis produces. Four diploid cells with copied chromatids describes no real division, since nothing in meiosis yields four cells that are still diploid.

  26. Which molecule serves as the final electron acceptor in the electron transport chain of aerobic respiration?

    • A.Elemental sulfur
    • B.Carbonate anions
    • C.Molecular oxygen
    • D.Gaseous nitrogen
    Show answerHide answer

    Correct answer: Molecular oxygen

    Correct answer: Molecular oxygen. Explanation: In aerobic respiration complex IV passes electrons from the transport chain to oxygen, which takes up protons to form water, and without that terminal acceptor the chain backs up and ATP synthesis stops. Elemental sulfur and carbonate anions are terminal acceptors for certain anaerobes, not for cells respiring with air. Gaseous nitrogen is not reduced by the respiratory chain at all; the nitrogen species some bacteria use anaerobically is nitrate.

  27. In the Hardy-Weinberg principle, which condition is NOT required for a population to be in genetic equilibrium?

    • A.Random pairing within the overall population
    • B.Complete absence of migration between groups
    • C.Sufficiently large numbers of breeding pairs
    • D.Unequal survival among the various genotypes
    Show answerHide answer

    Correct answer: Unequal survival among the various genotypes

    Correct answer: Unequal survival among the various genotypes. Explanation: Hardy-Weinberg equilibrium assumes that no natural selection is acting, so unequal survival among genotypes is exactly the condition the model excludes rather than requires. Random pairing within the overall population is required, because assortative mating shifts genotype frequencies. Complete absence of migration between groups is required, because gene flow imports alleles from elsewhere. Sufficiently large numbers of breeding pairs is required so that genetic drift does not move allele frequencies by chance.

  28. What type of cell signaling involves a cell targeting itself with signal molecules?

    • A.Autocrine stimulation
    • B.Endocrine circulation
    • C.Paracrine propagation
    • D.Juxtacrine attachment
    Show answerHide answer

    Correct answer: Autocrine stimulation

    Correct answer: Autocrine stimulation. Explanation: A cell using autocrine stimulation releases a messenger and then binds that same messenger with its own surface receptors, so it is both the source and the target; the pattern is common in immune cells and in tumors. Endocrine circulation carries hormones through the bloodstream to distant tissues. Paracrine propagation acts on neighboring cells a short distance away. Juxtacrine attachment needs direct contact between two different cells, with the signal held on one membrane.

  29. A biochemistry student measures the rate of an enzyme-catalyzed reaction at increasing substrate concentrations, both with and without a small molecule that binds reversibly to the enzyme's active site. In the presence of this molecule, the apparent Km increases but the Vmax is unchanged. What type of inhibition is occurring?

    • A.Classical competitive inhibition
    • B.Simple noncompetitive inhibition
    • C.Partial uncompetitive inhibition
    • D.Covalent irreversible inhibition
    Show answerHide answer

    Correct answer: Classical competitive inhibition

    The molecule competes for the active site itself, so more substrate is needed to reach half-maximal velocity and the apparent Km rises, while a large enough substrate excess still saturates the enzyme and leaves Vmax untouched; that pairing is the classical competitive pattern. A noncompetitive inhibitor binds away from the active site and lowers Vmax while leaving Km unchanged. An uncompetitive inhibitor binds only the enzyme-substrate complex and lowers Km and Vmax together. A covalent irreversible inhibitor removes enzyme molecules from the pool for good, which lowers Vmax rather than raising Km.

  30. Carl Woese's three-domain system reorganized the classification of cellular life based largely on small-subunit ribosomal RNA sequence comparisons. According to this system, which two domains share a more recent common ancestor with each other than either does with the third?

    • A.Bacteria and Archaea
    • B.Archaea and Eukarya
    • C.Monera and Protista
    • D.Bacteria and Eukarya
    Show answerHide answer

    Correct answer: Archaea and Eukarya

    Comparisons of small-subunit ribosomal RNA place Archaea and Eukarya on a shared branch, so those two share a more recent common ancestor than either shares with Bacteria. Pairing Bacteria with Archaea restores the older prokaryote grouping that this very analysis overturned, and pairing Bacteria with Eukarya conflicts with the ribosomal RNA trees Woese published. Monera and Protista are kingdoms from an earlier classification rather than domains, so they are not candidates within the three-domain system.

  31. After a person eats a carbohydrate-rich meal, blood glucose rises sharply. Which pancreatic hormone is secreted in response, and what is its primary effect on target tissues?

    • A.Glucagon, freeing stored sugar from the liver
    • B.Epinephrine, releasing sugar out of the liver
    • C.Insulin, driving blood glucose into the cells
    • D.Cortisol, pushing the tissues to burn glucose
    Show answerHide answer

    Correct answer: Insulin, driving blood glucose into the cells

    Rising blood glucose after a meal makes the pancreatic beta cells release insulin, which drives glucose into muscle and fat cells and stores it in the liver as glycogen, bringing blood glucose back toward its set point. Glucagon comes from the alpha cells when glucose is low and frees stored sugar from the liver, the opposite of what a carbohydrate meal calls for. Cortisol does not push tissues to burn glucose; it raises blood glucose through gluconeogenesis. Epinephrine also releases liver sugar, and it is an adrenal rather than a pancreatic hormone.

  32. Which of the following is NOT a characteristic of organisms in kingdom Fungi?

    • A.Nuclei bounded by a nuclear membrane
    • B.Cell walls made largely of cellulose
    • C.Glycogen stored as the reserve sugar
    • D.Digestion that starts outside a cell
    Show answerHide answer

    Correct answer: Cell walls made largely of cellulose

    Correct answer: Cell walls made largely of cellulose. True fungi build their walls from chitin and glucans; cellulose walls belong to plants and to fungus-like protists such as water molds. Glycogen looks like the odd one out to many students who expect plant-like starch, but fungi store carbohydrate as glycogen, as animals do. Fungi also secrete enzymes and digest food outside the cell before absorbing it, and as eukaryotes they have membrane-bound nuclei.

  33. A recessive disorder affects 1 in every 2,500 newborns in a population assumed to be in Hardy-Weinberg equilibrium. About what percentage of the population are unaffected carriers?

    • A.3.92%
    • B.0.08%
    • C.0.04%
    • D.2.00%
    Show answerHide answer

    Correct answer: 3.92%

    Correct answer: 3.92%. Affected newborns give q squared = 1/2,500 = 0.0004, so q = 0.02 and p = 0.98, and the carrier frequency is 2pq = 2(0.98)(0.02) = 0.0392, or 3.92%. Stopping at q gives 2.00%, which is the frequency of the recessive allele, not of carriers. Using 0.0004 as q without taking the square root gives about 0.08%, and 0.04% is the frequency of affected individuals.

  34. An isolated population of 40,000 people is in Hardy-Weinberg equilibrium for an autosomal recessive condition, and 16 people have the condition. About how many people in the population are heterozygous carriers?

    • A.1,584 carriers
    • B.1,568 carriers
    • C.800 carriers
    • D.1,600 carriers
    Show answerHide answer

    Correct answer: 1,568 carriers

    Here q squared = 16/40,000 = 0.0004, so q = 0.02 and p = 0.98, giving a carrier frequency of 2pq = 2(0.98)(0.02) = 0.0392, and 0.0392 x 40,000 = 1,568 carriers. The tempting 1,600 carriers comes from using 2q and rounding p to 1, which overstates the count; 1,584 wrongly adds the 16 affected homozygotes, who are not carriers, and 800 uses the allele frequency q as if it were the carrier frequency.

