Your FREE OAR (Officer Aptitude Rating) Practice Test 2026 – 250+ Q&A
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OAR Practice Questions
If 3x+7=22, what is the value of x?
9
6
5
7
Correct answer: 5
Subtracting 7 from both sides leaves 3x equal to 15, and dividing that by 3 gives 5. The value 7 comes from dividing 22 by 3 before the 7 is removed, 6 comes from reading the right side as 25, and 9 comes from adding 7 to 22 instead of subtracting it and then dividing.
A car travels 240 miles in 4 hours. What is its average speed in miles per hour?
48
60
50
55
Correct answer: 60
Average speed is distance divided by time, so 240 miles over 4 hours gives 60 miles per hour. The value 48 divides the same distance by 5 hours, 50 uses a distance of 200 miles, and 55 uses a distance of 220 miles; each keeps the right method but feeds it a figure the question did not give.
What is 35% of 80?
35
45
28
52
Correct answer: 28
A percentage is applied by converting it to a decimal and multiplying, so 0.35 times 80 gives 28. The value 35 repeats the percentage instead of applying it to anything, 45 subtracts 35 from 80 as though the percent sign were absent, and 52 is the remaining 65 percent of 80 rather than the share the question asks for.
If a rectangle has a length of 12 and a width of 5, what is its area?
34
60
72
48
Correct answer: 60
Area of a rectangle is length multiplied by width, so 12 times 5 gives 60 square units. The value 34 is the perimeter, which adds the four sides rather than multiplying two of them, while 48 works from a width of 4 and 72 from a width of 6.
Solve for y: 2y−9=11.
10
25
15
20
Correct answer: 10
Adding 9 to both sides gives 2y equal to 20, and dividing by 2 gives 10. The value 20 stops at that intermediate total and never divides, 15 follows from reading the right side as 21, and 25 from reading it as 41.
What is the value of 4 squared plus 3 cubed?
35
43
17
25
Correct answer: 43
Four squared is 16 and three cubed is 27, and the two totals combine to 43. The value 17 multiplies each base by its exponent rather than raising it, 25 squares both terms so it adds 16 and 9, and 35 keeps the correct 27 but pairs it with 8 for four squared.
A shirt costs $40 and is discounted by 25%. What is the sale price?
$20
$40
$10
$30
Correct answer: $30
One quarter of 40is10, and removing that from the ticket price leaves 30.Thefigure10 is the discount itself rather than what the buyer pays, 20wouldbetheresultofahalf−pricecut,and40 is the original price with no reduction applied at all.
If 5 pencils cost $2.00, how much do 12 pencils cost at the same rate?
$4.80
$3.60
$4.40
$4.00
Correct answer: $4.80
Five pencils for 2.00worksoutat0.40 each, and 12 of them at that rate cost 4.80.Thefigure3.60 prices only nine pencils, 4.00doublesthefive−pencilpriceandstopsatten,and4.40 stops one pencil short at eleven.
What is the least common multiple of 6 and 8?
24
18
12
30
Correct answer: 24
The least common multiple is the smallest number that both 6 and 8 divide into exactly, and that number is 24. The values 12, 18 and 30 are each a multiple of 6, but none of them divides by 8 without a remainder, so none can be a common multiple of the pair.
Simplify the fraction 18/24.
2/3
1/2
5/8
3/4
Correct answer: 3/4
The greatest common factor of 18 and 24 is 6, and dividing both parts by 6 leaves 3/4. The value 2/3 comes from subtracting 6 from each part instead of dividing, 1/2 from using different divisors on top and bottom, and 5/8 from reading the numerator as 15.
If x=4, what is the value of 2x2−3x+1?
21
23
17
19
Correct answer: 21
With x equal to 4, twice x squared is 32 and three x is 12, so 32 minus 12 plus 1 gives 21. The value 19 subtracts the final 1 rather than adding it, 17 subtracts 3 at the end in place of adding 1, and 23 adds the coefficient 3 where the constant 1 belongs.
A triangle has a base of 10 and a height of 6. What is its area?
42
30
24
36
Correct answer: 30
A triangle covers half the area of the rectangle around it, so half of 10 times 6 gives 30 square units. The values 24, 36 and 42 all halve base times height correctly but start from a base of 8, 12 and 14 in turn, none of which the question supplies.
What is 7/8 expressed as a decimal?
0.625
0.875
0.750
0.825
Correct answer: 0.875
A fraction converts to a decimal by dividing the numerator by the denominator, and 7 divided by 8 gives 0.875. The value 0.750 is the decimal for 3/4, 0.625 is the decimal for 5/8, and 0.825 comes from a slip in the middle step of the long division, which drops a 2 into the place the 7 belongs.
If the ratio of boys to girls in a class is 3:5 and there are 15 boys, how many girls are there?
35
40
25
30
Correct answer: 25
Fifteen boys fill the three boy units of the ratio, so one unit is 5 students and the five girl units come to 25. The value 30 treats the ratio as 3 to 6, 35 treats it as 3 to 7, and 40 is the size of the whole class rather than the number of girls in it.
What is the sum of the interior angles of a triangle?
360
120
270
180
Correct answer: 180
The three interior angles of a triangle total 180 degrees, which is why the third angle is fixed once the other two are known. The value 360 is the total for a four-sided figure or a complete turn, 270 is three right angles, and 120 is a complete turn shared equally among three sides.
Solve for x: 4x=9.
36
54
27
45
Correct answer: 36
Multiplying both sides by 4 undoes the division and leaves 36. The value 27 would follow if the equation divided x by 3, 45 if it divided by 5, and 54 if it divided by 6; each one multiplies 9 by a divisor the equation does not use.
A number increased by 15 equals 42. What is the number?
42
57
27
12
Correct answer: 27
The unknown plus 15 makes 42, so subtracting 15 from 42 recovers it as 27. The value 57 adds 15 rather than subtracting it, 42 repeats the total the question already supplies, and 12 subtracts 15 a second time from a figure that was already correct.
What is 12 percent of 250?
54
42
30
18
Correct answer: 30
Twelve percent is 0.12 as a decimal, and 0.12 multiplied by 250 gives 30. The value 18 applies the same 12 percent to 150, 42 applies it to 350, and 54 applies it to 450; the method is right in each case but the total is not the one given.
If a square has a perimeter of 36, what is the length of one side?
6
4
8
9
Correct answer: 9
A square has four equal sides, so one side is the perimeter divided by 4, and 36 divided by 4 is 9. The value 6 is the square root of 36, which would be the side only if 36 were the area, 4 is the number of sides rather than a length, and 8 follows from dividing 32 by 4 after misreading the perimeter.
Evaluate: (8+4)/2+5.
11
21
15
17
Correct answer: 11
The bracket is worked first: 8 plus 4 is 12, dividing by 2 leaves 6, and adding 5 gives 11. The value 17 adds 5 to 12 without dividing at all, 15 divides only the 4 before adding, and 21 totals every figure on the line and ignores the operations.
What is the value of 0.6 multiplied by 0.5?
0.35
0.30
0.20
0.25
Correct answer: 0.30
Six tenths multiplied by five tenths gives 30 hundredths, written 0.30, because multiplying two one-place decimals produces a two-place decimal. The value 0.25 comes from reading the first factor as 0.5, 0.35 from reading it as 0.7, and 0.20 from reading it as 0.4.
If 4 workers can finish a job in 6 days, how many days will it take 8 workers at the same rate?
8
3
9
6
Correct answer: 3
The work is fixed, so doubling the crew halves the time and 6 days becomes 3 days. The value 6 leaves the original time unchanged, 9 applies the three-day saving in the wrong direction by adding it, and 8 repeats the number of workers instead of counting days.
What is 144?
16
10
12
14
Correct answer: 12
A square root is the number that multiplies by itself to give the original, and 12 times 12 is 144. Squaring the others falls wide: 10 gives 100, 14 gives 196, and 16 gives 256, so not one of them returns 144.
A recipe requires 2 cups of flour for 12 cookies. How much flour is needed for 30 cookies?
3
2
4
5
Correct answer: 5
Twelve cookies take 2 cups, so one cookie takes a sixth of a cup and 30 cookies take 5 cups. The value 4 scales the recipe to 24 cookies rather than 30, 3 rounds the two and a half batches up and then reports batches as cups, and 2 repeats the quantity the recipe already lists.
Solve the inequality: 3x>18.
x > 8
x > 4
x > 2
x > 6
Correct answer: x > 6
Dividing both sides by 3 leaves x > 6, and the direction of the sign is unchanged because 3 is positive. The value x > 8 divides 24 by 3 after misreading the right side, x > 4 reads that side as 12, and x > 2 divides by 9 rather than by the coefficient 3.
What is the average of 14, 18, and 22?
27
14
22
18
Correct answer: 18
An average is the total divided by how many values were added, and 14 plus 18 plus 22 is 54, which divided by 3 gives 18. The value 27 divides that same total by 2, while 14 and 22 repeat the smallest and the largest figure in the list rather than balancing them.
If a circle has a radius of 7, what is its circumference? (Use π=3.14)
50.24
31.40
43.96
37.68
Correct answer: 43.96
Circumference is twice pi times the radius, so 2 times 3.14 times 7 gives 43.96. The value 31.40 works from a radius of 5, 37.68 from a radius of 6, and 50.24 from a radius of 8; the formula is right in each case but the radius is not the one given.
What is 53 plus 41?
11/20
17/20
16/20
13/20
Correct answer: 17/20
Rewriting both fractions over a denominator of 20 gives 12/20 plus 5/20, which totals 17/20. The value 13/20 converts the fifths but leaves the quarter as 1/20, 16/20 turns that quarter into 4/20, and 11/20 subtracts the stray 1/20 instead of adding a properly converted quarter.
A train leaves at 2:15 PM and arrives at 5:45 PM. How long is the trip?
2 hr 30 min
3 hr 00 min
4 hr 30 min
3 hr 30 min
Correct answer: 3 hr 30 min
From 2:15 to 5:15 is three whole hours, and the further stretch to 5:45 adds half an hour, giving 3 hr 30 min. The value 3 hr 00 min ignores the minutes even though they move from quarter past to quarter to, while 4 hr 30 min and 2 hr 30 min miscount the whole hours between 2 and 5 as four and as two.
If 2(x+3)=16, what is x?
8
6
5
7
Correct answer: 5
Dividing both sides by 2 leaves x plus 3 equal to 8, and taking 3 off gives 5. The value 8 stops at that intermediate total and reports it as x, while 6 and 7 come from subtracting the 3 before dividing, which leaves 13 to be halved and then rounded one way or the other.
What is 144 divided by 12, then multiplied by 3?
36
12
60
84
Correct answer: 36
Working left to right, 144 divided by 12 is 12, and that quotient multiplied by 3 gives 36. The value 12 stops at the quotient and never multiplies, while 60 and 84 multiply the quotient by 5 and by 7 in place of the 3 the question names.
A jacket originally priced at $60 is now $48. What is the percent decrease?
20%
40%
25%
30%
Correct answer: 20%
The price falls by 12,andapercentdecreasemeasuresthatfallagainsttheoriginalprice,so12dividedby60is0.20,or2048 sale price instead of the starting price, 30% treats the fall as 18,and4024.
What is the value of 5! (5 factorial)?
120
625
360
720
Correct answer: 120
A factorial multiplies every whole number from the given one down to 1, so 5 times 4 times 3 times 2 times 1 gives 120. The value 720 is the factorial of 6, which is what an off-by-one at the top of the chain produces when the run is started one number too high. The value 625 is 5 raised to the fourth power, from multiplying 5 by itself once for each of the four numbers below it instead of multiplying by those numbers. The value 360 comes from losing place in the descending run and writing the 3 twice, 5 times 4 times 3 times 3 times 2.
If a map scale is 1 inch = 50 miles, how many miles is 3.5 inches?
225
200
150
175
Correct answer: 175
Each inch on the map stands for 50 miles, so 3.5 inches stands for 3.5 multiplied by 50, which is 175 miles. The value 150 drops the half inch and works from 3 inches, 200 rounds the length up to 4 inches, and 225 works from 4.5 inches.
Solve for x: x2=49.
5
9
7
3
Correct answer: 7
Solving x squared equals 49 means finding the number that multiplies by itself to give 49, and 7 times 7 is 49. Squaring the others lands elsewhere: 3 gives 9, 5 gives 25, and 9 gives 81, so not one of them satisfies the equation.
What is the next number in the sequence 2, 6, 18, 54, ...?
486
162
324
216
Correct answer: 162
Each term is three times the term before it, since 2 becomes 6, 6 becomes 18 and 18 becomes 54, so 54 times 3 gives 162. The value 216 multiplies 54 by 4, 324 doubles the correct term, and 486 runs the pattern one step too far by tripling 162 as well.
If 30% of a number is 45, what is the number?
180
105
150
225
Correct answer: 150
Thirty percent of the number is 45, so the number is 45 divided by 0.30, which is 150. Check it: 30 percent of 150 is 45. The value 180 comes from dividing 45 by 0.25, reading the rate as a quarter. The value 105 is the other 70 percent of the number rather than the whole. The value 225 comes from dividing 45 by 0.20, reading the rate as a fifth.
A box contains 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble?
4 in 12
3 in 12
5 in 12
9 in 12
Correct answer: 3 in 12
The box holds 4 plus 3 plus 5, which is 12 marbles, and 3 of them are blue, so the chance of drawing blue is 3 in 12, the same as one quarter. The figure 4 in 12 counts the red marbles instead of the blue. The figure 9 in 12 is the chance of drawing a marble that is not blue. The figure 5 in 12 counts the green marbles instead of the blue.
What is the value of 9+6×2−4?
26
30
21
17
Correct answer: 17
Order of operations puts multiplication before addition and subtraction, so 6 times 2 is 12, and then 9 plus 12 minus 4 gives 17. The value 30 works left to right and also drops the final step, adding 9 and 6 to reach 15 and doubling it. The value 21 handles the product correctly but leaves out the subtraction of 4. The value 26 works strictly left to right, reaching 30 and then subtracting 4.
If a rectangular tank measures 2 ft by 3 ft by 4 ft, what is its volume?
16 cu ft
20 cu ft
24 cu ft
28 cu ft
Correct answer: 24 cu ft
Volume of a rectangular tank is length times width times height, so 2 times 3 times 4 gives 24 cu ft. The figure 16 cu ft is the combined area of the two 2 by 4 faces, which is an area and not a volume. The figure 20 cu ft adds the 3 by 4 face to the 2 by 4 face, mixing areas with volume again. The figure 28 cu ft doubles the 2 by 3 and 2 by 4 faces, a partial surface area rather than the space enclosed.
The lighthouse keeper, Elena, had tended the coastal beacon for nearly thirty years. She knew the rhythm of the tides better than the calendar on her wall and could predict a storm from the color of the morning sky. Though the work was solitary, she never felt alone; the steady pulse of the light and the distant horns of passing ships were companions enough. When the new automated system arrived to replace her, the harbor authority offered her a comfortable retirement in town. Elena declined, choosing instead to remain in a small cottage within sight of the tower she had faithfully kept.
Why does Elena decline the retirement offer in town?
She wants to resist the systems she now doubts
She wants to train the keeper she thinks ready
She wants to live beside the tower she guarded
She wants to watch the ships she safely guided
Correct answer: She wants to live beside the tower she guarded
Elena turns down the town retirement and moves into a cottage within sight of the tower she had faithfully kept, so she wants to live beside the tower she guarded. The passage records no objection to the automated equipment, so she wants to resist the systems she now doubts is not stated. No successor appears anywhere in the account, so she wants to train the keeper she thinks ready is invented. The passing vessels are described as company during her working years, not as a reason for staying, so she wants to watch the ships she safely guided misreads the ending.
Coral reefs are among the most biologically diverse ecosystems on Earth, supporting roughly a quarter of all marine species despite covering less than one percent of the ocean floor. These reefs are built by tiny animals called polyps, which secrete calcium carbonate to form hard skeletons over thousands of years. Rising ocean temperatures, however, cause polyps to expel the algae that give them both color and nourishment, a process known as bleaching. If temperatures remain elevated for too long, the weakened coral can die, threatening the countless organisms that depend on the reef for shelter and food.
According to the passage, what causes coral bleaching?
Failing carbonate skeletons
Warmer surrounding seawater
Persistent shelter shortage
Unchecked marine harvesting
Correct answer: Warmer surrounding seawater
The passage says rising ocean temperatures make polyps expel the algae that feed and color them, and it names that expulsion as bleaching, so warmer surrounding seawater is the stated cause. Failing carbonate skeletons would slow reef building rather than trigger the loss of algae. Unchecked marine harvesting is never raised anywhere in the passage. A persistent shelter shortage is presented as a consequence for the organisms living on a dying reef, not as the trigger for bleaching.
When the city council proposed converting an abandoned rail line into a public greenway, reactions were mixed. Supporters argued that the trail would provide safe space for walking and cycling while preserving a piece of local history. Opponents worried about the cost of maintenance and the potential for increased foot traffic near residential yards. After months of debate and several public hearings, the council approved a scaled-down version of the plan, funding the first mile while postponing decisions about the remaining route.
What was the outcome of the council's debate?
The council approved the trimmed initial mile
The council auctioned the whole rail corridor
The council rejected the greenway trail today
The council endorsed the entire cycling route
Correct answer: The council approved the trimmed initial mile
After months of hearings the council backed a scaled down version that paid for one mile and left the rest of the route undecided, so the council approved the trimmed initial mile. Nothing in the passage puts the corridor up for sale, so the council auctioned the whole rail corridor is not supported. The plan moved forward rather than being turned down, so the council rejected the greenway trail today reverses the outcome. Funding stopped at the first mile, so the council endorsed the entire cycling route overstates what was agreed.
Marcus had always assumed that learning a second language required living abroad. After being assigned to an overseas post, he discovered that immersion alone was not enough; without deliberate study, he picked up only scattered phrases. It was not until he committed to daily practice with a tutor, paired with the constant exposure of his surroundings, that real progress began. He came to believe that fluency demanded both consistent effort and an environment rich with opportunities to use the language.
What conclusion does Marcus reach about learning a language?
Fluency comes from years spent living fully overseas
Fluency comes from steady study plus daily immersion
Fluency comes from practice once formal tutors leave
Fluency comes from scattered phrases picked up daily
Correct answer: Fluency comes from steady study plus daily immersion
Marcus finds that being surrounded by the language gave him only fragments until he added daily work with a tutor, and he concludes that fluency comes from steady study plus daily immersion. His own experience abroad disproves the claim that fluency comes from years spent living fully overseas. He credits the tutor for the turn in his progress, so fluency comes from practice once formal tutors leave contradicts him. He treats the fragments he absorbed as evidence of failure, so fluency comes from scattered phrases picked up daily is the position he abandoned.
The invention of the mechanical clock transformed the way people organized their lives. Before its widespread use, communities measured time loosely by the position of the sun or the ringing of church bells. The clock introduced a precise, shared standard that allowed activities such as markets, schooling, and labor to be coordinated across an entire town. Some historians argue that this newfound precision laid the groundwork for the disciplined schedules that would later define industrial society.
What does the passage suggest the mechanical clock made possible?
Diminishing church bell influence
Vanishing seasonal farming cycles
Shared timetables throughout town
Extended workday industrial labor
Correct answer: Shared timetables throughout town
The passage credits the clock with a precise common standard that let markets, schooling and labor be coordinated across a whole town, so shared timetables throughout town is what it made possible. Diminishing church bell influence describes what the bells stopped doing, which the passage mentions only as the older way of marking time. Vanishing seasonal farming cycles appears nowhere in the passage. Extended workday industrial labor is a later development the passage links to disciplined schedules, not something the clock itself is said to have produced.
Although honey never truly spoils, its appearance can change dramatically over time. Crystallization, in which the sugars form solid granules, often leads people to believe the honey has gone bad. In reality, this is a natural process that can be reversed by gently warming the jar. The low moisture content and natural acidity of honey create an environment in which bacteria cannot survive, which is why archaeologists have discovered edible honey in ancient tombs.
Why does honey resist spoiling, according to the passage?
Low moisture plus acidity blocks bacterial growth
Sugar granules crush harmful microbes fairly fast
Airtight jars exclude outside moisture quite well
Gentle warming kills resident bacteria year round
Correct answer: Low moisture plus acidity blocks bacterial growth
The passage says honey's low moisture content and natural acidity create conditions bacteria cannot survive in, so low moisture plus acidity blocks bacterial growth is the stated reason. Warming is described only as a way to undo crystallization, so gentle warming kills resident bacteria year round misuses that detail. Crystallization is called a harmless natural change, so sugar granules crush harmful microbes fairly fast credits it with something the passage denies. Honey found in ancient tombs kept without modern packaging, so airtight jars exclude outside moisture quite well is not the explanation given.
The factory had operated on the same production schedule for decades, but a new supervisor noticed that defects spiked every afternoon. Rather than blaming the workers, she studied the data and found that fatigue and a poorly timed lunch break were the likely culprits. By rearranging shifts and adding a short midafternoon rest, she reduced errors significantly without lowering output. Her approach demonstrated that examining a problem carefully often reveals solutions that punishment cannot.
What is the main point of the passage?
The supervisor studies the data instead of faulting the staff, finds fatigue and a badly placed break, and cuts errors by rescheduling, which shows that careful analysis reveals fixes blame overlooks. The long standing schedule is what produced the afternoon spike, so older factory routines produce stronger output is contradicted. The passage credits rescheduling rather than discipline, so punishing tired workers ends afternoon defects is the approach she declined. She added rest instead of taking it away, so removing midday breaks raises afternoon output reverses her fix.
Deserts are often imagined as lifeless expanses of sand, but they teem with organisms adapted to extreme conditions. Many desert animals are nocturnal, avoiding the punishing daytime heat by remaining in burrows until dusk. Plants such as cacti store water in thick stems and reduce moisture loss with waxy coatings and spines instead of leaves. These adaptations allow life to flourish where rainfall may not fall for months at a time.
Which statement best reflects the passage's view of deserts?
Deserts sustain creatures through clever adjustment
Deserts receive frequent rainfall through downpours
Deserts remain barren wastelands through summertime
Deserts support animals through vanished vegetation
Correct answer: Deserts sustain creatures through clever adjustment
The passage sets nocturnal habits, water storing stems, waxy coatings and spines against the picture of an empty landscape, so deserts sustain creatures through clever adjustment is the view it takes. It states that rain may not fall for months, so deserts receive frequent rainfall through downpours is the opposite of the text. It opens by rejecting the lifeless image, so deserts remain barren wastelands through summertime is the assumption it corrects. Cacti are given as a central example, so deserts support animals through vanished vegetation ignores the plants the passage describes.
When Priya volunteered to lead the school recycling drive, she expected enthusiasm from her classmates. Instead, participation was low until she changed her strategy. Rather than simply asking students to bring in materials, she organized a friendly competition between homerooms, complete with a weekly tally posted in the hallway. Almost overnight, collection rates soared, and what had once felt like a chore became a point of pride.
What strategy increased participation in the recycling drive?
Starting the rival homeroom contest
Making the drive mandatory homework
Lowering the weekly material target
Offering the classmates cash prizes
Correct answer: Starting the rival homeroom contest
Participation stayed flat until Priya set the homerooms against one another and posted a running tally, after which collection rates soared, so starting the rival homeroom contest is the strategy that worked. She never eased the quota, so lowering the weekly material target is not in the passage. Nothing was compelled, so making the drive mandatory homework misstates a voluntary effort. The only reward described is a posted tally and a sense of pride, so offering the classmates cash prizes adds an incentive the passage does not contain.
The human brain consumes a disproportionate share of the body's energy. Though it accounts for only about two percent of body weight, it uses roughly twenty percent of the energy a person burns at rest. This demand reflects the constant electrical activity of billions of neurons, which never fully shut down even during sleep. Researchers continue to study how the brain manages such high energy needs while maintaining the delicate balance required for thought and memory.
What does the passage emphasize about the brain?
It switches off entirely once its owner sleeps
It marks twenty percent toward its body weight
It demands nothing further once its owner naps
It devours reserves well beyond its small bulk
Correct answer: It devours reserves well beyond its small bulk
The passage sets about two percent of body weight against roughly twenty percent of resting energy, so it devours reserves well beyond its small bulk is the point being made. Neurons are described as never fully shutting down, so it switches off entirely once its owner sleeps contradicts the text. The twenty percent figure is a share of energy and not of mass, so it marks twenty percent toward its body weight swaps the two numbers. Resting is exactly when the twenty percent is measured, so it demands nothing further once its owner naps reverses the finding.
In the early days of aviation, pilots navigated largely by sight, following rivers, roads, and rail lines below them. This method, known as pilotage, worked well in clear weather but failed at night or in heavy clouds. The development of radio beacons and, later, instrument flying allowed aircraft to travel safely regardless of visibility. These advances expanded air travel from a fair-weather novelty into a dependable form of transportation.
Why was pilotage an unreliable navigation method?
It suited flights above wide ocean water
It broke down whenever thick fog arrived
It needed costly onboard radio sets then
It met official bans from air regulators
Correct answer: It broke down whenever thick fog arrived
Flying by landmarks worked in clear weather and stopped working at night or in heavy cloud, so it broke down whenever thick fog arrived is why the method was unreliable. Landmarks are rivers, roads and rail lines, so it suited flights above wide ocean water inverts the conditions it needed. Radio equipment belongs to the later fix rather than to the method itself, so it needed costly onboard radio sets then confuses the two eras. No prohibition appears anywhere, so it met official bans from air regulators is invented.
The committee had gathered to decide the fate of the old town theater, a building that had stood empty for years. Some members favored demolition, citing safety hazards and the cost of repairs. Others insisted the theater was a cultural landmark worth saving. A local architect proposed a compromise: restore the historic facade while modernizing the interior for community events. The plan won enough support to move forward, preserving the building's character while giving it a practical new purpose.
What did the architect's proposal accomplish?
It left the empty building awaiting further study
It saved the aged facade behind updated interiors
It sent the whole theater toward rapid demolition
It turned the theater toward rented office suites
Correct answer: It saved the aged facade behind updated interiors
The architect offered a middle course that kept the historic front and refitted the inside for community use, and it won support, so it saved the aged facade behind updated interiors. The plan moved forward at once, so it left the empty building awaiting further study describes the deadlock the compromise ended. Demolition was the position the compromise defeated, so it sent the whole theater toward rapid demolition names the losing side. The refitted space is for community events, so it turned the theater toward rented office suites changes the purpose.
Sleep is not a single uniform state but a cycle of distinct stages. During deep sleep, the body repairs tissue and strengthens the immune system, while during the dreaming stage the brain consolidates memories from the day. Disrupting these cycles, even without reducing total sleep time, can leave a person feeling unrested. This is why experts emphasize the quality of sleep, not merely its duration.
What does the passage suggest about restful sleep?
Sleep quality matters beyond mere duration
Dreaming stages block bodily tissue repair
Total sleep hours decide overall alertness
Deep sleep provides little lasting benefit
Correct answer: Sleep quality matters beyond mere duration
Because broken cycles leave a person unrested even when the hours are unchanged, the passage ends on the view that sleep quality matters beyond mere duration. It says explicitly that unchanged total time can still leave someone tired, so total sleep hours decide overall alertness is ruled out. The dreaming stage is credited with consolidating memories, so dreaming stages block bodily tissue repair invents a conflict. Deep sleep is where tissue repair and immune strengthening happen, so deep sleep provides little lasting benefit contradicts the passage.
The startup had grown quickly, but its rapid expansion created confusion about who was responsible for what. Decisions stalled as employees waited for someone else to take charge. Recognizing the problem, the founder introduced clear roles and a simple chain of approval. Within weeks, projects that had once languished began moving forward, proving that even a small organization benefits from defined structure.
What problem did the startup face before the founder acted?
Fast growth left nobody sure who owned what, and work halted while people waited on each other, so unclear duties froze routine decisions names the problem. Money is never mentioned, so limited startup investor cash reserves is outside the passage. The company had grown quickly and had people to spare, so meager experienced employee head count misreads the situation. The founder added a chain of approval as the cure, so heavy written internal approval habits describes the fix rather than the fault.
Bioluminescence, the production of light by living organisms, occurs in creatures ranging from fireflies to deep-sea fish. In the ocean depths where sunlight never reaches, many animals generate their own light to attract prey, find mates, or confuse predators. The light is produced by a chemical reaction involving a molecule called luciferin and an enzyme that triggers it. Unlike a household bulb, this glow generates almost no heat, making it remarkably efficient.
According to the passage, why is bioluminescence considered efficient?
It releases very little wasted heat
It avoids the chemical trigger step
It lasts through an animal lifetime
It throws a startlingly bright glow
Correct answer: It releases very little wasted heat
The passage contrasts the glow with a household bulb and says it produces almost none of the heat a bulb wastes, so it releases very little wasted heat is the stated reason for calling it efficient. Luciferin and its enzyme are named as the mechanism, so it avoids the chemical trigger step denies the very process described. Duration is never discussed, so it lasts through an animal lifetime is not supported. Brightness is never claimed either, so it throws a startlingly bright glow is beside the point the passage makes.
The young coach inherited a team that had lost every game the previous season. Rather than focusing immediately on winning, he emphasized fundamentals and effort, praising improvement over results. Players who had once dreaded practice began to show up early. By midseason the team had not become champions, but they had become competitive, and more importantly, they had learned to believe in their own progress.
What did the coach prioritize at first?
Shorter weekly squad practice sessions
Instant championship game trophy plans
Fresh outside player recruitment trips
Sound fundamentals plus patient effort
Correct answer: Sound fundamentals plus patient effort
The coach set aside the scoreboard and praised improvement instead, which is why sound fundamentals plus patient effort describes what he put first. Players began arriving early rather than practicing less, so shorter weekly squad practice sessions reverses what happened. He worked with the squad he inherited, so fresh outside player recruitment trips adds something the passage never mentions. Chasing silverware is exactly what he declined to do at the start, so instant championship game trophy plans is the opposite of his approach.
Glaciers act as natural reservoirs, storing water as ice during cold seasons and releasing it gradually as they melt. Many rivers that supply drinking water and irrigation to millions of people are fed by glacial meltwater. As global temperatures rise, however, glaciers are shrinking faster than they can be replenished by snowfall. Scientists warn that the loss of these frozen reservoirs could threaten water supplies for communities that have relied on them for generations.
Why are shrinking glaciers a concern, according to the passage?