  35. During a hard sprint, the working leg muscles produce more CO2, more H+, and more heat. Compared with blood in resting muscle, how does the oxyhemoglobin dissociation curve of blood in these muscle capillaries change?

    • A.It shifts left with a raised P50, so more O2 unloads at a given PO2
    • B.It shifts right with a raised P50, so more O2 unloads at a given PO2
    • C.It shifts left with a reduced P50, so more O2 unloads at a given PO2
    • D.It shifts right with a reduced P50, so more O2 unloads at a given PO2
    Show answerHide answer

    Correct answer: It shifts right with a raised P50, so more O2 unloads at a given PO2

    Higher CO2, more H+ (lower pH), and higher temperature lower hemoglobin's oxygen affinity (the Bohr effect), shifting the curve to the right and raising the P50, the PO2 at which hemoglobin is 50% saturated, so more O2 is released to the active muscle at any given PO2. The most tempting distractor pairs the right shift with a reduced P50, but a right shift means a higher PO2 is needed to reach 50% saturation, so P50 rises. A left shift with a reduced P50 is the opposite case, with tighter O2 binding, as with cold tissue or reduced 2,3-BPG.

  36. In a bird population, the share of individuals in three beak-size classes was tracked for ten generations after a change in the seeds available. Small beaks went from 20% to 33%, medium beaks from 60% to 34%, and large beaks from 20% to 33%. The average beak size stayed about the same. Which type of natural selection does this pattern show?

    • A.Directional selection, since the seed change shifted which beak sizes were favored
    • B.Disruptive selection, since both extreme classes gained as the middle class shrank
    • C.Stabilizing selection, since the average beak size held at about the same value
    • D.Stabilizing selection, since the medium class is still the most common class
    Show answerHide answer

    Correct answer: Disruptive selection, since both extreme classes gained as the middle class shrank

    Disruptive selection, since both extreme classes gained as the middle class shrank, is correct: selection favored both extremes, so variation grew while the mean held. Stabilizing selection is tempting because the mean is unchanged and medium is still the largest class, but stabilizing selection would make the medium class grow and variation narrow, the opposite of what happened. Directional selection shifts the mean toward one extreme, which did not occur.

General Chemistry (54)

  1. In the context of chemical equilibrium, which statement accurately describes the effect of increasing the temperature on an exothermic reaction at equilibrium?

    • A.Applied heat drives the system ahead toward products
    • B.Applied heat pushes the system back toward reactants
    • C.The equilibrium constant grows larger as heat enters
    • D.The equilibrium constant holds steady as heat enters
    Show answerHide answer

    Correct answer: Applied heat pushes the system back toward reactants

    Correct answer: Applied heat pushes the system back toward reactants. Explanation: An exothermic reaction gives off heat, so heat behaves like a product; adding heat is a stress the system relieves by consuming it, which moves the equilibrium position toward the reactants and lowers the yield. Applied heat driving the system ahead toward products is what happens to an endothermic reaction, not this one. The equilibrium constant growing larger as heat enters is again the endothermic case, since for an exothermic reaction the constant falls as temperature rises. The equilibrium constant holding steady as heat enters is wrong because the constant is fixed only at a fixed temperature, and temperature is the one stress that changes its value.

  2. What is the hybridization of the carbon atoms in ethylene (CX2HX4 \ce{C2H4} )?

    • A.sp sp
    • B.sp3 sp^3
    • C.sp2 sp^2
    • D.sp3d sp^3d
    Show answerHide answer

    Correct answer: sp2 sp^2

    Correct answer: sp2 sp^2 . Explanation: Each carbon in ethylene forms three sigma bonds, two to hydrogen and one to the other carbon, and keeps one unhybridized p orbital for the pi bond, which is the sp2 sp^2 arrangement and gives the flat geometry with bond angles near 120 degrees. sp sp hybridization would mean two sigma bonds and two pi bonds, as in acetylene. sp3 sp^3 would mean four sigma bonds and no pi bond, as in ethane. sp3d sp^3d requires five electron domains and an expanded octet, which a second-period carbon atom cannot form.

  3. What is the pH of a 0.01 M HCl solution?

    • A.1
    • B.3
    • C.4
    • D.2
    Show answerHide answer

    Correct answer: 2

    Correct answer: 2. Explanation: Hydrochloric acid is a strong acid and dissociates completely, so a 0.01 M solution contains 0.01 M hydrogen ions and pH = -log(0.01) = 2. A value of 1 would belong to a 0.1 M solution, ten times more concentrated than the one described. A value of 3 would belong to a 0.001 M solution, ten times more dilute. A value of 4 is two orders of magnitude more dilute still.

  4. Which of the following elements has the highest electronegativity?

    • A.Fluorine
    • B.Chlorine
    • C.Nitrogen
    • D.Hydrogen
    Show answerHide answer

    Correct answer: Fluorine

    Correct answer: Fluorine. Explanation: Fluorine has a very small atomic radius and a high effective nuclear charge, so its nucleus pulls hardest on a shared electron pair and it carries the largest Pauling electronegativity of any element. Chlorine sits one period lower with its valence shell further from the nucleus and is meaningfully less electronegative. Nitrogen is lower again despite being a small second-period atom. Hydrogen is the least electronegative of the four and is often the atom that loses electron density in a bond.

  5. Which principle explains the increase in ionization energy across a period in the periodic table?

    • A.Stronger shielding from filled shells
    • B.Growing attraction from added protons
    • C.Expanding radius across whole periods
    • D.Increased pairing among full orbitals
    Show answerHide answer

    Correct answer: Growing attraction from added protons

    Correct answer: Growing attraction from added protons. Explanation: Moving left to right across a period adds a proton to the nucleus at every step while the extra electrons enter the same shell, so shielding barely changes and the effective nuclear charge felt by the outer electrons climbs, making them harder to remove. Stronger shielding from filled shells acts the other way, lowering ionization energy, and it grows going down a group rather than across a period. Expanding radius across whole periods is backwards, because atoms get smaller from left to right. Increased pairing among full orbitals explains small local dips, such as the one between nitrogen and oxygen, not the overall rise.

  6. In the formation of a salt from a reaction between an acid and a base, what is the role of the acid?

    • A.Takes a proton from the base
    • B.Gives the metal ion to salts
    • C.Donates a proton to the base
    • D.Takes a metal ion from salts
    Show answerHide answer

    Correct answer: Donates a proton to the base

    Correct answer: Donates a proton to the base. Explanation: Under the Bronsted-Lowry definition an acid is a proton donor, and in a neutralization the proton it releases combines with hydroxide from the base to form water while the remaining ions make up the salt. Taking a proton from the base reverses the two roles, since accepting protons is what makes a species a base. Giving the metal ion to salts is the base's contribution, because the cation of a salt normally comes from the base while the acid supplies the anion. Taking a metal ion from salts plays no part in a neutralization, since no metal is stripped out of an existing salt when an acid and a base react.