They cut yearly snowfall over frozen reservoirs
They endanger ice fed supplies miles downstream
They raise inland river salinity levels steeply
They slowly lower sea levels across communities
Correct answer: They endanger ice fed supplies miles downstream
Rivers carrying drinking water and irrigation to millions are fed by glacial melt, and scientists warn those supplies are at risk as the ice shrinks, so they endanger ice fed supplies miles downstream. Snowfall is what fails to replace the ice rather than something the glaciers reduce, so they cut yearly snowfall over frozen reservoirs reverses the relationship. Salt content is never raised in the passage, so they raise inland river salinity levels steeply is invented. Melting ice adds water rather than removing it, so they slowly lower sea levels across communities runs the wrong way.
The librarian noticed that the children's reading room was rarely used, despite a generous collection of books. After speaking with families, she learned that parents found the formal, quiet atmosphere intimidating for young children. In response, she introduced weekly story hours, soft seating, and a relaxed policy on noise. Attendance climbed steadily, and the room became one of the busiest parts of the library.
What caused the children's reading room to be underused at first?
A steady weekly reading charge
A stiff formal library setting
A small picture book selection
A poor daily opening timetable
Correct answer: A stiff formal library setting
Parents told the librarian the hush and formality put young children off, so a stiff formal library setting is what kept the room empty. No charge is mentioned anywhere, so a steady weekly reading charge is invented. Opening times are never raised as an obstacle, so a poor daily opening timetable is unsupported. The passage says the collection was generous, so a small picture book selection contradicts the text directly.
Volcanic eruptions can have effects that reach far beyond the immediate area. When a large eruption ejects ash and gases high into the atmosphere, these particles can spread around the globe and reflect sunlight back into space. The result is a temporary cooling of the planet's surface. Historical records describe years following major eruptions in which crops failed and summers turned unusually cold, illustrating how a single event can influence weather worldwide.
How can a large volcanic eruption affect global climate?
By briefly cooling the surface using reflected light
By sharply raising the rainfall soaking crop regions
By slowly thickening the ozone gases massed overhead
By gently warming the whole planet enduringly onward
Correct answer: By briefly cooling the surface using reflected light
Ash and gas thrown high into the atmosphere spread worldwide and bounce sunlight back into space, dropping surface temperatures for a time, so by briefly cooling the surface using reflected light is the mechanism given. Crops are said to fail in the years afterward, so by sharply raising the rainfall soaking crop regions misreads that detail. The ozone layer is never mentioned, so by slowly thickening the ozone gases massed overhead is invented. The effect described is cooling and temporary, so by gently warming the whole planet enduringly onward is wrong in both direction and duration.
After the storm knocked out power to the neighborhood, the residents discovered an unexpected sense of community. With phones dimmed and televisions dark, families gathered on porches and shared meals cooked over grills. Neighbors who had barely spoken introduced themselves and checked on the elderly down the street. When the lights finally returned, several remarked that they almost missed the quiet days of connection.
What unexpected effect did the power outage have?
It deepened the household phone routines
It wrecked the nearby porches completely
It pulled the distant neighbors together
It propelled the longtime residents away
Correct answer: It pulled the distant neighbors together
With screens dark, families ate on porches, strangers introduced themselves and people checked on the elderly, so it pulled the distant neighbors together is the unexpected effect. Phones were dimmed and televisions dark, so it deepened the household phone routines is the reverse of what the passage reports. Damage to property is never described, so it wrecked the nearby porches completely is invented. Residents stayed and later missed the quiet days, so it propelled the longtime residents away contradicts the ending.
The migration of monarch butterflies is one of nature's most remarkable journeys. Each year, these fragile insects travel thousands of miles between North America and central Mexico, a trip that spans multiple generations. No single butterfly completes the entire round journey; instead, offspring continue a route their parents began. How they navigate with such precision, returning to the same forests their ancestors left, remains a subject of scientific wonder.
What is unusual about the monarch migration described in the passage?
The route changes considerably yearly
The butterflies travel past nightfall
The voyage occupies several lifetimes
Single insects complete the roundtrip
Correct answer: The voyage occupies several lifetimes
No individual butterfly finishes the whole circuit; offspring carry on a route their parents started, so the voyage occupies several lifetimes is what the passage calls remarkable. Time of day is never discussed, so the butterflies travel past nightfall is not supported. The passage stresses precision and a return to the same forests, so the route changes considerably yearly contradicts it. The text states outright that no single butterfly makes the full round trip, so single insects complete the roundtrip is the claim it denies.
The negotiation between the two companies had stalled for weeks over a single disputed clause. Each side feared that conceding would signal weakness. A mediator suggested that both parties step back and identify their underlying interests rather than their stated positions. Once they realized their goals were not truly in conflict, a creative solution emerged that satisfied both. The deal closed within days.
What allowed the negotiation to succeed?
Quietly abandoning the stalled deal entirely
Conceding the disputed clause fairly quickly
Naming the hidden interests behind positions
Hiring the toughest possible outside advisor
Correct answer: Naming the hidden interests behind positions
The mediator told both sides to look past their stated demands to what each actually needed, they found their goals compatible, and the deal closed, so naming the hidden interests behind positions is what broke the deadlock. The agreement was signed rather than dropped, so quietly abandoning the stalled deal entirely reverses the ending. A mediator rather than a hard bargainer was brought in, so hiring the toughest possible outside advisor misreads the role. Both sides feared looking weak and neither gave way, so conceding the disputed clause fairly quickly is the move they avoided.
Antibiotics revolutionized medicine by making once-deadly infections treatable, but their overuse has created a serious problem. When bacteria are repeatedly exposed to these drugs, the few that survive pass on their resistance to future generations. Over time, strains emerge that no longer respond to common treatments. Doctors now urge careful, limited use of antibiotics to slow the spread of resistant bacteria.
What is the consequence of antibiotic overuse described in the passage?
Survivors of repeated exposure hand their resistance to later generations until the drugs stop working, so tougher bacterial strains gradually multiply is the consequence described. The drugs lose ground rather than gaining it, so antibiotics become steadily stronger overall inverts the passage. Detection is never mentioned, so infections escape routine hospital detection is invented. Resistant survivors keep breeding, which is the whole mechanism, so bacteria halt reproduction almost completely contradicts the text.
The new employee orientation had always been a dull affair of lengthy lectures and stacks of paperwork. A human resources manager decided to redesign it around hands-on activities and conversations with current staff. New hires now spent their first day touring departments, asking questions, and solving sample problems. Surveys showed that employees felt more prepared and connected, and turnover among first-year workers dropped noticeably.
What was the result of redesigning the orientation?
Basic training shrank and newer hires knew little
Paperwork stacks grew and office morale sank fast
Sessions ran longer and duller lectures came back
Early turnover fell and recent hires felt readier
Correct answer: Early turnover fell and recent hires felt readier
Surveys after the redesign showed staff feeling better prepared and connected while departures in the first year declined, so early turnover fell and recent hires felt readier. The new day was full of tours, questions and sample problems, so basic training shrank and newer hires knew little misstates the change. Paperwork was what the redesign removed, so paperwork stacks grew and office morale sank fast reverses it. Lectures were replaced by activities, so sessions ran longer and duller lectures came back describes the old format.
Tides are caused primarily by the gravitational pull of the moon on the Earth's oceans. As the moon orbits, it draws the water toward it, creating a bulge that produces high tide, while areas at right angles experience low tide. The sun also influences tides, though to a lesser degree. When the sun and moon align, their combined pull produces especially high tides known as spring tides.
What primarily causes ocean tides, according to the passage?
Continuous lunar tidal attraction
Ordinary daily planetary rotation
Changing ocean temperature layers
Persistent offshore wind patterns
Correct answer: Continuous lunar tidal attraction
The passage opens by saying tides come chiefly from the moon drawing the oceans toward it, so continuous lunar tidal attraction is the primary cause. Spin alone is never given as a cause, so ordinary daily planetary rotation is unsupported. Heat is never mentioned in connection with tides, so changing ocean temperature layers is invented. Only the sun is credited with a secondary role, so persistent offshore wind patterns names a force the passage never raises.
When the small bakery introduced an online ordering system, the owner worried it would feel impersonal. To her surprise, the change freed her staff from taking phone orders, giving them more time to chat with customers in the shop. Regulars appreciated skipping the line, and new customers discovered the bakery through its website. Far from replacing the personal touch, technology had made room for it.
What does the passage suggest about the online ordering system?
It abolished the need for shop assistants
It made the bakery itself feel impersonal
It shrank the weekly customer count badly
It allowed the counter staff longer chats
Correct answer: It allowed the counter staff longer chats
Taking orders online lifted the phone work off the counter and left more room for talking with people in the shop, so it allowed the counter staff longer chats. Staff were still needed and simply did different work, so it abolished the need for shop assistants overstates the change. New customers found the shop through its website, so it shrank the weekly customer count badly is the opposite of what happened. The owner's fear proved unfounded, so it made the bakery itself feel impersonal is the outcome the passage rules out.
The Renaissance was marked by a renewed interest in the art and learning of ancient Greece and Rome. Scholars rediscovered classical texts that had been preserved in monasteries and distant libraries, sparking fresh inquiry into science, philosophy, and the arts. Wealthy patrons funded artists and thinkers, and the invention of the printing press spread these ideas across Europe with unprecedented speed. This convergence of curiosity, money, and technology transformed the continent.
Which factor helped spread Renaissance ideas rapidly across Europe?
The gradual wealthy patron withdrawal
The widening classical text shortages
The sharply reduced overseas commerce
The recently perfected printing press
Correct answer: The recently perfected printing press
The passage credits one technology with carrying the new thinking across the continent at unprecedented speed, so the recently perfected printing press is the factor named. Trade is never discussed, so the sharply reduced overseas commerce is outside the text. Classical works were being rediscovered rather than lost, so the widening classical text shortages reverses the situation. Wealthy patrons are described as funding artists and thinkers, so the gradual wealthy patron withdrawal contradicts the passage.
The expedition team had trained for months, but nothing prepared them for the thin mountain air above the base camp. Simple tasks left them breathless, and progress slowed to a crawl. Their guide insisted on a measured pace and frequent rest, explaining that the body needed time to adjust to the altitude. Those who heeded the advice eventually reached the summit, while one climber who pushed ahead too quickly was forced to turn back.
What lesson does the passage convey about high-altitude climbing?
Hard training erases the whole climbing danger
Quicker climbers reach the summit ahead anyway
Rest proves needless across the highest slopes
The body needs unhurried days adjusting upward
Correct answer: The body needs unhurried days adjusting upward
The guide insists on a measured pace and frequent halts because acclimatizing takes time, and the climbers who obeyed reached the top, so the body needs unhurried days adjusting upward. The passage says months of preparation left them unready for the thin air, so hard training erases the whole climbing danger is refuted in its opening line. The climber who hurried had to turn back, so quicker climbers reach the summit ahead anyway is contradicted by the ending. Frequent rest is the guide's central instruction, so rest proves needless across the highest slopes denies it.
A community garden began as a single plot tended by a retired teacher who wanted fresh vegetables. Curious neighbors asked to join, and soon the empty lot was divided into dozens of beds. Beyond the produce, the garden became a gathering place where people of different ages and backgrounds traded seeds, recipes, and stories. What started as one person's hobby had grown into a shared resource that nourished both bodies and relationships.
How did the community garden change over time?
It grew showy blossoms alone lacking food crops
It expanded past one patch toward shared ground
It passed quietly toward one large produce farm
It sat unused once its local neighbors departed
Correct answer: It expanded past one patch toward shared ground
One teacher's vegetable bed drew curious neighbors until the lot held dozens of beds and became a place to trade seeds, recipes and stories, so it expanded past one patch toward shared ground. Ownership never changes hands, so it passed quietly toward one large produce farm is invented. Fresh vegetables are the starting point and the produce is named throughout, so it grew showy blossoms alone lacking food crops contradicts the text. Neighbors joined rather than left, so it sat unused once its local neighbors departed reverses the story.
Camouflage in nature takes many forms beyond simply blending into the background. Some creatures mimic the appearance of dangerous animals to ward off predators, while others change color to match shifting surroundings. Certain insects resemble twigs or leaves so closely that they vanish in plain sight. These strategies, refined over countless generations, demonstrate the inventive ways living things avoid becoming prey.
What is the main idea of the passage?
The passage lists mimicry of dangerous animals, color change to match surroundings, and bodies shaped like twigs or leaves, so camouflage adopts widely varied physical shapes is its main idea. These strategies are presented as effective ways of avoiding becoming prey, so camouflage rarely fools alert hunting predators works against the text. Insects are one example among several, so camouflage occurs solely among crawling insects narrows the passage wrongly. Variety is the whole point, so camouflage follows one identical natural method states the reverse.
The author of the report had buried its most important finding deep in the final pages. As a result, busy executives skimmed the opening summary and missed the urgent warning entirely. When a colleague pointed out the oversight, the author revised the document to lead with the critical conclusion. The episode underscored a lesson familiar to skilled writers: place the most vital information where readers will actually find it.
What lesson does the passage illustrate?
Busy executives avoid opening summaries entirely
Serious warnings deserve quiet protective burial
Lengthy reports outperform shorter clearer texts
Vital findings deserve prominent early placement
Correct answer: Vital findings deserve prominent early placement
The warning went unread until the author moved it to the front, and the closing line tells writers to put the most important material where readers will actually look, so vital findings deserve prominent early placement. Length is never praised, so lengthy reports outperform shorter clearer texts is unsupported. Burying the warning is the mistake the episode corrects, so serious warnings deserve quiet protective burial states the error as a rule. The executives did read the summary and only missed what was hidden later, so busy executives avoid opening summaries entirely misreads them.
The river that wound through the valley had shaped the region for centuries. Farmers depended on its waters for irrigation, and merchants used it as a highway for goods. Yet the same river that brought prosperity could turn destructive, flooding fields and homes after heavy rains. The people who lived along its banks learned to respect both its generosity and its dangers, building their lives around its unpredictable moods.
How did the people view the river, according to the passage?
As a menace needing eradication
As a wholly beneficial neighbor
As a generous perilous presence
As a worthless shipping channel
Correct answer: As a generous perilous presence
The people along the banks learned to respect the river's generosity and its dangers together and shaped their lives around both, so as a generous perilous presence is how they saw it. They built their lives around the river rather than trying to be rid of it, so as a menace needing eradication misses the balance. Merchants used it as a highway for goods, so as a worthless shipping channel contradicts the passage. Floods ruined fields and homes, so as a wholly beneficial neighbor leaves out half of what the passage says.
Memory is far less reliable than most people assume. Rather than storing events like a video recording, the brain reconstructs them each time they are recalled, often filling gaps with assumptions or details borrowed from later experiences. This means that a vivid memory can feel completely accurate while containing significant errors. Researchers caution that confidence in a memory is no guarantee of its truth.
What does the passage say about confident memories?
Confident memories are sometimes seriously mistaken
Confident memories are permanently fixed recordings
Confident memories are single unrepeatable episodes
Confident memories are invariably entirely faithful
Correct answer: Confident memories are sometimes seriously mistaken
The passage closes by cautioning that confidence in a memory is no guarantee of its truth, so confident memories are sometimes seriously mistaken. They are not invariably entirely faithful, because recall fills gaps with assumptions and details borrowed from later experiences. They are not permanently fixed recordings, since the brain rebuilds an event every time it is retrieved rather than storing it like video. And they are not single unrepeatable episodes; the passage describes the same memory being recalled again and again.