  7. What is the primary factor that determines the boiling point of a molecular compound?

    • A.Strength that binds atoms within molecules
    • B.Weight that each separate molecule carries
    • C.Electrons that circle inside each molecule
    • D.Forces that act between separate molecules
    Show answerHide answer

    Correct answer: Forces that act between separate molecules

    Correct answer: Forces that act between separate molecules. Explanation: Boiling pulls whole molecules away from one another, so the energy required is set by the strength of the intermolecular attractions, namely hydrogen bonding, dipole-dipole forces and London dispersion. Strength that binds atoms within molecules is covalent bond energy, and those bonds survive intact when a molecular compound boils. Weight that each separate molecule carries is not the deciding factor: water is lighter than hydrogen sulfide yet boils far higher, because it hydrogen bonds. Electrons that circle inside each molecule set the chemistry of the substance but do not by themselves fix the boiling point.

  8. Which of the following is a property of gases that increases with an increase in temperature at constant pressure?

    • A.Molar volume
    • B.Mass density
    • C.Molar weight
    • D.Water uptake
    Show answerHide answer

    Correct answer: Molar volume

    Correct answer: Molar volume. Explanation: Charles's law states that at constant pressure the volume of a fixed amount of gas is proportional to absolute temperature, so the space occupied by one mole expands as the gas is heated. Mass density falls instead, because the same mass now spreads through a larger volume. Molar weight is a property of the substance itself and does not change with temperature. Water uptake describes how much of the gas dissolves, and gas solubility in water decreases as temperature rises.

  9. Which concept explains the observation that the shape of a molecule with three bonded atoms and one lone pair on the central atom is trigonal pyramidal?

    • A.Repulsion between valence electron pairs
    • B.Overlap between adjacent atomic orbitals
    • C.Blending different orbitals into hybrids
    • D.Displaying electron pairs around symbols
    Show answerHide answer

    Correct answer: Repulsion between valence electron pairs

    Correct answer: Repulsion between valence electron pairs. Explanation: The valence shell electron pair repulsion model treats every bonding pair and lone pair on the central atom as a charge cloud that pushes the others as far apart as it can. Four electron groups spread toward a tetrahedral arrangement, and when one of the four is a lone pair only three bonded atoms remain visible, so the molecule is trigonal pyramidal. Overlap between adjacent atomic orbitals is valence bond theory, which accounts for where the bonding electrons sit rather than for the angles between groups. Blending different orbitals into hybrids assigns a hybrid set that matches a geometry already known, so it describes the shape instead of predicting it from repulsion. Displaying electron pairs around symbols is the Lewis method, a flat bookkeeping device that shows how many pairs are present but assigns no three-dimensional shape.

  10. What is the outcome of mixing an aqueous solution of silver nitrate (AgNOX3 \ce{AgNO3} ) with an aqueous solution of sodium chloride (NaCl \ce{NaCl} )?

    • A.Insoluble sodium nitrate deposits out of solution
    • B.Metallic silver plates out while sodium dissolves
    • C.Water plus salt form via acid-base neutralization
    • D.Insoluble silver chloride settles out of solution
    Show answerHide answer

    Correct answer: Insoluble silver chloride settles out of solution

    Correct answer: Insoluble silver chloride settles out of solution. Explanation: Silver ions from the silver nitrate meet chloride ions from the sodium chloride, and silver chloride is one of the few insoluble chlorides, so it leaves the water as a white solid while sodium and nitrate ions stay dissolved. Insoluble sodium nitrate deposits out of solution is wrong because every common nitrate, sodium nitrate included, is freely soluble. Metallic silver plates out while sodium dissolves is wrong because no oxidation states change here; silver stays as a positive ion in the solid it forms. Water plus salt form via acid-base neutralization is wrong because neither reactant supplies hydrogen ions or hydroxide ions, so no water can be produced.

  11. What principle is violated when two electrons with the same spin occupy the same orbital in an atom?

    • A.Hund's rule for parallel spins
    • B.Aufbau order of energy filling
    • C.Pauli's rule on opposite spins
    • D.Bohr's rule on orbit distances
    Show answerHide answer

    Correct answer: Pauli's rule on opposite spins

    Correct answer: Pauli's rule on opposite spins. Explanation: No two electrons in one atom may share all four quantum numbers, so two electrons sharing an orbital must differ in spin; giving both the same spin breaks that limit. Hund's rule for parallel spins governs how electrons spread across orbitals of equal energy before they pair, which says nothing about two electrons already inside one orbital. Aufbau order of energy filling only fixes the sequence in which orbitals are occupied, from lowest energy upward. Bohr's rule on orbit distances describes fixed circular orbits in an outdated model and makes no statement about electron spin.

  12. Which term best describes the energy change associated with the removal of an electron from a gaseous atom?

    • A.Electron affinity
    • B.Ionization energy
    • C.Activation energy
    • D.Excitation energy
    Show answerHide answer

    Correct answer: Ionization energy

    Correct answer: Ionization energy. Explanation: Ionization energy is the energy needed to pull an electron away from a neutral gaseous atom, leaving a positive ion, and it measures how tightly the nucleus holds that outer electron. Electron affinity is the energy change when a gaseous atom gains an electron, the opposite process. Activation energy is the minimum energy colliding particles need before a reaction can proceed, a kinetics quantity rather than an atomic one. Excitation energy lifts an electron to a higher orbital within the same atom without ever removing it.

  13. In a redox reaction, what is the role of the substance that is oxidized?

    • A.It gives up electrons, so its oxidation state rises.
    • B.It takes in electrons, so its oxidation state drops.
    • C.It picks up hydrogen, so its oxidation state climbs.
    • D.It sheds bound oxygen, so its oxidation state drops.
    Show answerHide answer

    Correct answer: It gives up electrons, so its oxidation state rises.

    Correct answer: It gives up electrons, so its oxidation state rises. Explanation: Oxidation is defined as the loss of electrons, and losing negative charge drives the oxidation number of that atom upward while the partner species collects those electrons. It takes in electrons, so its oxidation state drops describes the species being reduced, which is the partner of the oxidized substance rather than the substance itself. It picks up hydrogen, so its oxidation state climbs is wrong in both halves: gaining hydrogen adds electron density and lowers the oxidation number. It sheds bound oxygen, so its oxidation state drops describes reduction as well, since removing oxygen lowers the oxidation number instead of raising it.

  14. What type of intermolecular force is primarily responsible for the high boiling point of water compared to other group 16 hydrides?

    • A.Dipole alignment between adjacent molecules
    • B.Induced coupling between adjacent molecules
    • C.Ionic attraction between adjacent molecules
    • D.Hydrogen bonding between adjacent molecules
    Show answerHide answer

    Correct answer: Hydrogen bonding between adjacent molecules

    Correct answer: Hydrogen bonding between adjacent molecules. Explanation: Water's hydrogen atoms are bonded to a small, strongly electronegative oxygen, so each molecule can form strong directional links to the lone pairs of its neighbors, and breaking that network takes far more energy than boiling the heavier hydrides of the same group. Dipole alignment between adjacent molecules is present in hydrogen sulfide and its heavier relatives too, and on its own it is far too weak to explain the jump. Induced coupling between adjacent molecules, the induced-dipole dispersion force, actually grows with molecular size, so it would predict the opposite trend, with water boiling lowest. Ionic attraction between adjacent molecules requires charged ions, and liquid water is molecular rather than ionic.