The remote village had no doctor, so when illness struck, residents traveled hours to the nearest clinic. A nonprofit organization addressed the gap by training local volunteers to handle basic medical needs and recognize serious cases requiring transport. Equipped with simple tools and a radio link to distant physicians, these volunteers dramatically improved care. The program showed that meaningful health gains do not always require expensive hospitals.
What was the key to improving health care in the village?
Supplying the village itself with salaried city doctors
Coaching the village helpers with faraway expert backup
Treating the village sick with distant monthly journeys
Providing the village elders with costly hospital wards
Correct answer: Coaching the village helpers with faraway expert backup
Care improved by coaching the village helpers with faraway expert backup: a nonprofit trained local volunteers, gave them simple tools, and put them on a radio link to distant physicians. Supplying the village itself with salaried city doctors never happened, and the passage says the place still had no doctor of its own. Treating the village sick with distant monthly journeys is the problem the program removed, not the remedy it supplied. Providing the village elders with costly hospital wards is exactly what the closing line says meaningful health gains do not require.
Bridges must be designed to handle forces that constantly push and pull against their structures. Engineers account for the steady weight of the bridge itself, the changing load of traffic, and dynamic forces such as wind and earthquakes. A successful design distributes these stresses so that no single part bears too much. The elegance of a great bridge lies not only in its appearance but in the invisible balance of forces holding it together.
According to the passage, what defines a successful bridge design?
Polishing the surface alone around the front
Choosing the heaviest metals around the deck
Spreading the strain evenly around the frame
Ignoring the gusting winds around the valley
Correct answer: Spreading the strain evenly around the frame
A successful design distributes stresses so that no single part bears too much, which is spreading the strain evenly around the frame. Polishing the surface alone around the front fails because the passage says elegance lies in the invisible balance of forces rather than in appearance. Choosing the heaviest metals around the deck only adds to the steady dead weight that the passage lists as one of the loads a design must already carry. Ignoring the gusting winds around the valley contradicts the requirement to account for dynamic forces such as wind and earthquakes.
Two children sit on a seesaw. If one child is heavier, where should the lighter child sit to balance it?
A slightly shorter stretch from the pivot
A wholly negligible offset from the pivot
A markedly longer distance from the pivot
A totally arbitrary spread from the pivot
Correct answer: A markedly longer distance from the pivot
A seesaw balances when weight multiplied by distance matches on both sides, so the lighter child needs a markedly longer distance from the pivot to build the same moment as the heavier one. A slightly shorter stretch from the pivot shrinks the lighter child's moment and tips the board even further. A wholly negligible offset from the pivot leaves almost no moment arm, so the lighter child contributes almost nothing. A totally arbitrary spread from the pivot cannot balance the board, because only one separation satisfies the moment equation.
A first-class lever has the fulcrum located where?
Resting underneath the effort and the load
Overhanging beyond the effort and the load
Precisely dividing the effort and the load
Standing alongside the effort and the load
Correct answer: Precisely dividing the effort and the load
A first-class lever carries its pivot precisely dividing the effort and the load, so that one arm falls on either side of it, as in a seesaw or a pair of scissors. Resting underneath the effort and the load would leave the two arms no separation along the bar, so pressing down could raise nothing. Overhanging beyond the effort and the load puts the pivot off the bar altogether, which matches no lever class. Standing alongside the effort and the load shrinks the load arm to nothing, so the bar would simply lift as one rigid piece.
Which simple machine is a doorknob an example of?
A rope and pulley rig
A wheel and axle unit
A beam and lever pair
A slope and wedge set
Correct answer: A wheel and axle unit
Turning a doorknob rotates a large outer knob that drives a much narrower inner spindle, and that pairing of a broad turning grip with a slim shaft is a wheel and axle unit. A rope and pulley rig would need a flexible line running in a grooved sheave to redirect a pull, and the knob has no line. A beam and lever pair would need a fulcrum with effort and load set apart along a rigid bar, which the knob does not provide. A slope and wedge set works by driving a sloping face into something, and nothing inside a doorknob slopes.
If two gears mesh and the driver gear is larger than the driven gear, the driven gear will turn:
At a markedly slower rate
At a wildly unsteady rate
At a fully unchanged rate
At a plainly quicker rate
Correct answer: At a plainly quicker rate
The smaller driven gear carries fewer teeth, so it must complete several revolutions for each revolution of the larger driver, and it therefore turns at a plainly quicker rate. At a markedly slower rate describes the opposite pairing, in which the driven gear is the bigger of the two. At a fully unchanged rate would require both gears to carry the same tooth count. At a wildly unsteady rate is impossible, because meshed teeth lock the two shafts into one fixed ratio.
A pulley system with two supporting rope segments provides a mechanical advantage of approximately:
2
6
3
5
Correct answer: 2
The mechanical advantage of a pulley block is set by how many lengths of rope actually carry the load, so a system with two supporting segments gives about 2. A value of 3 would require a third supporting length threaded through the blocks. A value of 5 would require five such lengths, and a value of 6 would require six, neither of which matches the system described.
Increasing the length of a ramp while keeping the height the same will:
Enlarge the effort exerted along the slope
Steady the tension endured along the slope
Diminish the force applied along the slope
Multiply the weight hauled along the slope
Correct answer: Diminish the force applied along the slope
A longer ramp reaching the same height has a gentler gradient, so it will diminish the force applied along the slope while lengthening the distance traveled. Enlarge the effort exerted along the slope reverses the relationship, since a shallower incline demands less push rather than more. Steady the tension endured along the slope ignores the gradient change entirely, and a ramp's whole advantage comes from that gradient. Multiply the weight hauled along the slope confuses force with weight; the load weighs the same however long the ramp is.
Which material is the best conductor of electricity?
Thick rubber sheet
Bright copper wire
Polished glass rod
Seasoned oak plank
Correct answer: Bright copper wire
Copper is a metal whose loosely held outer electrons drift freely through the lattice, so bright copper wire carries current far better than the other choices. Thick rubber sheet is a standard insulator, used precisely because it blocks current. Polished glass rod is also an insulator, and polishing alters only its surface, never its resistance. Seasoned oak plank conducts poorly as well, and seasoning drives out the trace moisture that might otherwise let a little current pass.
When a fluid flows through a pipe that narrows, the fluid's speed:
Sinks markedly at that point
Collapses fast at that point
Remains steady at that point
Climbs sharply at that point
Correct answer: Climbs sharply at that point
The same volume of fluid must cross every section of a filled pipe each second, so where the bore shrinks the flow climbs sharply at that point. Sinks markedly at that point would mean less fluid leaving the constriction than entering it, which the continuity principle forbids. Remains steady at that point ignores the change in cross-section altogether. Collapses fast at that point describes a blockage rather than a taper, and a narrowed pipe still passes the whole flow.
A wedge is essentially which simple machine?
A revolving spiral screw
A rolling grooved pulley
A sliding inclined plane
A swinging pivoted lever
Correct answer: A sliding inclined plane
A wedge is a sliding inclined plane: rather than an object being pushed up a fixed slope, the slope itself is driven forward and forces material apart. A revolving spiral screw does its work by turning in place so that a thread draws material along, rather than by being driven bodily forward. A rolling grooved pulley redirects a line over a wheel and presents no sloping face at all. A swinging pivoted lever turns about a fulcrum, and a wedge has no fulcrum.
If you double the number of supporting ropes in a pulley system, the force needed to lift a load will:
Practically half the earlier pull
Nearly quadruple the earlier pull
Exactly matching the earlier pull
Precisely double the earlier pull
Correct answer: Practically half the earlier pull
Doubling the number of rope segments that support the load doubles the mechanical advantage, so the effort drops to practically half the earlier pull. Precisely double the earlier pull inverts the relationship, since adding supporting segments eases a lift rather than burdening it. Nearly quadruple the earlier pull compounds that same error. Exactly matching the earlier pull would mean the extra segments carry none of the weight, which is not how a block and tackle shares a load.
Which of these increases the friction between two surfaces?
Polishing the sliding metal
Roughening the mating faces
Greasing the loaded contact
Lifting the pressing burden
Correct answer: Roughening the mating faces
Friction grows when the microscopic high points of two bodies interlock more deeply, so roughening the mating faces raises it. Polishing the sliding metal does the reverse by flattening those high points. Greasing the loaded contact slips a fluid film between the bodies so they ride over one another instead of catching. Lifting the pressing burden cuts the normal force, and frictional resistance falls in direct proportion to that force.
A heavy object floats in water because:
Its mass undercuts the chilly salt water
Its ascent shows the water lacks density
Its cavities hold the trapped rain water
Its weight equals the water pushed aside
Correct answer: Its weight equals the water pushed aside
A body floats when the water it shoves out of the way weighs as much as the body itself, so its weight equals the water pushed aside. Its mass undercuts the chilly salt water is false of a steel ship, whose plating is many times denser than seawater. Its cavities hold the trapped rain water describes a swamped object, which is what sinks a hull rather than what keeps it up. Its ascent shows the water lacks density is impossible, since water has a definite density and that density is precisely what generates the upward push.
Torque is best described as:
A settled or pressing weight
A straight or shoving thrust
A gentle or revolving motion
A rotating or twisting force
Correct answer: A rotating or twisting force
Torque is a rotating or twisting force, the action that makes a body turn about an axis, and it grows with both the force applied and its distance from that axis. A settled or pressing weight acts straight downward and carries no rotational sense of its own. A straight or shoving thrust drives along a line and produces no rotation unless it is offset from an axis. A gentle or revolving motion describes how fast something already spins, which is angular speed rather than the agent that changes it.
Two gears are connected by a chain. They will rotate:
Blocking the complete motion
Retaining the shared heading
Reversing the input rotation
Repeating the identical rate
Correct answer: Retaining the shared heading
A chain wraps the same way around both sprockets, so the driven wheel ends up retaining the shared heading of the driver, exactly as a bicycle chainwheel and rear sprocket turn together. Blocking the complete motion would require the chain to bind, which is a fault rather than normal running. Repeating the identical rate holds only when the two sprockets carry the same number of teeth. Reversing the input rotation would require the two wheels to press tooth against tooth, whereas a chain pulls both sprockets from the same side of the loop.
Which has more potential energy: a rock at the top of a hill or the same rock at the bottom?
The uppermost perch
The deepest hollows
The balanced levels
The absent reserves
Correct answer: The uppermost perch
Gravitational potential energy grows with height above a reference level, so the rock waiting at the uppermost perch holds more of it than the identical rock lying below. The deepest hollows sit at the smallest height, so the store there is at its least rather than its greatest. The balanced levels would require both positions to be the same height, which the question rules out by naming a top and a bottom. The absent reserves cannot be right, because a mass held above a lower level always carries some gravitational potential energy.
A screw is a combination of which simple machine wrapped around a cylinder?
The steady inclined plane
The grooved cable pulleys
The pivoted wooden levers
The broader wheeled axles
Correct answer: The steady inclined plane
A screw is the steady inclined plane wound helically around a shaft, so that turning it converts rotation into slow linear travel and multiplies force. The grooved cable pulleys redirect a line over a wheel and involve no slope whatever. The pivoted wooden levers turn about a fulcrum, which a thread does not have. The broader wheeled axles trade turning distance for torque about a single shaft, but nothing in that pairing rises gradually the way a thread does.
If the temperature of a gas in a sealed rigid container increases, the pressure will:
Grow markedly stronger
Remain wholly constant
Slide plainly downward
Vanish completely away
Correct answer: Grow markedly stronger
Heating a gas makes its molecules move faster, and in a rigid sealed vessel they strike the walls harder and more often, so the pressure will grow markedly stronger. Slide plainly downward reverses the relationship between temperature and pressure at fixed volume. Remain wholly constant would hold only if the vessel could expand to absorb the change, which a rigid container cannot do. Vanish completely away would require the gas itself to disappear, and a sealed container keeps its contents inside.
A bimetallic strip bends when heated because the two metals:
Melt at identical points
Conduct at feeble levels
Expand at unequal speeds
Insulate at equal grades
Correct answer: Expand at unequal speeds
A bimetallic strip curls because its two bonded metals expand at unequal speeds for the same rise in temperature, so the faster-growing metal is forced to the outside of the curve. Melt at identical points is irrelevant, since the strip works far below either melting point. Conduct at feeble levels is false of metals, which conduct well, and poor conduction would not bend anything. Insulate at equal grades fails for the same reason: two identical behaviors could never produce the difference that makes the strip bend.
Which requires the least effort to lift a heavy box onto a truck bed?
Easing it up a steeper ascent
Pushing it up a lengthy slope
Hauling it up a sheer surface
Throwing it up a sudden curve
Correct answer: Pushing it up a lengthy slope
A long ramp spreads the same rise over a far greater distance, so pushing it up a lengthy slope needs the smallest force of the four, even though the box travels farther. Easing it up a steeper ascent shortens the journey but raises the required force in the same proportion. Hauling it up a sheer surface means lifting against the full weight with no mechanical advantage whatever. Throwing it up a sudden curve demands the largest force of all, delivered in a very short burst.
In a hydraulic system, applying force to a small piston produces a larger force on a large piston because:
Friction is removed wholly around the pipework
Pressure is passed evenly throughout the fluid
Liquid is squashed easily inside the cylinders
Weight is lessened greatly behind the cylinder
Correct answer: Pressure is passed evenly throughout the fluid
A pressure change in a confined liquid reaches every part of it undiminished, so pressure is passed evenly throughout the fluid and the wider face, having more area, feels a proportionally larger force. Friction is removed wholly around the pipework is false, since real systems lose a little to friction and would multiply force even without that loss. Liquid is squashed easily inside the cylinders is the reverse of the truth: hydraulics work precisely because liquid barely compresses. Weight is lessened greatly behind the cylinder confuses the moving part's own weight with the force the fluid delivers to it.
An object moving in a circle at constant speed is:
Untroubled because its motion persists
Balanced because its forces counteract
Accelerating because its heading turns
Decelerating because its speed shrinks
Correct answer: Accelerating because its heading turns
Velocity carries both size and direction, so a body running round a circle at a steady rate is accelerating because its heading turns from instant to instant, and that acceleration points toward the center. Untroubled because its motion persists mistakes constant speed for constant velocity. Balanced because its forces counteract is wrong, since a net inward force is exactly what bends a straight path into a circle. Decelerating because its speed shrinks contradicts the stem, which fixes the speed as constant.
Which class of lever always produces a mechanical advantage greater than 1?
The centered pivot lever class
The third lever class entirely
The overall lever class family
The regular second lever class
Correct answer: The regular second lever class
In the regular second lever class the load sits between the fulcrum and the effort, so the effort arm is necessarily longer than the load arm and the mechanical advantage exceeds one; a wheelbarrow is the everyday example. The centered pivot lever class can give an advantage above or below one, depending on how far the pivot sits from each end of the bar. The third lever class entirely fails the test, since it puts the effort between fulcrum and load and its advantage is always below one. The overall lever class family cannot be the answer, because the three classes behave differently from one another.