  15. What is the oxidation state of manganese in potassium permanganate (KMnOX4 \ce{KMnO4} )?

    • A.+3
    • B.+5
    • C.+7
    • D.+9
    Show answerHide answer

    Correct answer: +7

    Correct answer: +7. Explanation: In potassium permanganate the potassium ion contributes +1 and each of the four oxygen atoms contributes -2, for -8 in total, and the compound is neutral, so manganese must be +7. The value +3 comes from treating the oxygens as peroxide oxygens at -1 each. The value +5 comes from counting only three oxygen atoms. The value +9 comes from giving potassium a negative charge instead of a positive one.

  16. In the context of molecular orbital theory, what is the bond order of diatomic nitrogen (NX2 \ce{N2} )?

    • A.3
    • B.2
    • C.4
    • D.5
    Show answerHide answer

    Correct answer: 3

    Correct answer: 3. Explanation: Filling the molecular orbitals of diatomic nitrogen with its ten valence electrons places eight in bonding orbitals and two in an antibonding orbital, and bond order is the bonding count minus the antibonding count, divided by two, which gives 3 and matches the triple bond drawn in Lewis structures. The value 2 comes from counting only the pi electrons. The value 4 comes from ignoring the antibonding pair. The value 5 comes from dividing all ten valence electrons by two without subtracting anything.

  17. Which of the following is a characteristic of a reaction that is first-order in reactant A?

    • A.The half-life dips as the amount of A doubles.
    • B.A graph of one over the amount remains linear.
    • C.The rate constant is given in moles per liter.
    • D.The rate doubles when the amount of A doubles.
    Show answerHide answer

    Correct answer: The rate doubles when the amount of A doubles.

    Correct answer: The rate doubles when the amount of A doubles. Explanation: A first-order reaction obeys rate equals k times the concentration of A raised to the first power, so the rate tracks that concentration in direct proportion and doubling the reactant doubles the rate. The half-life dips as the amount of A doubles is wrong because a first-order half-life equals the natural logarithm of 2 divided by k, a value that does not depend on how much reactant is present. A graph of one over the amount remains linear describes second-order behavior; first-order data give a straight line only when the natural logarithm of the concentration is plotted against time. The rate constant is given in moles per liter is wrong because a first-order rate constant carries units of reciprocal time, such as per second.

  18. What type of solid is characterized by a high melting point, electrical conductivity in molten state, and is composed of positive and negative ions?

    • A.A giant covalent solid
    • B.A soft molecular solid
    • C.A salt crystal lattice
    • D.A packed metal lattice
    Show answerHide answer

    Correct answer: A salt crystal lattice

    Correct answer: A salt crystal lattice. Explanation: A salt crystal lattice is built from alternating positive and negative ions held by strong electrostatic attraction, which explains the high melting point, and once molten the ions are free to move and carry current. A giant covalent solid such as quartz also melts high but has no ions at all, so the melt does not conduct. A soft molecular solid is held together by weak intermolecular forces and melts at low temperature. A packed metal lattice conducts as a solid as well as a liquid and contains no negative ions, only cations in a shared electron sea.

  19. Which of the following statements is true regarding the solubility product constant (Ksp) of a sparingly soluble salt?

    • A.A change in temperature leaves the Ksp steady.
    • B.Greater solubility of the salt raises its Ksp.
    • C.Adding a common ion raises solubility and Ksp.
    • D.A larger Ksp means this salt dissolves slower.
    Show answerHide answer

    Correct answer: Greater solubility of the salt raises its Ksp.

    Correct answer: Greater solubility of the salt raises its Ksp. Explanation: The solubility product is the equilibrium constant for a salt breaking into its ions, so for a given salt more dissolved ions at saturation means a larger product of ion concentrations and a larger Ksp. A change in temperature leaves the Ksp steady is wrong because Ksp is an equilibrium constant and every equilibrium constant is defined at a stated temperature. Adding a common ion raises solubility and Ksp is wrong on both counts: extra common ion pushes the equilibrium back toward the solid and lowers solubility, while Ksp itself is untouched. A larger Ksp means this salt dissolves slower confuses position with speed, since Ksp describes the equilibrium reached and says nothing about how fast dissolving happens.

  20. What is the primary mechanism by which radiation causes damage to biological tissues?

    • A.Excitation, lifting electrons toward empty orbitals
    • B.Heating, denaturing this cell's structural proteins
    • C.Photodissociation, splitting bonds using weak light
    • D.Ionization, releasing highly reactive free radicals
    Show answerHide answer

    Correct answer: Ionization, releasing highly reactive free radicals

    Correct answer: Ionization, releasing highly reactive free radicals. Explanation: Ionizing radiation carries enough energy to strip electrons from molecules it passes through, above all from the water that fills a cell, and the fragments left behind are free radicals that attack DNA, proteins and membranes. Excitation, lifting electrons toward empty orbitals happens as well, but an excited molecule usually sheds the extra energy harmlessly without breaking apart. Heating, denaturing this cell's structural proteins is not the route, because the temperature rise from a diagnostic exposure is far too small to unfold proteins. Photodissociation, splitting bonds using weak light describes low-energy photons that lack the energy to ionize at all.

  21. What effect does a catalyst have on the activation energy of a chemical reaction?

    • A.It builds a taller barrier for the forward stage.
    • B.It cuts the energy stored in the final compounds.
    • C.It offers a lower path around the energy barrier.
    • D.It lifts the warmth needed to start the reaction.
    Show answerHide answer

    Correct answer: It offers a lower path around the energy barrier.

    Correct answer: It offers a lower path around the energy barrier. Explanation: A catalyst binds the reactants and offers an alternative mechanism whose highest energy point sits below that of the uncatalyzed route, so a larger share of collisions carries enough energy to react and the reaction speeds up while the catalyst itself is recovered. It builds a taller barrier for the forward stage describes an inhibitor, the opposite effect. It cuts the energy stored in the final compounds is wrong because a catalyst leaves the energies of reactants and products exactly where they were. It lifts the warmth needed to start the reaction is wrong because catalysts let reactions run at lower temperatures, not higher ones.

  22. Which statement accurately describes the behavior of an ideal gas according to the kinetic molecular theory?

    • A.Particles in close contact attract each other powerfully.
    • B.Particles in constant motion collide without energy loss.
    • C.Particles fill nearly all the available container volume.
    • D.Particles lose average speed when the temperature climbs.
    Show answerHide answer

    Correct answer: Particles in constant motion collide without energy loss.

    Correct answer: Particles in constant motion collide without energy loss. Explanation: The kinetic molecular model pictures gas particles moving ceaselessly in straight lines in random directions, rebounding from each other and from the walls in perfectly elastic collisions, so no kinetic energy is drained away and the pressure stays steady. Particles in close contact attract each other powerfully is the opposite of the model, which assumes negligible attraction between particles. Particles fill nearly all the available container volume is ruled out as well, since the model treats the volume of the particles themselves as negligible next to the container. Particles lose average speed when the temperature climbs reverses the central link of the model, in which average kinetic energy is proportional to absolute temperature.

  23. Which of the following accurately describes the effect of a catalyst on the equilibrium position of a reversible reaction?

    • A.It speeds both directions equally, leaving the mix unchanged.
    • B.It accelerates the forward step, boosting the product amount.
    • C.It accelerates the reverse step, raising the reactant amount.
    • D.It leaves both reaction rates alone, keeping yield unchanged.
    Show answerHide answer

    Correct answer: It speeds both directions equally, leaving the mix unchanged.