Heat transfer through direct contact between materials is called:
Rapid fluid convection
Steady wall conduction
Thin rubber insulation
Nearby flame radiation
Correct answer: Steady wall conduction
Energy moving from one body to another where they physically touch is conduction, so steady wall conduction is the process being named. Rapid fluid convection carries energy by the bulk movement of a liquid or gas, not by contact between solids. Thin rubber insulation names a material choice that slows the flow rather than a mode of transfer. Nearby flame radiation crosses empty space as electromagnetic waves and needs no contact whatever.
A flywheel is used in machines primarily to:
Raise unwanted friction and absorb effort
Chill overheated cylinders and vent steam
Generate electric current and drive lamps
Store rotational energy and steady motion
Correct answer: Store rotational energy and steady motion
A flywheel exists to store rotational energy and steady motion: its inertia soaks up energy during a power stroke and gives it back between strokes, so the shaft turns evenly. Raise unwanted friction and absorb effort describes a brake, whereas a flywheel is built to lose as little as it can. Generate electric current and drive lamps needs windings and a magnetic field, which a plain spinning mass does not have. Chill overheated cylinders and vent steam is the work of a cooling system rather than of a flywheel.
If two springs are identical and connected in parallel to support a load, compared to a single spring they will be:
Firmer and tougher under load
Flimsier and unfit under load
Slacker and softer under load
Unchanged and flat under load
Correct answer: Firmer and tougher under load
Two identical springs side by side each carry a share of the weight, so the pair deflects only half as far as one spring would and the combination is firmer and tougher under load. Slacker and softer under load describes springs joined end to end in series, not side by side. Flimsier and unfit under load is wrong because splitting a weight between two springs raises the capacity rather than lowering it. Unchanged and flat under load ignores the second spring altogether, when in fact its stiffness adds directly to the first.
Water seeks its own level in connected containers because of:
Magnetism from the metals of the walls
Voltage from the charge of the beakers
Pressure from the weight of the liquid
Tension from the surfaces of the water
Correct answer: Pressure from the weight of the liquid
Water levels out in linked vessels because of pressure from the weight of the liquid standing above each point, and flow continues until those pressures match at every depth. Magnetism from the metals of the walls plays no part, since water levels out in glass and plastic containers just the same. Voltage from the charge of the beakers is equally irrelevant to a still column of water. Tension from the surfaces of the water shapes droplets and menisci on a small scale but is far too weak to raise or lower a whole column.
A larger driving gear with 40 teeth turns a smaller gear with 10 teeth. For each turn of the large gear, the small gear turns:
6
3
4
5
Correct answer: 4
The tooth ratio is forty to ten, which reduces to four to one, so the small gear completes 4 turns for every single turn of the large one. A figure of 3 would follow from a thirty-tooth driver, and a figure of 5 from a fifty-tooth driver. A figure of 6 would need sixty teeth on the driving gear, which is not the pairing described.
Which of these is an example of Newton's third law of motion?
A puck gliding straight ahead and holding speed
A ball spinning ever slower and shedding motion
A cart rolling gently onward and halting nearby
A rocket forcing gas downward and climbing high
Correct answer: A rocket forcing gas downward and climbing high
Newton's third law pairs equal and opposite forces acting on two different bodies, and a rocket forcing gas downward and climbing high is precisely that pair: the engine pushes the exhaust one way and the exhaust pushes the rocket the other. A puck gliding straight ahead and holding speed illustrates the first law, since a body with no net force on it keeps its velocity. A cart rolling gently onward and halting nearby illustrates the second law, with a retarding force producing an acceleration. A ball spinning ever slower and shedding motion is the same second-law case, driven by friction.
An object with greater mass requires what to achieve the same acceleration as a lighter object?
A larger applied push
A repeated firm shove
A smaller steady pull
A zero external heave
Correct answer: A larger applied push
Force equals mass multiplied by acceleration, so a heavier body needs a larger applied push to reach the same acceleration as a light one. A smaller steady pull would give the heavier body less acceleration, not an equal amount. A repeated firm shove leaves the force where it was, which cannot make up for the extra mass. A zero external heave produces no acceleration whatever, so the heavier body would simply keep its existing motion.
A barometer is an instrument used to measure:
The local air pressure
The seasonal air vapor
The steady air current
The outdoor air warmth
Correct answer: The local air pressure
A barometer balances the column of atmosphere standing above it, so what it reports is the local air pressure, and a falling reading is the classic sign of worsening weather. The outdoor air warmth is the business of a thermometer. The seasonal air vapor is measured by a hygrometer. The steady air current is measured by an anemometer, which counts the turns of a set of cups rather than weighing a column of air.
In a block and tackle, what is gained at the cost of having to pull more rope?
The directional velocity
The mechanical advantage
The unwanted temperature
The considerable tonnage
Correct answer: The mechanical advantage
A block and tackle multiplies the force you apply, so what is bought at the price of hauling extra rope is the mechanical advantage. The directional velocity of the load actually falls, because the load rises more slowly than your hand travels. The unwanted temperature rise caused by friction in the sheaves is a small loss, not a gain. The considerable tonnage of the load is set by the load itself and is not altered by the tackle at all.
Why does a sharpened knife cut more easily than a dull one?
It sheds weight beneath a worn handle
It drives drag toward a flawless zero
It carries cold along a chilled blade
It packs force inside a slimmer strip
Correct answer: It packs force inside a slimmer strip
Pressure is force divided by the area it acts on, so a sharpened knife works because it packs force inside a slimmer strip of material, raising the pressure enough to part the fibers. It sheds weight beneath a worn handle is beside the point, since cutting depends on the edge and not on how much the tool weighs. It carries cold along a chilled blade has no bearing either; a warm sharp edge cuts just as well as a cold one. It drives drag toward a flawless zero overstates the case, because friction is never removed entirely and sharpening does not set out to remove it.
Which way will the second gear turn if two gears are directly meshed and the first turns clockwise?
The repeated clockwise rotation
The completely motionless shaft
The unpredictable double motion
The plain counterclockwise spin
Correct answer: The plain counterclockwise spin
Directly meshed gears must move in opposite senses, because the teeth of one push sideways on the teeth of its neighbor, so a clockwise driver produces the plain counterclockwise spin in the gear beside it. The repeated clockwise rotation would need some intermediate element carrying the drive between the two wheels, which a direct mesh does not have. The completely motionless shaft would mean the teeth had jammed rather than meshed properly. The unpredictable double motion is impossible, since meshed teeth fix the sense of rotation as firmly as they fix the speed ratio.
Centrifugal effect tends to push objects in a spinning system:
Inward, drawn from the border
Outward, away from the middle
Static, halted from the whirl
Upward, clear from the ground
Correct answer: Outward, away from the middle
Rotation throws objects outward, away from the middle of the circular path, which is what the correct choice states. Inward, drawn from the border names the centripetal pull that holds an object on the circle instead of the apparent outward push. Static, halted from the whirl is wrong because a spinning system keeps its contents moving. Upward, clear from the ground names a vertical lift that rotation does not supply.
Which type of bridge support is strongest against compression forces?
A woven cable
A slotted pin
A flat girder
A curved arch
Correct answer: A curved arch
The support that carries compression best is a curved arch, which channels the load down its curve into the abutments as pure compression. A woven cable carries tension only and collapses the moment it is pushed rather than pulled. A flat girder works mainly in bending and sags long before an arch of the same material would. A slotted pin is a pivot for transferring motion, not a member sized to carry a compressive load.
If a 10-pound weight hangs from a single fixed pulley, how much force is needed to hold it (ignoring friction)?
Five pounds
Ten pounds
Thirty pounds
Twelve pounds
Correct answer: Ten pounds
Holding the weight takes ten pounds of force. A single fixed pulley changes only the direction of the pull, never its size, so the effort equals the load. Five pounds would be correct for a movable pulley, where two rope sections share the load, but this pulley is fixed. Twelve pounds assumes the pulley itself adds resistance, and the problem excludes friction. Thirty pounds treats the pulley as multiplying the required effort, which no fixed pulley does.
The boiling point of water is lower at high altitude because:
Available oxygen increases
Circulating liquid freezes
Atmospheric pressure drops
Nearby gravity strengthens
Correct answer: Atmospheric pressure drops
Water boils once its vapor pressure matches the pressure pressing down on it, so the reason is that atmospheric pressure drops as altitude rises and the boiling point falls with it. Circulating liquid freezes is wrong because the water's own temperature is not what altitude changes. Available oxygen increases fails twice: oxygen thins out with height and takes no part in boiling. Nearby gravity strengthens reverses reality, and gravity does not set a boiling point.
A cam in a machine is used to:
Convert pressure into visible numbers
Convert rotation into straight travel
Convert friction into cooler surfaces
Convert current into chemical storage
Correct answer: Convert rotation into straight travel
A cam exists to convert rotation into straight travel, driving a follower back and forth as the shaft turns. Convert pressure into visible numbers describes a gauge, which reads a value rather than moving a follower. Convert friction into cooler surfaces reverses what rubbing does, since friction raises temperature. Convert current into chemical storage describes a battery cell and has nothing to do with a shaped rotating profile.
Two identical boxes are pushed across the floor; one is full and one is empty. The full box is harder to move because it has:
Thinner materials and lighter friction
Heavier contents and stronger friction
Smoother surfaces and reduced friction
Narrower footprint and slight friction
Correct answer: Heavier contents and stronger friction
The loaded box resists because of heavier contents and stronger friction: the frictional force grows in proportion to how hard the surfaces are pressed together. Thinner materials and lighter friction describes the empty box, which is the easier one to push. Smoother surfaces and reduced friction would make the box slide more freely, not less. Narrower footprint and slight friction is wrong twice over, because contact area is identical for the two boxes and would not change the friction anyway.
Which describes the mechanical advantage of a machine?
Force exerted divided by weight moved
Load lifted divided by effort applied
Output motion divided by input motion
Useful energy divided by time elapsed
Correct answer: Load lifted divided by effort applied
Mechanical advantage is load lifted divided by effort applied, the factor by which a machine multiplies the force a user supplies. Force exerted divided by weight moved inverts that ratio and would report a number below one for every helpful machine. Output motion divided by input motion is the velocity ratio, a separate quantity that compares distances rather than forces. Useful energy divided by time elapsed defines power, which says nothing about force multiplication.
When a moving car suddenly stops, passengers lurch forward due to:
Their inertia
Their impulse
Their density
Their gravity
Correct answer: Their inertia
Passengers pitch forward because of their inertia, the tendency of a mass to keep its existing motion until some force changes it. Their gravity acts straight downward and cannot push anyone toward the windshield. Their impulse names the force delivered over the stopping interval, which the brakes apply to the car rather than to the people inside it. Their density is a property of the material they are made of and has no bearing on the lurch.
A longer wrench handle makes loosening a bolt easier because it:
Reduces the friction present
Increases the applied torque
Diminishes the anchor weight
Chills the exposed fasteners
Correct answer: Increases the applied torque
A longer handle increases the applied torque, since torque equals force multiplied by the distance from the turning axis. Reduces the friction present is wrong because handle length does nothing to the threads gripping one another. Diminishes the anchor weight is irrelevant, as the weight of a bolt never resists loosening. Chills the exposed fasteners describes a temperature change that turning a wrench does not produce.
In a series of three meshed gears, the first and third gears rotate:
In the identical direction
In the backward revolution
In the accelerated cadence
In the stalled arrangement
Correct answer: In the identical direction
Each mesh reverses the sense of rotation, so two meshes restore it and the third gear runs in the identical direction as the first. In the backward revolution describes the middle gear, which is the one directly reversed. In the accelerated cadence confuses direction with speed, and an idler between two gears alters neither. In the stalled arrangement is wrong because meshed gears in a working train all turn.
Steam can do work in an engine because, compared to liquid water, it:
Chills and resists movement
Expands and raises pressure
Condenses and drains warmth
Compresses and gains weight
Correct answer: Expands and raises pressure
Steam does work because it expands and raises pressure, filling far more volume than the water it came from and driving the piston along its stroke. Chills and resists movement is the opposite of what a working fluid does in an engine. Condenses and drains warmth describes what happens after the work stroke, in the condenser. Compresses and gains weight is wrong because steam is far less dense than liquid water.
Which factor does NOT affect the period of a simple pendulum?
Support length
Gravity effect
Both variables
Suspended mass
Correct answer: Suspended mass
The period of a simple pendulum is set by length and gravity alone, so the quantity that makes no difference is the suspended mass. Support length changes the period directly, with a longer support swinging more slowly. Gravity effect changes it too, which is why the same pendulum keeps different time on the moon. Both variables would mean length and gravity are equally irrelevant, yet both of them appear in the period formula.
Two ships leave the same port at the same time, one heading due north at 18 knots and the other due east at 24 knots. After 3 hours, how far apart are they in nautical miles?
54 nm
30 nm
90 nm
72 nm
Correct answer: 90 nm
The ships end up 90 nm apart, that is 90 nautical miles. Each ship covers its speed times 3 hours, so one runs 54 nm north and the other 72 nm east, and because the two courses are perpendicular the gap is the hypotenuse of a 54 by 72 right triangle, which is 90. The figure 30 is only the rate at which the ships separate, in knots, and still has to be multiplied by the 3 hours. The figure 54 is the northbound leg alone and 72 is the eastbound leg alone; neither one measures the distance between the two ships.
A patrol boat travels 105 nautical miles in 3.5 hours. At the same speed, how long will it take to cover 135 nautical miles?
3.5
4.0
5.0
4.5
Correct answer: 4.5
The run takes 4.5 hours. Speed is distance over time, so 105 divided by 3.5 gives 30 knots, and 135 divided by 30 gives 4.5 hours. The figure 3.5 just repeats the time given for the first run and answers nothing. The figure 4.0 comes from dropping the remainder when dividing 135 by 30. The figure 5.0 comes from reading the second distance as 150 rather than 135.
A drill yields 92 of 115 recruits passing. What percent passed?
80%
77%
74%
83%
Correct answer: 80%
80% of the recruits passed. Divide the number who passed by the number who took the drill: 92 divided by 115 is 0.80, which is 80 percent. The figure 77% comes from treating the 23 who failed as a percentage and subtracting that from 100. The figure 83% comes from dividing 92 by 110 after misreading the total. The figure 74% comes from dividing by 125 instead of 115.
Solve the system: x+y=14 and x−y=4. What is the value of x?
x = 4
x = 5
x = 8
x = 9
Correct answer: x = 9
The answer is x = 9. Adding the two equations cancels y and leaves 2x equal to 18, so x is 9 and y is 5. The reading x = 5 gives the value of y, the other unknown, not the one the question asks for. The reading x = 8 comes from adding 14 and 4 as 16 before halving. The reading x = 4 is the stated difference between the two numbers rather than either number itself.
Solve for x: x2−5x+6=0.
x = 2 or x = 3
x = 6 or x = 1
x = 0 or x = 5
x = 5 or x = 6
Correct answer: x = 2 or x = 3
The roots are x = 2 or x = 3. The trinomial factors into x minus 2 times x minus 3, because that pair multiplies to positive 6 and adds to negative 5. The pair x = 6 or x = 1 multiplies to 6 as well but adds to 7, so it cannot produce the middle term. The pair x = 0 or x = 5 comes from dropping the constant and factoring only x squared minus 5x. The pair x = 5 or x = 6 reads the coefficient and the constant straight off the equation as though they were the roots.
What is the value of 2 to the fourth power multiplied by 2 cubed?
112
144
96
128
Correct answer: 128
The product is 128. Powers of the same base combine by adding exponents, so 2 to the fourth times 2 cubed is 2 to the seventh, which is 128; multiplying 16 by 8 gives the same figure. The figure 112 comes from using the exponent sum as a multiplier and computing 16 times 7. The figure 96 comes from reading 2 cubed as 2 times 3 and computing 16 times 6. The figure 144 comes from confusing 2 cubed with 3 squared and computing 16 times 9.
Simplify 72.
8√3
6√3
6√2
3√8
Correct answer: 6√2
The simplified form is 6√2. Take the largest perfect square out of 72: it is 36 times 2, and the square root of 36 is 6. The form 3√8 carries the same value but is not simplified, because 8 still holds the perfect square 4; a simplified radical must have no square factor left. The form 6√3 would require 36 times 3, which is 108, not 72. The form 8√3 would require 64 times 3, which is 192.
What is 65 minus 83?
14/24
11/24
29/24
17/24
Correct answer: 11/24
The difference is 11/24. The least common denominator of 6 and 8 is 24, so 5/6 becomes 20/24 and 3/8 becomes 9/24, and 20 minus 9 leaves 11 twenty-fourths. The figure 14/24 comes from converting 3/8 to 6/24, doubling the numerator when the denominator was tripled. The figure 17/24 comes from writing 3/8 as 3/24 and never scaling its numerator. The figure 29/24 comes from adding the two converted fractions instead of subtracting.
What is 32 divided by 94?
8/27
2/3
3/2
27/8
Correct answer: 3/2
The quotient is 3/2. Dividing by a fraction means multiplying by its reciprocal, so 2/3 times 9/4 is 18/12, which reduces to 3/2. The figure 8/27 comes from multiplying straight across without flipping the divisor. The figure 2/3 comes from dividing the wrong way round, taking 4/9 divided by 2/3. The figure 27/8 comes from inverting the first fraction rather than the second and then multiplying.
A bag holds 5 black, 3 white, and 2 red chips. If one chip is drawn at random, what is the probability it is NOT white?
3/10
5/10
2/10
7/10
Correct answer: 7/10
The probability is 7/10. The bag holds 10 chips and 3 of them are white, so 7 of the 10 are not white. The figure 3/10 gives the chance of drawing a white chip, which is the opposite of what was asked. The figure 5/10 counts the black chips only and the figure 2/10 counts the red chips only; each one leaves out a color that also counts as not white.
The average of four test scores is 82. If three of the scores are 78, 85, and 90, what is the fourth score?
75
82
78
84
Correct answer: 75
The fourth score is 75. Four scores averaging 82 must total 4 times 82, or 328, and the three known scores add to 253, so the missing one is 328 minus 253. The figure 84 is the average of the three known scores and ignores the total the fourth score has to produce. The figure 82 assumes the missing score equals the mean, which holds only when the other scores already average 82. The figure 78 comes from rounding the known total to 250 before subtracting.
A map uses a scale where 2 inches represents 75 miles. How many miles do 5 inches represent?
225.0
262.5
187.5
375.0
Correct answer: 187.5
Five inches stands for 187.5 miles. The scale gives 75 divided by 2, or 37.5 miles to the inch, and 5 times 37.5 is 187.5. The figure 375.0 comes from multiplying 5 by 75 and never dividing by the 2 inches in the scale. The figure 225.0 comes from counting 6 inches rather than 5. The figure 262.5 comes from adding the 2 scale inches to the 5 and working from 7 inches.
A rectangular field is 60 yards long and 45 yards wide. What is its perimeter?
120
150
180
210
Correct answer: 210
The perimeter is 210 yards. Perimeter is twice the sum of the two side lengths, so 60 plus 45 is 105 and twice 105 is 210. The figure 150 adds only three sides, 60 plus 45 plus 45, and leaves one side out. The figure 180 treats the field as a square 45 yards on every side. The figure 120 doubles the 60-yard length twice over and never counts the two 45-yard sides. None of the three accounts for a rectangle having two different side lengths, each used twice.
Two angles are complementary, and one measures 37 degrees. What is the measure of the other angle?
43
73
63
53
Correct answer: 53
The other angle is 53 degrees. Complementary angles add to a right angle, so the missing measure is 90 minus 37. The figure 63 comes from subtracting 37 from 100 rather than from 90. The figure 43 subtracts from 80, and the figure 73 subtracts from 110; each uses a total that no pair of complementary angles can reach. Subtracting from 180 would give a supplement instead, which the question does not ask for.
What is 248 plus 197 using mental math?
442
451
445
448
Correct answer: 445
The sum is 445. Round 197 up to 200, add that to 248 for 448, then hand back the 3 that was added. The figure 448 stops one step early and leaves the rounding inside the answer. The figure 451 adjusts in the wrong direction, adding the 3 instead of subtracting it. The figure 442 comes from reading the first number as 245.
If 3x−2=5x+8, what is the value of x?
5
-3
-5
3
Correct answer: -5
The value of x is -5. Subtracting 3x from both sides leaves -2 equal to 2x plus 8, and subtracting 8 leaves -10 equal to 2x, so x is -5. The figure 5 has the right size and the wrong sign, which is what happens when the negative is dropped at the final division. The figure -3 comes from combining -2 and 8 as -6 rather than -10. The figure 3 makes that same combining error and loses the sign as well.
The line described by 2x+3y=12 crosses the y-axis at what value of y?
y = 4
y = 2
y = 6
y = 9
Correct answer: y = 4
The line crosses the y-axis at y = 4. A graph meets that axis where x is 0, so the equation becomes 3y equal to 12 and y is 4. The reading y = 6 is the x-intercept, which comes from setting y to 0 instead of x. The reading y = 9 comes from subtracting 3 from 12 rather than dividing by it. The reading y = 2 is just the coefficient of x read straight off the equation.
A tank is 53 full and holds 90 gallons at that level. What is the tank's full capacity?
150
270
180
225
Correct answer: 150
The tank holds 150 gallons when full. If three fifths of the capacity is 90 gallons, then one fifth is 30 gallons and the whole tank is five times that. The figure 270 multiplies by the numerator instead of dividing by it, giving 90 times 3. The figure 225 reads the three fifths as the share that is empty, so 90 gallons becomes two fifths and the work runs 90 divided by 2 times 5. The figure 180 reads three fifths as one half and simply doubles the 90.
An alloy mixes copper and zinc in a 5:3 ratio. If a sample contains 200 grams of copper, how many grams of zinc does it contain?
160
200
240
120
Correct answer: 120
The sample holds 120 grams of zinc. A 5 to 3 ratio with 200 grams of copper makes each ratio unit 200 divided by 5, or 40 grams, so the three zinc units come to 120 grams. The figure 160 takes a single 40-gram unit off the copper instead of counting three units from scratch. The figure 200 assumes the two metals weigh the same, which the ratio rules out. The figure 240 adds a unit to the copper rather than scaling down to the smaller share.
A price rises from $80 to $100. By what percent did it increase?
25%
22%
27%
20%
Correct answer: 25%
The price rose by 25%. Percent increase is the change divided by the original amount: the rise is 20 dollars and 20 divided by 80 is 0.25. The figure 20% divides that same rise by the new price of 100 rather than by the starting price. The figure 22% divides by 90, the average of the two prices, which answers a different question. The figure 27% comes from dividing by 75 after misreading the starting price.
What is 30 percent of 60 percent of 500?
150
90
300
450
Correct answer: 90
The result is 90. Take 60 percent of 500 first, which is 300, then take 30 percent of that 300, which is 90. The figure 300 stops at the first step and reports the intermediate amount. The figure 150 applies only the 30 percent and never uses the 60 percent at all. The figure 450 adds the two percentages into 90 percent and applies that single figure to 500, which is not how successive percentages work.
What is the value of 7+12/(2+1)×2?
11
19
15
22
Correct answer: 15
The value is 15. Clear the parentheses first to get 3, then take division and multiplication left to right: 12 divided by 3 is 4, and 4 times 2 is 8, so 7 plus 8 is 15. The figure 11 stops after the division and never multiplies by 2. The figure 22 adds the 7 in before multiplying, giving 11 times 2. The figure 19 adds 7 and 12 and ignores the rest of the expression.
How many distinct three-letter codes can be formed from the letters A, B, C, and D if no letter repeats?
24
48
36
60
Correct answer: 24
There are 24 codes. The first slot has 4 letters to choose from, the second has 3 and the third has 2, and 4 times 3 times 2 is 24. The figure 36 leaves 3 choices in the last slot, forgetting that a second letter has already been used. The figure 48 leaves 4 choices in the second slot, which would allow a letter to repeat. The figure 60 counts five available letters rather than the four the question supplies.
The OAR Math Skills Test draws on which three broad areas of mathematics?
Calculus, logic, and trigonometry
Probability, topology, and proofs
Algebra, arithmetic, and geometry
Economics, commerce, and taxation
Correct answer: Algebra, arithmetic, and geometry
The section rests on algebra, arithmetic, and geometry. It asks for operations on whole numbers, fractions, decimals and percentages; for solving equations and handling exponents and roots; and for angles, area and perimeter. Calculus, logic, and trigonometry lists three subjects the section never reaches. Probability, topology, and proofs fails for the same reason, since neither topology nor formal proof appears anywhere on this test. Economics, commerce, and taxation describes business material that belongs to no part of a mathematics skills section.
Read the passage, then answer the question.
The Officer Aptitude Rating reading section does not assume you arrive with specialized knowledge of any topic. Instead, every correct answer must be supported by information stated or directly implied within the passage itself. Test-takers who rely on outside facts they happen to know, rather than on the text in front of them, frequently select answers that seem true in general but are not backed by the passage. The skill being measured is the ability to work strictly from the given material.
According to the passage, why might a well-informed test-taker still answer incorrectly?
Using hurried impressions instead of the passage
Using instruction wording instead of the passage
Using confident intuition instead of the passage
Using remembered learning instead of the passage
Correct answer: Using remembered learning instead of the passage
A well-informed test-taker goes wrong when using remembered learning instead of the passage. The text says those who rely on outside facts they happen to know, rather than the material in front of them, pick answers that merely seem true in general. Hurried impressions and confident intuition are never named as the cause, and the section is scored on the given material, so instruction wording is not what the answer must rest on.
Read the passage, then answer the question.
Finding the main idea of a passage means identifying the single point the author most wants the reader to take away, rather than any one supporting detail. A useful method is to ask what idea every sentence in the passage works to support. Details, examples, and statistics are not themselves the main idea; they are the evidence that builds toward it. When several sentences all point toward one general statement, that statement is usually the main idea.
Based on the passage, how can a reader best identify the main idea?
Marking the sentences that introduce the passage
Selecting the sentences that stretch the longest
Trusting the sentences that surprise the readers
Naming the view that sentences jointly reinforce
Correct answer: Naming the view that sentences jointly reinforce
A reader finds the main idea by naming the view that sentences jointly reinforce. The passage says the main idea is the single point every sentence works to support, and that details, examples and figures are evidence building toward it rather than the point itself. Marking the sentences that introduce the passage or selecting the sentences that stretch the longest judges layout, not meaning, and trusting the sentences that surprise the readers mistakes a striking figure for the point it serves.
Read the passage, then answer the question.
An inference question asks you to reach a conclusion that the passage does not state outright but clearly supports. The correct inference stays close to the text, going only one small step beyond what is written. Answers that require large assumptions, introduce new information, or contradict the passage are wrong, even if they sound reasonable. Good readers test each option by asking whether the passage gives enough evidence to justify it.
What distinguishes a correct inference from an incorrect one, according to the passage?
It builds on the reason that the passage supplies
It feeds on the phrases that the passage reprints
It trades on the drama that the passage withholds
It rides on the guesswork that the passage denies
Correct answer: It builds on the reason that the passage supplies
A sound inference is the one that builds on the reason that the passage supplies, staying close to the text and going only one small step beyond it. Riding on guesswork the passage denies fails, since answers that demand large assumptions or contradict the text are wrong. Feeding on phrases the passage reprints yields a stated fact rather than an inference, and trading on drama the passage withholds adds information the text never provides.
Read the passage, then answer the question.
The supply officer reviewed the requisition twice before forwarding it. The ship was scheduled to remain at sea for an additional six weeks, yet the original order had been calculated for a four-week deployment. Rather than approve the shortfall and hope replenishment would catch up, she revised the quantities upward and flagged the discrepancy for the logistics chief. Her note explained that approving the order as written would have left the crew short of essential stores well before the next resupply.
Why did the supply officer revise the requisition?
The order met a planned deployment fully
The chief wanted a smaller reserve order
The order covered too brief a deployment
The officer sought a lighter stores load
Correct answer: The order covered too brief a deployment
She revised it because the order covered too brief a deployment: the quantities had been calculated for four weeks while the ship was to stay at sea for an additional six. The chief wanted a smaller reserve order is backward, since she raised the quantities and flagged the shortfall for him. The order met a planned deployment fully contradicts the mismatch she found, and a lighter stores load was never her aim, because leaving the crew short before resupply was the risk she was avoiding.
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In its original sense, the word 'muster' referred simply to gathering troops together for inspection or counting. Aboard a modern vessel, the term has retained this core meaning: a muster is an assembly at which personnel are accounted for, often during drills or emergencies. When the announcement directs all hands to muster at their stations, it is calling them to assemble and be counted, not to begin any particular task.
As used in the passage, the word 'muster' most nearly means:
To disperse and be excused
To convene and be numbered
To repair and be inspected
To march and be dispatched
Correct answer: To convene and be numbered
In this passage 'muster' most nearly means to convene and be numbered. The text defines a muster as an assembly at which personnel are accounted for, and says the call to muster at stations is a call to gather and be counted. To march and be dispatched describes setting out on a task, to repair and be inspected describes work on equipment, and to disperse and be excused is the opposite of assembling, so none of them fits the sense the passage gives.
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The training manual stressed that a checklist is not a sign of incompetence but a safeguard against it. Even experienced operators, it argued, can skip a step when distracted or fatigued, and the consequences in complex systems can be severe. By forcing each action to be confirmed in sequence, a checklist catches the lapses that confidence alone cannot prevent. The most skilled professionals, the manual noted, are often the most disciplined about using them.
What is the main idea of the passage?
Checklists distract expert workers from tasks
Checklists excuse untrained workers from care
Checklists shield seasoned workers from slips
Checklists spare competent workers from blame
Correct answer: Checklists shield seasoned workers from slips
The main idea is that checklists shield seasoned workers from slips. The manual calls a checklist a safeguard rather than a sign of incompetence, notes that experienced operators skip steps when distracted or fatigued, and observes that the most skilled professionals are the most disciplined about using them. That rules out the claim that checklists distract expert workers from tasks, and it contradicts the idea that checklists excuse untrained workers from care. Sparing competent workers from blame is never offered as the purpose.
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The research vessel had been tracking the storm for three days, adjusting its course each morning based on the latest forecasts. By the fourth day, the captain made a decision that surprised the science team: rather than racing to complete the survey before the weather closed in, he ordered a return to port. He explained that incomplete data gathered safely was worth more than complete data gathered at the cost of the ship and crew.
What can be inferred about the captain's priorities?