    Correct answer: It speeds both directions equally, leaving the mix unchanged. Explanation: A catalyst lowers the activation barrier for the forward and reverse steps by the same amount, so both rate constants rise by the same factor, their ratio, the equilibrium constant, is untouched, and the reaction simply reaches the same equilibrium sooner. It accelerates the forward step, boosting the product amount would change the equilibrium constant, which a catalyst cannot do. It accelerates the reverse step, raising the reactant amount fails for the same reason. It leaves both reaction rates alone, keeping yield unchanged is wrong in its first half, because raising both rates is precisely what a catalyst does.

  24. In the context of acid-base chemistry, what is the significance of the pKa value of an acid?

    • A.It predicts the acidity of any diluted acid solution.
    • B.It counts the protons that a single molecule carries.
    • C.It fixes the exact base volume needed for neutrality.
    • D.It ranks acid strength by the extent of dissociation.
    Show answerHide answer

    Correct answer: It ranks acid strength by the extent of dissociation.

    Correct answer: It ranks acid strength by the extent of dissociation. Explanation: The pKa is the negative logarithm of the acid dissociation constant, so it places acids on a scale of how far they split into ions in water, with a lower pKa marking the stronger acid. It predicts the acidity of any diluted acid solution is wrong because the measured pH also depends on how concentrated the solution is. It counts the protons that a single molecule carries describes how many ionizable hydrogens an acid has, a different property entirely. It fixes the exact base volume needed for neutrality is wrong because that volume is set by how much acid is present and how concentrated it is, not by the pKa.

  25. Which element has the highest first ionization energy in the periodic table?

    • A.Oxygen
    • B.Carbon
    • C.Helium
    • D.Cesium
    Show answerHide answer

    Correct answer: Helium

    Correct answer: Helium. Explanation: Helium's two electrons sit in a filled first shell very close to the nucleus with almost no shielding, so removing one takes more energy than for any other element, about 24.6 electron volts. Oxygen and carbon both hold their outer electrons in the second shell, farther from the nucleus and screened by inner electrons, so each gives one up more readily. Cesium is the extreme opposite case, with a single loosely held outer electron that is among the easiest of all elements to remove.

  26. What is the result of mixing equal volumes of 0.1 M HCl and 0.1 M NaOH?

    • A.A weakly acidic mixture at a pH near four
    • B.A neutral salt mixture at a pH near seven
    • C.A slightly basic mixture at a pH near ten
    • D.A buffered salt solution at a pH near six
    Show answerHide answer

    Correct answer: A neutral salt mixture at a pH near seven

    Correct answer: A neutral salt mixture at a pH near seven. Explanation: Equal volumes of 0.1 M hydrochloric acid and 0.1 M sodium hydroxide supply equal moles of hydrogen ion and hydroxide ion, which combine completely to form water and leave sodium chloride, a salt of a strong acid and a strong base that does not shift the pH from 7. A weakly acidic mixture at a pH near four would require leftover acid, which cannot happen when the moles match. A slightly basic mixture at a pH near ten would require leftover base, which likewise cannot happen. A buffered salt solution at a pH near six is wrong because a buffer needs a weak acid with its conjugate base, and neither survives this reaction.

  27. Which principle explains why electrons fill degenerate orbitals singly before pairing?

    • A.Hund's rule on parallel spins
    • B.Pauli's rule on opposite spin
    • C.Aufbau order of rising energy
    • D.Bohr's rule on orbit energies
    Show answerHide answer

    Correct answer: Hund's rule on parallel spins

    Correct answer: Hund's rule on parallel spins. Explanation: Electrons repel one another, so within a set of orbitals of equal energy they occupy separate orbitals with their spins aligned before any orbital takes a second electron, which lowers the repulsion and gives the more stable arrangement. Pauli's rule on opposite spin only limits what may share one orbital once pairing does occur. Aufbau order of rising energy fixes which subshell is filled next, not how electrons distribute within a degenerate set. Bohr's rule on orbit energies belongs to an early planetary model of the atom and says nothing about how orbitals of equal energy are occupied.

  28. A technician needs to prepare a dilute hydrochloric acid solution by diluting a concentrated stock. Starting with 25.0 mL of 6.0 M HCl and adding water until the final volume is 500. mL, what is the molarity of the diluted solution?

    • A.0.60 M
    • B.0.15 M
    • C.0.45 M
    • D.0.30 M
    Show answerHide answer

    Correct answer: 0.30 M

    Dilution conserves the moles of solute, so the final concentration is 6.0 M times 25.0 mL divided by 500. mL, which is 0.30 M. The figure 0.15 is the number of moles of HCl taken from the stock rather than a concentration. A result of 0.60 M would follow from a final volume of 250 mL, and 0.45 M would need either a stock stronger than 6.0 M or a smaller final volume.

  29. Ammonia is produced by the reaction NX2+3 HX2→2 NHX3 \ce{N2 + 3 H2 -> 2 NH3} . If a reaction vessel is charged with 2.0 mol of NX2 \ce{N2} and 3.0 mol of HX2 \ce{H2} , what is the maximum number of moles of NHX3 \ce{NH3} that can form?

    • A.3.0 mol
    • B.1.0 mol
    • C.2.0 mol
    • D.4.0 mol
    Show answerHide answer

    Correct answer: 2.0 mol

    Reacting all 2.0 mol of N2 would require 6.0 mol of H2, but the vessel holds only 3.0 mol, so hydrogen limits the reaction: 3.0 mol of H2 times the 2 to 3 ratio of NH3 to H2 gives 2.0 mol of NH3. Treating N2 as limiting and applying the 1 to 2 ratio gives 4.0 mol. Pairing H2 with NH3 one for one gives 3.0 mol. The figure 1.0 mol is the amount of N2 actually consumed, not the ammonia produced.

  30. A compound is found by analysis to contain 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. Using atomic masses C = 12.0, H = 1.0, and O = 16.0 g/mol, what is its empirical formula?

    • A.CHX2O \ce{CH2O}
    • B.CX2HX4OX2 \ce{C2H4O2}
    • C.CHO \ce{CHO}
    • D.CHX4O \ce{CH4O}
    Show answerHide answer

    Correct answer: CHX2O \ce{CH2O}

    In a 100 g sample the moles are 40.0 divided by 12.0, or 3.33, for carbon, 6.7 divided by 1.0, or 6.7, for hydrogen, and 53.3 divided by 16.0, or 3.33, for oxygen; dividing each by 3.33 gives a 1 to 2 to 1 ratio, so the empirical formula is CH2O. A 1 to 1 to 1 ratio, CHO, ignores that hydrogen has twice the mole count of carbon. CH4O carries twice the hydrogen per carbon the analysis allows and works out to 12.5 percent hydrogen. C2H4O2 has the same percent composition as CH2O but is a multiple of the ratio rather than the simplest whole-number form the question asks for.

  31. Aluminum reacts with chlorine gas according to 2 Al + 3 Cl2 → 2 AlCl3. A student combines 5.40 g of Al with 10.65 g of Cl2 and isolates 10.68 g of AlCl3. Using molar masses Al = 27.0, Cl2 = 71.0, and AlCl3 = 133.5 g/mol, what is the percent yield?