He rated crew safety above survey progress
He rated calm weather above storm warnings
He rated port comfort above survey results
He rated crew doubts above storm forecasts
Correct answer: He rated crew safety above survey progress
The captain rated crew safety above survey progress. He turned back rather than race the weather and said incomplete data gathered safely was worth more than complete data gathered at the cost of the ship and crew. He had adjusted course each morning on the forecasts, so he rated crew doubts above storm forecasts is unsupported, and expecting calm weather is ruled out by his retreat. Port comfort above survey results misreads him, because he still valued the data, just not at that price.
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Tidal energy has long attracted engineers because tides are extraordinarily predictable, following the gravitational rhythm of the moon rather than the variable patterns of wind or sun. A tidal generator can therefore forecast its output years in advance. The obstacle has never been reliability but cost: building structures that withstand constant saltwater corrosion and powerful currents remains expensive. Until these costs fall, tidal power is likely to stay a minor contributor to the energy supply.
According to the passage, what is the main obstacle to wider use of tidal energy?
The uncertain rhythm of seasonal movements
The enormous expense of durable structures
The limited choice of sheltered structures
The endless protest of coastal communities
Correct answer: The enormous expense of durable structures
The obstacle the passage names is the enormous expense of durable structures: works that withstand constant saltwater corrosion and powerful currents remain costly, and tidal power stays a minor contributor until those costs fall. The uncertain rhythm of seasonal movements is the reverse of what the text says, since tides are called extraordinarily predictable and a generator can forecast its output years ahead. A limited choice of sheltered structures and endless protest of coastal communities are never raised.
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The new analyst was eager to present her findings, but her supervisor cautioned her to separate what the data showed from what she suspected. The sales decline coincided with a competitor's new advertisement, she noted, but coincidence in timing was not the same as cause. Other explanations, such as a seasonal slowdown or a pricing change, had not yet been ruled out. A responsible conclusion, the supervisor said, would acknowledge the correlation without claiming proof of cause.
What point is the supervisor making?
Overlap in dates does not prove causation
Rivalry in adverts does not damage income
Weakness in data does not permit analysis
Slowdown in trade does not explain losses
Correct answer: Overlap in dates does not prove causation
The supervisor's point is that overlap in dates does not prove causation. She stresses that the decline merely coincided with the competitor's advertisement, that a seasonal slowdown or a pricing change had not been ruled out, and that a responsible conclusion acknowledges the correlation without claiming proof. She never argues that weakness in data does not permit analysis, nor that rivalry in adverts does not damage income, and she keeps a slowdown in trade alive as an explanation rather than dismissing it.
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The fledgling colony's survival depended on a single freshwater spring at the edge of the settlement. As the population grew, the spring's flow could no longer meet daily demand, and rationing began to breed resentment. A surveyor eventually traced an underground stream to a higher elevation and proposed a simple gravity-fed channel to bring its water down. Within a season, the new supply ended the rationing and quieted the disputes that scarcity had provoked.
What solved the colony's water shortage?
A pumped delivery from distant rivers
A stricter ration from existing wells
A downhill conduit from upland brooks
A planned exodus from crowded hamlets
Correct answer: A downhill conduit from upland brooks
The shortage was solved by a downhill conduit from upland brooks. A surveyor traced an underground stream at a higher elevation and proposed a simple gravity-fed channel to bring its water down, and within a season the new supply ended the rationing. A pumped delivery from distant rivers is not what the text describes, a stricter ration from existing wells was the failing stopgap rather than the remedy, and a planned exodus from crowded hamlets never occurred, since the population grew.
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The aircraft's checklist distinguished sharply between a 'caution' and a 'warning.' A caution alerted the crew to a condition that required attention but allowed time to respond methodically. A warning, by contrast, signaled an immediate threat demanding instant action. Confusing the two could be dangerous in opposite directions: treating a warning as a caution risked disaster, while treating a caution as a warning could provoke a hasty, unnecessary response.
Based on the passage, how does a warning differ from a caution?
A warning permits leisurely study
A warning deserves little concern
A warning suggests milder trouble
A warning compels prompt reaction
Correct answer: A warning compels prompt reaction
A warning compels prompt reaction, and that is what separates it from a caution. The checklist defines a warning as signaling an immediate threat demanding instant action, while a caution flags a condition that allows time to respond methodically. So a warning permits leisurely study reverses the two, a warning suggests milder trouble makes it the lesser signal when it is the graver one, and a warning deserves little concern is exactly the mistake the passage calls a risk of disaster.
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When the museum digitized its archives, curators expected scholars to be the main beneficiaries. Instead, the largest surge in use came from ordinary citizens researching their own family histories. Letters, photographs, and shipping records that had sat untouched for decades suddenly connected people to ancestors they had never known. The project's director remarked that the collection's value had multiplied not because it changed, but because access to it did.
What does the director's remark suggest?
Budgets, not scans, decided the collection's worth
Experts, not staff, decided the collection's worth
Rewrites, not care, decided the collection's worth
Reach, not content, decided the collection's worth
Correct answer: Reach, not content, decided the collection's worth
The remark suggests that reach, not content, decided the collection's worth: the director says the value multiplied not because the collection changed but because access to it did. Experts, not staff, decided the collection's worth is the expectation the passage overturns, since ordinary citizens drove the surge in use. Rewrites, not care, decided the collection's worth is wrong because nothing was rewritten, and budgets, not scans, decided the collection's worth is never claimed anywhere in the text.
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A passage can support a statement directly, by saying it outright, or indirectly, by providing facts from which the statement reasonably follows. On the reading section, a question may ask which statement the passage supports rather than which it states. The correct choice need not appear word for word in the text; it must simply be consistent with and backed by what the passage provides. Statements that go beyond the evidence, however logical they seem, are not supported.
According to the passage, a statement is 'supported' by a passage when it:
Duplicates what the passage supplies
Matches what the passage establishes
Overtakes what the passage justifies
Disputes what the passage guarantees
Correct answer: Matches what the passage establishes
A statement is supported when it matches what the passage establishes, whether the passage says so outright or provides facts from which it reasonably follows. Duplicates what the passage supplies describes a verbatim restatement, which the text says is not required for support. Overtakes what the passage justifies is the case the text rules out, since statements going beyond the evidence are unsupported however logical they sound, and disputes what the passage guarantees contradicts the text instead of following it.
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The chief engineer kept a worn notebook in which he recorded every machinery failure he had ever responded to, along with its cause and fix. Junior sailors sometimes mocked the habit as old-fashioned in an age of digital logs. Yet when a pump failed in a way the computer diagnostics could not explain, it was a decade-old entry in that notebook that pointed to the answer. After that night, the notebook was treated with new respect.
Why did attitudes toward the notebook change?
The notebook solved a breakdown the machines missed
The notebook replaced a program the sailors trusted
The notebook earned a deference the chief commanded
The notebook silenced a sensor the engineers valued
Correct answer: The notebook solved a breakdown the machines missed
Attitudes shifted because the notebook solved a breakdown the machines missed: a decade-old entry pointed to the answer when the computer diagnostics could not explain a pump failure. The notebook earned a deference the chief commanded is wrong because the change came from a result, not an order. The notebook replaced a program the sailors trusted reverses the story, since the digital logs stayed in use, and the notebook silenced a sensor the engineers valued describes something the passage never reports.
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Sea fog forms when warm, moist air drifts over colder water, chilling the air until its moisture condenses into a thick haze near the surface. Because it depends on the temperature difference between air and water rather than on rainfall, sea fog can appear suddenly on an otherwise clear day. Mariners learn to anticipate it by watching for warm air moving across cool currents, a combination that often signals reduced visibility ahead.
What can be inferred about predicting sea fog?
Predicting it means counting rainfall and water averages
Predicting it means watching air and cloudy disturbances
Predicting it means comparing air and water temperatures
Predicting it means timing sunrise and temperature peaks
Correct answer: Predicting it means comparing air and water temperatures
Predicting it means comparing air and water temperatures. The passage says sea fog depends on the temperature difference between air and water, and that mariners anticipate it by watching for warm air moving across cool currents. Predicting it means counting rainfall and water averages is ruled out, because the text states the process does not depend on rainfall. Watching air and cloudy disturbances and timing sunrise and temperature peaks name signals the passage never ties to fog at all.
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The author opens by describing a quiet harbor at dawn, then introduces a fisherman repairing his nets, and finally reflects on how generations of his family have worked the same waters. Although the passage contains vivid scenery and a single character, none of these is its central concern. The harbor and the fisherman serve a larger purpose: to illustrate the endurance of a way of life passed from parent to child across many years.
What is the central concern of the passage?
The survival of a craft carried through bloodlines
The collapse of a fishery squeezed through markets
The routine of a repairer learned through practice
The stillness of a harbor spotted through daybreak
Correct answer: The survival of a craft carried through bloodlines
The central concern is the survival of a craft carried through bloodlines. The passage says outright that the harbor and the fisherman serve a larger purpose, to illustrate a way of life passed from parent to child across many years. The routine of a repairer learned through practice and the stillness of a harbor spotted through daybreak are the supporting details the text explicitly sets aside, and the collapse of a fishery squeezed through markets describes a decline the passage never mentions.
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The committee's report ran to ninety pages, but its recommendation occupied a single paragraph near the end. Reviewers who skimmed the document came away with conflicting impressions because the body presented arguments on every side without clearly signaling which the committee favored. Only the final paragraph resolved the matter. A clearer report, one analyst observed, would have stated its conclusion at the outset and used the body to defend it.
What criticism does the analyst make of the report?
The report withheld its verdict through the pages
The report misstated its totals through the pages
The report compressed its claim through the pages
The report omitted its protests through the pages
Correct answer: The report withheld its verdict through the pages
The analyst's criticism is that the report withheld its verdict through the pages: the recommendation sat in a single paragraph near the end, and a clearer report would have stated its conclusion at the outset and used the body to defend it. The report compressed its claim through the pages is wrong because the document ran to ninety pages. The report omitted its protests through the pages is also wrong, since the body presented arguments on every side, and no factual error is alleged, so the report misstated its totals through the pages has no support.
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In navigation, the word 'bearing' refers to the direction of one object from another, measured as an angle from a reference such as north. It is distinct from distance, which tells how far away the object lies. A lookout who reports a contact's bearing is stating which way to look, not how near it is. To fix a position precisely, a navigator must combine bearing with distance, since neither alone locates an object.
As used in the passage, 'bearing' refers to:
The regular spacing of one object from another
The partial masking of one object from another
The compass heading of one object from another
The gradual parting of one object from another
Correct answer: The compass heading of one object from another
As the passage uses it, bearing is the compass heading of one object from another, measured as an angle from a reference such as north. The regular spacing of one object from another is distance, which the text explicitly separates from bearing by saying a bearing states which way to look rather than how near a contact lies. The partial masking of one object from another and the gradual parting of one object from another are neither direction nor distance, and the passage defines neither.
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The mentorship program paired senior officers with new recruits, but its designers warned against a common misunderstanding. A mentor's role, they emphasized, was not to make decisions for the recruit but to help the recruit learn to make sound decisions independently. A mentor who solved every problem would produce someone dependent rather than capable. The measure of success was a recruit who eventually needed the mentor less, not more.
What does the passage indicate is the goal of mentorship?
To remove the recruit's daily decisions
To feed the recruit's constant reliance
To build the recruit's unaided judgment
To shrink the recruit's annual workload
Correct answer: To build the recruit's unaided judgment
The goal of mentorship is to build the recruit's unaided judgment. The designers say a mentor's role is not to decide for the recruit but to help the recruit learn to make sound decisions independently, and that success means needing the mentor less over time. To remove the recruit's daily decisions is precisely the misunderstanding they warn against, to feed the recruit's constant reliance produces the dependence they call a failure, and to shrink the recruit's annual workload is never mentioned as an aim.
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The drought had lasted two years, and the reservoir stood at a quarter of its capacity. City officials faced a choice between mandatory restrictions, which the public resented, and voluntary appeals, which had so far produced little change. A council member proposed a third path: tiered pricing that left basic use affordable while charging steeply for excess. Consumption fell within a month, and the reservoir stabilized without the heavy-handed bans residents had feared.
Which approach ultimately reduced water consumption?
Gentle appeals that spread with printed posters
Blanket curbs that arrived with official orders
Graded charges that climbed with wasteful usage
Deeper wells that opened with seasonal rainfall
Correct answer: Graded charges that climbed with wasteful usage
Consumption fell under graded charges that climbed with wasteful usage. The council member's third path kept basic use affordable while charging steeply for excess, and within a month the reservoir stabilized. Blanket curbs that arrived with official orders describes the mandatory restrictions the public resented and the bans residents feared, which were avoided. Gentle appeals that spread with printed posters had produced little change, and deeper wells that opened with seasonal rainfall appear nowhere in the passage.
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Some readers approach a difficult passage by trying to memorize every detail, but this often backfires. Holding many isolated facts in mind leaves little attention for grasping how they relate. A more effective strategy is to read for structure first, noting how the passage is organized and where its main point lies, then return for details only as the questions require. Understanding the shape of an argument makes its parts far easier to locate and recall.
What reading strategy does the passage recommend?
Mapping the framework and central claim early
Storing the phrasing and precise detail early
Dodging the passage and reading queries early
Scanning the ending and working upwards early
Correct answer: Mapping the framework and central claim early
The strategy recommended is mapping the framework and central claim early, then returning for details only as the questions require. The passage says storing the phrasing and precise detail early backfires, because holding isolated facts in mind leaves little attention for grasping how they relate. Dodging the passage and reading queries early is never suggested, and scanning the ending and working upwards early is not the organization-first approach the text describes.
Read the passage, then answer the question.
The veteran navigator distrusted any single instrument, no matter how modern. A satellite system could lose signal, a gyrocompass could drift, and a chart could be outdated. By cross-checking several independent sources, he could catch the moment one of them began to lie. He often told trainees that the dangerous error is not the one you detect but the one you trust without question.
What can be inferred about why the navigator cross-checks his instruments?
Advancement exposes the gauge that has drifted
Comparison exposes the gauge that has faltered
Isolation exposes the gauge that has slackened
Obsolescence exposes the gauge that has failed
Correct answer: Comparison exposes the gauge that has faltered
He cross-checks because comparison exposes the gauge that has faltered. The passage says that by checking several independent sources he can catch the moment one of them begins to lie, since a satellite system can lose signal, a gyrocompass can drift and a chart can go out of date. Isolation exposes the gauge that has slackened is the opposite of his practice, and he rejects neither new nor old equipment, so advancement exposes the gauge that has drifted and obsolescence exposes the gauge that has failed both misstate him.
A worker pushes a crate with a steady horizontal force of 50 newtons, moving it 8 meters across a level floor. How much work is done on the crate?
Fifty-eight joules
Eight hundred joules
Four thousand joules
Four hundred joules
Correct answer: Four hundred joules
The work done is four hundred joules. Work equals the force multiplied by the distance moved along the line of that force, and fifty newtons over eight meters gives four hundred joules. Fifty-eight joules comes from adding the two figures instead of multiplying them. Eight hundred joules doubles the true product, and four thousand joules slips the decimal place by treating the distance as eighty meters.
A 30-newton force is applied to a box, but the box does not move at all. According to the physics definition of work, how much work is done on the box?
Ninety joules of work
Thirty joules of work
Sixty joules of work
Zero joules of work
Correct answer: Zero joules of work
The answer is zero joules of work. Work equals force multiplied by the distance the object moves, so when the displacement is nothing the product is nothing, however large the applied force may be. Thirty joules of work simply reports the force as though newtons were joules. Sixty joules of work and ninety joules of work multiply that force by an imagined displacement, but the box never moved, so no mechanical work was performed on it.