    • A.53.3%
    • B.66.5%
    • C.40.0%
    • D.80.0%
    Show answerHide answer

    Correct answer: 80.0%

    The student has 0.200 mol Al, which would need 0.300 mol Cl2, but only 0.150 mol Cl2 is present, so Cl2 is limiting and gives 0.150 x 2/3 = 0.100 mol AlCl3, or 13.35 g, and 10.68/13.35 = 80.0%. Taking aluminum as limiting because it has more moles gives a theoretical 26.7 g and a false 40.0%. A 1:1 Cl2-to-AlCl3 ratio gives 53.3%, and dividing by the combined reactant mass of 16.05 g gives 66.5%.

  32. A hydrocarbon is 85.7% carbon and 14.3% hydrogen by mass, and its molar mass is 70 g/mol. Using C = 12.0 and H = 1.0 g/mol, what is its molecular formula?

    • A.C5H12
    • B.C6H12
    • C.C5H10
    • D.C6H14
    Show answerHide answer

    Correct answer: C5H10

    Per 100 g there are 85.7/12.0 = 7.14 mol C and 14.3 mol H, a 1:2 ratio, so the empirical formula is CH2 with a mass of 14; 70/14 = 5, giving C5H10. C5H12 gets the five carbons right but applies the alkane pattern CnH2n+2, which gives a molar mass of 72. C6H12 comes from dividing 70 by the mass of carbon alone, and its molar mass is 84.

  33. Which formula is paired with its correct systematic name?

    • A.N2O4, dinitrogen tetroxide
    • B.NaClO3, sodium perchlorate
    • C.MgCl2, magnesium dichloride
    • D.Fe2(SO4)3, iron(II) sulfate
    Show answerHide answer

    Correct answer: N2O4, dinitrogen tetroxide

    N2O4 is a molecular compound of two nonmetals, so Greek prefixes are used and dinitrogen tetroxide is correct. NaClO3 contains chlorate (ClO3-), and perchlorate is ClO4-. Ionic compounds such as MgCl2 never take prefixes, so it is magnesium chloride. In Fe2(SO4)3, three sulfate ions (2- each) balance two iron ions, so iron is +3 and the name is iron(III) sulfate, not iron(II).

  34. Each of the following comparisons of first ionization energy is correct EXCEPT which one?

    • A.Magnesium higher than aluminum
    • B.Nitrogen higher than oxygen
    • C.Neon higher than fluorine
    • D.Sulfur higher than phosphorus
    Show answerHide answer

    Correct answer: Sulfur higher than phosphorus

    Phosphorus (about 1012 kJ/mol) is higher than sulfur (about 1000 kJ/mol), because sulfur's fourth 3p electron is paired and easier to remove, so this comparison is wrong. Nitrogen above oxygen follows the same exception in period 2. Magnesium is above aluminum because aluminum's electron comes from a higher-energy 3p orbital. Neon above fluorine follows the normal increase across a period.

  35. A 6.00 L sample of gas at 27°C and 1.00 atm is heated to 127°C while it is compressed so that its pressure rises to 2.00 atm. What is the new volume of the gas?

    • A.16.0 L
    • B.14.1 L
    • C.4.00 L
    • D.8.00 L
    Show answerHide answer

    Correct answer: 4.00 L

    Using kelvin, V2 = 6.00 L x (1.00/2.00) x (400 K/300 K) = 4.00 L. The tempting 14.1 L comes from plugging in 127 and 27 in Celsius, which exaggerates the temperature ratio. The value 8.00 L ignores the pressure change, and 16.0 L inverts the pressure ratio.

  36. A rigid tank holds 8.0 g of helium and 16.0 g of oxygen gas (O2) at a total pressure of 5.0 atm. Using He = 4.0 and O = 16.0 g/mol, what is the partial pressure of the helium?

    • A.4.0 atm
    • B.3.3 atm
    • C.1.7 atm
    • D.2.5 atm
    Show answerHide answer

    Correct answer: 4.0 atm

    There are 8.0/4.0 = 2.0 mol He and 16.0/32.0 = 0.50 mol O2, so the mole fraction of helium is 2.0/2.5 = 0.80, and 0.80 x 5.0 atm = 4.0 atm. The tempting 3.3 atm uses 16.0 g/mol for O2, which doubles the oxygen moles. The value 1.7 atm uses mass fraction instead of mole fraction, and 2.5 atm splits the pressure evenly between the two gases.

  37. A lab needs 500. mL of 0.100 M copper(II) sulfate solution, but it only has the blue pentahydrate, CuSO4·5H2O (249.7 g/mol). Anhydrous CuSO4 is 159.6 g/mol. What mass of the pentahydrate must be dissolved and diluted to 500. mL?

    • A.25.0 g
    • B.12.5 g
    • C.7.98 g
    • D.4.50 g
    Show answerHide answer

    Correct answer: 12.5 g

    Correct answer: 12.5 g. Explanation: The solution needs 0.500 L x 0.100 mol/L = 0.0500 mol of CuSO4, and each mole of pentahydrate supplies one mole of CuSO4, so the mass is 0.0500 mol x 249.7 g/mol = 12.5 g. Using the anhydrous molar mass gives 7.98 g, which would leave the solution too dilute because part of the weighed solid is water. 25.0 g comes from treating the volume as a full liter, and 4.50 g is only the mass of the water of hydration.

  38. A technician must prepare 500. mL of 0.150 M sodium hypochlorite by diluting a 6.00 M stock solution with water. Which combination gives the correct final solution?

    • A.12.5 mL of stock and 487.5 mL of water
    • B.12.5 mL of stock and 500.0 mL of water
    • C.40.0 mL of stock and 500.0 mL of water
    • D.40.0 mL of stock and 460.0 mL of water
    Show answerHide answer

    Correct answer: 12.5 mL of stock and 487.5 mL of water

    Correct answer: 12.5 mL of stock and 487.5 mL of water. Explanation: From M1V1 = M2V2, the stock volume is (0.150 M x 500. mL)/6.00 M = 12.5 mL. Only enough water to bring the total to 500. mL is added, which is 487.5 mL. Adding a full 500.0 mL of water confuses the final volume with the water added and gives 512.5 mL of a weaker solution. 40.0 mL treats the dilution factor of 40 as if it were a volume.

  39. A student dissolves 0.500 mol of glucose in exactly 1.00 kg of water at 25 °C. How do the molality and the molarity of this solution compare with 0.500?

    • A.Molality is exactly 0.500 m; molarity is a bit above 0.500 M
    • B.Molality is exactly 0.500 m; molarity is a bit below 0.500 M
    • C.Molarity is exactly 0.500 M; molality is a bit above 0.500 m
    • D.Molarity is exactly 0.500 M; molality is a bit below 0.500 m
    Show answerHide answer

    Correct answer: Molality is exactly 0.500 m; molarity is a bit below 0.500 M

    Correct answer: Molality is exactly 0.500 m; molarity is a bit below 0.500 M. Explanation: Molality divides moles of solute by kilograms of solvent, so it is 0.500 mol/1.00 kg = 0.500 m exactly. Molarity divides by liters of the whole solution, and 1.00 kg of water already fills about 1.00 L before the dissolved glucose adds more volume, so the molarity comes out slightly under 0.500 M. Expecting it to be higher mixes up the solution's greater density with its concentration.

  40. A 5.55 g sample of calcium chloride, CaCl2 (111 g/mol), is dissolved in water, and the solution is diluted to a final volume of 250. mL. What is the concentration of chloride ions in the solution?

    • A.0.400 M
    • B.0.100 M
    • C.0.0125 M
    • D.0.200 M
    Show answerHide answer

    Correct answer: 0.400 M

    Correct answer: 0.400 M. Explanation: 5.55 g / 111 g/mol = 0.0500 mol of CaCl2, and 0.0500 mol / 0.250 L = 0.200 M CaCl2. Each formula unit releases two chloride ions, so the chloride concentration is 2 x 0.200 M = 0.400 M. 0.200 M is the concentration of the salt itself, not of its chloride ions.

  41. Assuming ideal behavior and complete dissociation of the ionic compounds, which aqueous solution has the lowest freezing point?

    • A.0.12 m MgSO4
    • B.0.10 m CaCl2
    • C.0.20 m NaCl
    • D.0.35 m glucose
    Show answerHide answer

    Correct answer: 0.20 m NaCl

    Correct answer: 0.20 m NaCl. Explanation: Freezing-point depression depends on the total molality of dissolved particles, i times m: NaCl gives 2 x 0.20 = 0.40 m, glucose gives 0.35 m, CaCl2 gives 3 x 0.10 = 0.30 m, and MgSO4 gives 2 x 0.12 = 0.24 m. The largest particle count lowers the freezing point the most. CaCl2 is tempting because it has the largest van 't Hoff factor, but its low molality makes the particle total smaller.

  42. A solution is made by dissolving 14.2 g of sodium sulfate, Na2SO4 (142 g/mol), in 250. g of water. Water's Kf is 1.86 °C·kg/mol. Assuming complete dissociation, what is the freezing point of the solution?

    • A.-0.744 °C
    • B.-0.558 °C
    • C.-2.23 °C
    • D.-1.49 °C
    Show answerHide answer

    Correct answer: -2.23 °C

    Correct answer: -2.23 °C. Explanation: 14.2 g / 142 g/mol = 0.100 mol in 0.250 kg of water, so the molality is 0.400 m, and Na2SO4 breaks into three ions, so i = 3. Then delta T = 3 x 1.86 x 0.400 = 2.23 °C, and the freezing point is -2.23 °C. -0.744 °C leaves out the van 't Hoff factor, and -1.49 °C counts only two ions.

  43. Each of the following liquids mixes with water in all proportions at room temperature EXCEPT:

    • A.1-Propanol
    • B.2-Propanol
    • C.1-Octanol
    • D.Methanol
    Show answerHide answer

    Correct answer: 1-Octanol

    Correct answer: 1-Octanol. Explanation: Every option has an OH group that can hydrogen-bond with water, but solubility depends on how much nonpolar hydrocarbon comes along with it. In 1-octanol the eight-carbon chain dominates, so only about half a gram dissolves per liter, while methanol and both propanols are fully miscible with water. Assuming that every alcohol dissolves because of its OH group is the 'like dissolves like' half-truth this item tests.

  44. A daily fluoride mouthrinse contains 0.05% sodium fluoride by mass. Using 42.0 g/mol for NaF and 19.0 g/mol for F, what is the rinse's fluoride ion concentration in parts per million?

    • A.1105 ppm
    • B.500 ppm
    • C.226 ppm
    • D.2260 ppm
    Show answerHide answer

    Correct answer: 226 ppm

    Correct answer: 226 ppm. Explanation: 0.05% means 0.05 g per 100 g, which is 500 ppm of NaF. Only 19.0/42.0 of that mass is fluoride, so the fluoride concentration is 500 x 0.452 = 226 ppm, the value printed on 0.05% NaF rinse labels. 500 ppm is the concentration of the whole salt, not of the fluoride ion.

  45. A uranium-238 nucleus emits one alpha particle, and the daughter nucleus then emits one beta-minus particle. Which nuclide is the final product?

    • A.Th-236 (Z = 90)
    • B.Ac-234 (Z = 89)
    • C.Th-234 (Z = 90)
    • D.Pa-234 (Z = 91)
    Show answerHide answer

    Correct answer: Pa-234 (Z = 91)

    Correct answer: Pa-234 (Z = 91). Explanation: Alpha emission removes 4 from the mass number and 2 from the atomic number, so U-238 (Z = 92) becomes Th-234 (Z = 90). Beta-minus emission turns a neutron into a proton, so the mass number stays at 234 and Z rises to 91, which is protactinium. Stopping at Th-234 assumes the massless beta particle changes nothing, and Ac-234 treats beta emission as lowering Z.

  46. Technetium-99m, used in medical imaging, has a half-life of 6.0 hours. What percentage of a freshly prepared dose has decayed 18 hours after it is prepared?

    • A.75.0%
    • B.12.5%
    • C.25.0%
    • D.87.5%
    Show answerHide answer

    Correct answer: 87.5%

    Correct answer: 87.5%. Explanation: Eighteen hours is three half-lives, so the fraction remaining is (1/2)^3 = 1/8, or 12.5%, and the fraction that has decayed is 100% - 12.5% = 87.5%. 12.5% is the amount still remaining, the right number for the wrong question. 75.0% would be correct after only two half-lives.

  47. Four students each weigh the same certified 10.00 g reference mass three times, each on a different balance. Which student's three readings best show a systematic error combined with little random error?

    • A.10.38 g, 9.64 g, 10.01 g
    • B.10.52 g, 10.31 g, 10.66 g
    • C.10.21 g, 10.23 g, 10.22 g
    • D.10.01 g, 9.99 g, 10.00 g
    Show answerHide answer

    Correct answer: 10.21 g, 10.23 g, 10.22 g

    A systematic error moves every reading the same way by about the same amount, so it shows as a tight cluster offset from the true value: 10.21 g, 10.23 g, 10.22 g sit within 0.02 g of each other but all about 0.22 g high. The set 10.52 g, 10.31 g, 10.66 g is farther from 10.00 g on average, but its 0.35 g spread shows large random error as well, so it does not fit 'little random error'. The set 10.38 g, 9.64 g, 10.01 g averages almost exactly 10.00 g, which is random error with no offset, and 10.01 g, 9.99 g, 10.00 g is both accurate and precise.

  48. A student finds the molarity of an HCl sample by titrating a pipetted 25.00 mL portion with standardized NaOH from a buret. Each of the following mistakes would make the calculated HCl molarity too high EXCEPT:

    • A.Starting with an air bubble in the buret tip that clears during the run
    • B.Filling the buret with NaOH right after rinsing it with distilled water
    • C.Running the NaOH past the endpoint until the solution turns deep pink
    • D.Titrating in an Erlenmeyer flask still wet with distilled water
    Show answerHide answer

    Correct answer: Titrating in an Erlenmeyer flask still wet with distilled water

    Titrating in an Erlenmeyer flask still wet with distilled water has no effect, because the pipetted 25.00 mL fixes the moles of HCl and extra water changes only the concentration in the flask, not the NaOH volume needed to neutralize it. Filling the buret right after a water rinse is the tempting choice, since both involve leftover water, but here the water dilutes the titrant: more NaOH volume is recorded, and M(HCl) = M(NaOH) x V(NaOH) / V(HCl) comes out too high. Overshooting the endpoint and a tip bubble that clears both make the recorded NaOH volume larger than the volume that actually reacted, which also inflates the result.

  49. A student records one volume from each piece of glassware below, following the rule of estimating one digit beyond the smallest marked division. Which recorded value is NOT consistent with the precision of the glassware used?

    • A.36.47 mL read from a 50 mL graduated cylinder marked every 1 mL
    • B.7.62 mL read from a 10 mL graduated cylinder marked every 0.1 mL
    • C.21.36 mL read from a 50 mL buret with lines marked every 0.1 mL
    • D.25.00 mL delivered by a 25 mL Class A volumetric transfer pipette
    Show answerHide answer

    Correct answer: 36.47 mL read from a 50 mL graduated cylinder marked every 1 mL

    A cylinder marked every 1 mL can be read only to the tenth of a milliliter, so 36.47 mL from a 50 mL graduated cylinder marked every 1 mL claims a digit the device cannot give; it should be recorded as 36.5 mL. The 10 mL cylinder is the tempting choice because cylinders feel imprecise, but its 0.1 mL markings do support an estimate to 0.01 mL, just as the buret's 0.1 mL lines support 21.36 mL. A Class A 25 mL volumetric pipette delivers its volume to within about 0.03 mL, so recording 25.00 mL is correct even though the pipette has only one mark.

  50. A student dilutes concentrated sulfuric acid at a fume hood and then cleans up the work area. Which of the following practices is NOT correct?

    • A.Treating a small acid spill on the bench with baking soda before wiping
    • B.Keeping the sash low and all of the work at least six inches inside the hood
    • C.Treating acid splashed on the forearm with baking soda before rinsing
    • D.Pouring the acid slowly into the water while working well inside the hood
    Show answerHide answer

    Correct answer: Treating acid splashed on the forearm with baking soda before rinsing

    Treating acid splashed on the forearm with baking soda before rinsing is wrong: a chemical splash on skin is flushed right away with large amounts of water for at least 15 minutes, because delaying the rinse prolongs the burn and neutralizing on skin releases more heat. Neutralizing a small spill on the bench with baking soda before wiping is the tempting look-alike, but it is the standard cleanup for a benchtop acid spill. Adding acid to water and keeping the sash low with work at least six inches inside the hood are both correct practice.

  51. A student heats equal masses of ice, starting at -20 °C, on the same steady burner, once at sea level (1.00 atm) and once at a mountain lab where the air pressure is 0.70 atm. Each time, temperature is plotted against time until about half of the liquid water has boiled away. Water's vapor pressure is 0.70 atm at about 90 °C. How does the mountain heating curve compare with the sea-level curve?

    • A.Its boiling plateau begins at 100 °C as usual, but the climb up to it takes longer
    • B.Its boiling plateau begins near 90 °C, and its melting plateau begins near -10 °C
    • C.Its boiling plateau is flat near 90 °C, while its melting plateau stays near 0 °C
    • D.Its boiling plateau begins near 90 °C, then creeps upward as more liquid boils off
    Show answerHide answer

    Correct answer: Its boiling plateau is flat near 90 °C, while its melting plateau stays near 0 °C

    Water boils when its vapor pressure equals the external pressure, so at 0.70 atm the boiling plateau sits near 90 °C, and like every phase-change plateau it stays flat because the added heat goes into breaking intermolecular attractions rather than raising the temperature. The melting point of water barely responds to pressure, so the melting plateau stays near 0 °C rather than dropping by a similar amount. Holding the boiling point at 100 °C ignores the pressure dependence, and a temperature that creeps upward during boiling describes a mixture, not a pure liquid at constant pressure.

  52. A student dilutes 10.0 mL of 0.0050 M barium hydroxide, Ba(OH)2, a strong base, with water to a total volume of 100.0 mL. What is the pH of the diluted solution at 25 °C?

    • A.12.00
    • B.11.70
    • C.13.00
    • D.11.00
    Show answerHide answer

    Correct answer: 11.00

    Each Ba(OH)2 releases two hydroxide ions, so the stock is 0.010 M OH-, and a tenfold dilution brings it to 0.0010 M; pOH is 3.00, so pH is 14.00 - 3.00 = 11.00. The value 12.00 is the pH of the undiluted stock, and 13.00 comes from applying the acid rule (dilution raises pH by one unit) to a base, whose pH must fall toward 7 on dilution. The value 11.70 comes from forgetting the second hydroxide and also skipping the dilution.

  53. A 50.0 g piece of an unknown metal is heated to 95.0 °C and dropped into 100.0 g of water at 20.0 °C in an insulated cup. The water and metal reach a final temperature of 24.0 °C. Taking the specific heat of water as 4.18 J/(g·°C) and assuming no heat is lost to the cup or the air, what is the specific heat of the metal?

    • A.0.471 J/(g·°C)
    • B.0.352 J/(g·°C)
    • C.0.118 J/(g·°C)
    • D.0.446 J/(g·°C)
    Show answerHide answer

    Correct answer: 0.471 J/(g·°C)

    The water gains q = (100.0 g)(4.18 J/(g·°C))(4.0 °C) = 1672 J, and the metal loses the same heat while cooling 71.0 °C, so c = 1672 J / (50.0 g x 71.0 °C) = 0.471 J/(g·°C). Using 75.0 °C, the gap between the two starting temperatures, as the metal's temperature change gives 0.446, and using the metal's starting temperature of 95.0 °C gives 0.352. Swapping the two masses gives 0.118.

  54. For the reaction 2 NO2(g) → N2O4(g), the standard enthalpy change is -57.2 kJ and the standard entropy change is -175.8 J/K. Assuming both values stay constant as temperature changes, under what condition is the reaction spontaneous with all species at standard state?

    • A.Above about 325 K, where the TΔS term outweighs the ΔH term
    • B.At no temperature, since a negative ΔS makes ΔG positive
    • C.At any temperature, since a negative ΔH makes ΔG negative
    • D.Below about 325 K, where the ΔH term outweighs the TΔS term
    Show answerHide answer

    Correct answer: Below about 325 K, where the ΔH term outweighs the TΔS term

    With ΔG = ΔH - TΔS, a negative ΔH favors spontaneity while the -TΔS term is positive and grows with temperature, so ΔG is negative only below T = ΔH/ΔS = 57,200 J / 175.8 J/K, about 325 K. Above 325 K the unfavorable TΔS term wins, so the reaction is nonspontaneous there, not spontaneous. A negative ΔH alone cannot guarantee spontaneity when ΔS is also negative, and a negative ΔS alone cannot rule it out when ΔH is negative.

References

  1. 1.ADA Department of Testing Services. “Admission Test for Dental Hygiene (ATDH).” ADA.org. ↑
  2. 2.ADA Department of Testing Services. “ATDH 2026 Candidate Guide (updated 08/04/2026).” ADA.org, 2026. ↑
  3. 3.ADA Department of Testing Services. “Apply for the Admission Test for Dental Hygiene (ATDH).” ADA.org. ↑
  4. 4.ADA Department of Testing Services. “Admission Test for Dental Hygiene (ATDH) Practice Questions.” ADA.org. ↑
  5. 5.Career Employer. “ATDH practice-test performance data.” careeremployer.com, updated daily, CC BY 4.0. ↑
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