A driver gear with 12 teeth meshes with a driven gear that has 36 teeth. Using the gear ratio formula, what is the gear ratio of this pair?
Twelve to one
One to thirty-six
Thirty-six to one
Three to one
Correct answer: Three to one
The gear ratio is three to one. The ratio divides the teeth on the driven gear by the teeth on the driver gear, and thirty-six divided by twelve is three, so the small driver must turn three times for the large driven gear to turn once. Twelve to one and thirty-six to one each quote a raw tooth count as though the other gear had a single tooth, and one to thirty-six inverts the comparison as well.
A small driver gear turns at 300 revolutions per minute and is connected to a larger driven gear in a 3 to 1 reduction. How fast does the driven gear turn?
Three hundred rpm
One hundred rpm
Nine hundred rpm
Nine thousand rpm
Correct answer: One hundred rpm
The driven gear turns at one hundred rpm. In a reduction the output speed is the input speed divided by the ratio, so three hundred divided by three is one hundred, and the larger driven gear turns more slowly while delivering more torque. Three hundred rpm leaves the input speed unchanged, nine hundred rpm multiplies by the ratio instead of dividing, and nine thousand rpm compounds that error with a decimal slip.
In a gear reduction where a small gear drives a large gear, what is gained at the driven gear as its speed is reduced?
Improved voltage
Increased torque
Reduced friction
Weaker vibration
Correct answer: Increased torque
What is gained is increased torque. A gear reduction trades rotational speed for turning effort, so as the large driven gear turns more slowly than the small driver it delivers proportionally greater turning force, which is why a low gear pulls harder but travels slower. Improved voltage belongs to electrical machines rather than gearing, and neither weaker vibration nor reduced friction follows from changing the tooth counts of a meshing pair.
A lever lifts a load with an output force of 600 newtons while the person applies an input effort of 150 newtons. What is the mechanical advantage of the lever?
A gain of seven fifty
A gain of one fourth
A gain of four times
A gain of six hundred
Correct answer: A gain of four times
The lever gives a gain of four times. Mechanical advantage is the output load force divided by the input effort force, and six hundred divided by one hundred and fifty is four, so the lever multiplies what the person applies four times over. A gain of one fourth inverts that division. A gain of seven fifty adds the two forces together instead of dividing them, and a gain of six hundred simply repeats the load force as though it were the ratio.
What does mechanical advantage describe about a simple machine?
How much the machine consumes the current
How much the machine burdens the platform
How much the machine generates the warmth
How much the machine multiplies the force
Correct answer: How much the machine multiplies the force
Mechanical advantage describes how much the machine multiplies the force, that is, the ratio of the output force to the input force applied to it. A value above one means the force delivered is larger than the force supplied. How much the machine consumes the current is an electrical quantity, how much the machine generates the warmth measures waste heat, and how much the machine burdens the platform is simply its weight, none of which is a force ratio.
A movable pulley is attached directly to a load while one rope end is anchored above. Compared with a single fixed pulley, the movable pulley provides:
Unaided effort for once the load
Third effort for triple the load
Doubled effort for half the load
Halved effort for twice the load
Correct answer: Halved effort for twice the load
A movable pulley gives roughly a mechanical advantage of two, which is halved effort for twice the load. Two rope segments share the weight, so the effort needed falls to about half of it. Unaided effort for once the load describes the single fixed pulley the question compares it with, which only redirects the force. Third effort for triple the load overstates a single movable sheave, and doubled effort for half the load would be worse than lifting by hand.
What is the main difference between a fixed pulley and a movable pulley?
Fixed ones steer force while movable ones lessen it
Fixed ones divide force while movable ones split it
Fixed ones double force while movable ones carry it
Fixed ones shrink force while movable ones point it
Correct answer: Fixed ones steer force while movable ones lessen it
The main difference is that fixed ones steer force while movable ones lessen it: a fixed pulley is attached to a stationary support and changes only the direction of the pull, giving a mechanical advantage of about one, whereas a movable pulley travels with the load and roughly halves the effort. Fixed ones shrink force while movable ones point it reverses the two. Fixed ones divide force while movable ones split it wrongly credits both with reducing effort, and fixed ones double force while movable ones carry it credits the fixed pulley with a gain it does not give.
A pulley system must lift a 240-pound load with four rope segments supporting it. Ignoring friction, about how much force is needed to lift it?
Thirty pounds of pull
Sixty pounds of effort
Eighty pounds of force
Forty pounds of pull
Correct answer: Sixty pounds of effort
The answer is sixty pounds of effort. Ignoring friction, the mechanical advantage of a pulley system is roughly the number of rope segments supporting the load, which is four here, so the required pull is the load divided by four. Thirty pounds of pull would follow from counting eight supporting segments, eighty pounds of force from counting three, and forty pounds of pull from counting six. The trade-off is that four feet of rope must be hauled for each foot the load rises.
A see-saw lever balances when the turning effect on each side is equal. If a 60-pound child sits 4 feet from the pivot, how far from the pivot must a 48-pound child sit on the other side to balance it?
Four feet off
Eight feet away
Five feet away
Three feet away
Correct answer: Five feet away
The lighter child must sit five feet away. A lever balances when weight multiplied by distance matches on both sides, and sixty pounds at four feet gives two hundred and forty, so the forty-eight pound child needs two hundred and forty divided by forty-eight. Four feet off simply copies the heavier child's distance, three feet away comes from working the ratio upside down, and eight feet away overshoots the balance point, since the lighter child sits farther out but not that far.
On a balanced plank lever, the fixed point on which the plank pivots and from which the effort and load distances are measured is called the:
Resistance arm
Lever fulcrum
Turning moment
Lever arm
Correct answer: Lever fulcrum
The fixed pivot is the lever fulcrum, and both the effort and load distances are measured from it. A resistance arm is the distance from that pivot out to the load, and a lever arm is the general name for such a perpendicular distance, so both are lengths rather than the point itself. A turning moment is a force multiplied by one of those lengths, which makes it an effect of the lever rather than the place it rests on.
In a class 1 lever the fulcrum sits between the effort and the load, while in a class 2 lever the load sits between the fulcrum and the effort. Which everyday tool is an example of a class 2 lever?
A heavy wheelbarrow
A pointed pitchfork
A galvanized shovel
A playground seesaw
Correct answer: A heavy wheelbarrow
A heavy wheelbarrow is the class 2 example. Its load sits between the wheel, which acts as the fulcrum, and the handles where the effort is applied, so it always yields a mechanical advantage above one. A playground seesaw is a class 1 lever, with the central pivot as the fulcrum sitting between the effort at one end and the load at the other. A pointed pitchfork and a galvanized shovel are class 3 levers, because the effort from the lower hand is applied between the fulcrum hand and the load at the far end.
A mechanic applies 90 newtons of force at the end of a wrench handle 0.5 meters long, perpendicular to the bolt. Using the torque formula, what torque is produced at the bolt?
Ninety newton-meters
Forty-five newton-meters
One eighty newton-meters
Four fifty newton-meters
Correct answer: Forty-five newton-meters
The torque produced is forty-five newton-meters. Torque is the applied force multiplied by the perpendicular lever arm, so ninety newtons acting at half a meter gives forty-five. Ninety newton-meters reports the force alone and ignores the handle length. One eighty newton-meters divides by the half-meter instead of multiplying by it, and four fifty newton-meters treats the handle as five meters long rather than half a meter.
A book rests motionless on a table and stays at rest until something pushes it. This tendency of an object to remain at rest unless acted on by an outside force illustrates which of Newton's laws of motion?
The law of inertia
The law of gravity
The law of entropy
The law of cooling
Correct answer: The law of inertia
The resting book illustrates the law of inertia, which is the first of Newton's three laws of motion: a body stays at rest, or keeps moving at a steady speed, until an unbalanced outside force acts on it. The law of gravity describes the pull between two masses rather than a body's resistance to any change in its state of motion, so it does not name what the book demonstrates. The law of cooling is also Newton's, but it sets the rate at which a warm object sheds heat and says nothing about rest or movement. The law of entropy belongs to thermodynamics and governs how disorder grows, which is a different subject altogether.
In a four-stroke gasoline engine, which stroke produces the power that turns the crankshaft?
The stroke in which the burning gases drive the piston down
The stroke in which the rising piston squeezes the fuel mix
The stroke in which the piston pushes the burned gases away
The stroke in which the fresh fuel charge fills the chamber
Correct answer: The stroke in which the burning gases drive the piston down
The crankshaft is turned by the stroke in which the burning gases drive the piston down. Ignition makes the compressed charge expand very rapidly, and that expansion is the only part of the cycle that delivers energy to the crankshaft. The stroke that lets the fresh fuel charge fill the chamber only loads the cylinder and takes energy from the crankshaft rather than adding any. The stroke in which the rising piston squeezes the fuel mix likewise absorbs energy to raise pressure before ignition. The stroke that pushes the burned gases away clears the cylinder afterward and produces no useful work.
A hydraulic press has an input piston with an area of 2 square inches and an output piston with an area of 20 square inches. What is the mechanical advantage of the press, ignoring friction?
18 to 1
40 to 1
10 to 1
22 to 1
Correct answer: 10 to 1
The mechanical advantage is 10 to 1. Pascal's principle transmits the same pressure through the confined fluid, so the force ratio equals the output area divided by the input area, and 20 divided by 2 is 10. A ratio of 40 to 1 comes from multiplying the two areas instead of dividing them. A ratio of 22 to 1 comes from adding the areas, and a ratio of 18 to 1 comes from subtracting them; neither operation yields a force ratio.
Which list correctly identifies three of the basic simple machines?
Engine, spring, and battery cable
Rotor, gasket, and hydraulic pump
Piston, magnet, and flywheel gear
Pulley, lever, and inclined plane
Correct answer: Pulley, lever, and inclined plane
The pulley, lever, and inclined plane are three of the six classic simple machines, along with the wheel and axle, the wedge, and the screw. Each changes the size or the direction of an applied force with no internal power source. An engine, a spring, and a battery cable are a compound assembly, an energy store, and a conductor, not simple machines. A piston, a magnet, and a flywheel gear are parts of larger mechanisms rather than machines in their own right. A rotor, a gasket, and a hydraulic pump are likewise components of complex systems.
What is the value of −8+5−(−3)?
3
8
0
6
Correct answer: 0
The value is 0. Work left to right: negative 8 plus 5 gives negative 3, and subtracting negative 3 is the same as adding 3, so negative 3 plus 3 leaves 0. A result of 3 comes from stopping at the intermediate total of negative 3 and reporting its size without the sign. A result of 8 comes from dropping the leading term altogether and evaluating only 5 minus negative 3. A result of 6 comes from reading the first term as positive 8 and then working 8 minus 5 plus 3.
A ladder is leaned against a wall so that it forms a right triangle. If the ladder reaches 8 feet up the wall and its base is 6 feet from the wall, how long is the ladder?
14 ft
16 ft
10 ft
12 ft
Correct answer: 10 ft
The ladder is 10 ft long. The wall and the ground meet at a right angle, so the ladder is the hypotenuse: square 8 and 6 to get 64 and 36, add them to get 100, and take the square root to get 10. A length of 14 ft comes from adding the two legs instead of working with their squares. A length of 16 ft doubles the 8 ft the ladder reaches up the wall. A length of 12 ft doubles the 6 ft from the wall to the base in the same way.
What is 43 of 64?
16
48
64
32
Correct answer: 48
The value is 48. Divide 64 into four equal parts of 16, then take three of those parts, which gives 48. A value of 16 stops at the intermediate quarter and never multiplies by 3. A value of 32 takes only two of the four parts, which is one half rather than three quarters. A value of 64 repeats the whole amount without taking any fraction of it at all.
If 6 is added to twice a number, the result is 20. What is the number?
14
7
20
10
Correct answer: 7
The number is 7. Twice the number plus 6 equals 20, so twice the number is 14, and half of 14 is 7. A value of 14 stops at that intermediate step and reports twice the number rather than the number. A value of 10 halves 20 first and never removes the 6. A value of 20 simply repeats the total stated in the question, which is the result of the operations and not the number they were applied to.
What is the median of the numbers 9, 3, 15, 7, and 11?
15
9
10
12
Correct answer: 9
The median is 9. Put the five values in order as 3, 7, 9, 11, 15 and take the one in the middle position, which is 9. A value of 15 is the middle number of the list only as it is printed, and the list has to be sorted before a middle position means anything; 15 is in fact the largest value. A value of 12 is the range, the largest value less the smallest, which measures how spread out the numbers are rather than where their center is. A value of 10 comes from averaging a middle pair, which is the rule for a list with an even count; this list holds five values, so a single value stands alone in the middle and nothing is averaged.
Multiply: (3×104)×(2×103). What is the result in scientific notation?
5 x 10^1
6 x 10^1
5 x 10^7
6 x 10^7
Correct answer: 6 x 10^7
The product is 6 x 10^7. Multiply the coefficients, 3 times 2, to get 6, and add the exponents, 4 plus 3, to get 7. A coefficient of 5 comes from adding 3 and 2 rather than multiplying them. An exponent of 1 comes from subtracting 3 from 4 rather than adding. The choice showing a coefficient of 5 with an exponent of 1 makes both of those slips at once.
A circle has a radius of 5. What is its area? (Use π=3.14)
78.5
31.4
62.8
50.0
Correct answer: 78.5
The area is 78.5. Area equals pi times the radius squared, so 3.14 times 25 gives 78.5. A value of 31.4 is the circumference, found by multiplying pi by twice the radius instead of by the radius squared. A value of 62.8 applies that same circumference formula after mistaking the diameter of 10 for the radius. A value of 50.0 squares the radius correctly but then doubles the 25 instead of multiplying it by pi.
Solve for x: 4x−3=2x+9.
4
1
2
6
Correct answer: 6
The solution is 6. Take 2x from both sides to leave 2x minus 3 equals 9, add 3 to both sides to get 2x equals 12, and halve that to get 6. A value of 2 comes from moving the x terms and the constants to the same sides with the wrong signs, which turns the equation into 6x equals 12. A value of 1 makes that same sign slip and also gathers the constants as 9 minus 3, giving 6x equals 6. A value of 4 just repeats the coefficient printed in front of the first term.
What fraction is equivalent to 0.375?
1/3
3/4
3/8
5/8
Correct answer: 3/8
The fraction is 3/8. Read 0.375 as 375 thousandths, then divide the top and the bottom by 125 to reach 3/8. The fraction 3/4 is 0.75, which is twice as large, and comes from reducing by 500 instead of 125. The fraction 5/8 is 0.625, the part left over when 0.375 is taken from a whole. The fraction 1/3 is about 0.333 and only resembles 0.375 in its leading digit.
A cube has edges of length 4 inches. What is its volume?
16 cu in
48 cu in
24 cu in
64 cu in
Correct answer: 64 cu in
The volume is 64 cu in. Volume of a cube is the edge multiplied by itself three times, so 4 times 4 times 4 gives 64. A value of 16 cu in squares the edge and stops, which gives the area of one face. A value of 48 cu in multiplies that face area by 3 for the three dimensions instead of by the edge. A value of 24 cu in multiplies the edge by the six faces of the cube, which counts faces rather than filling space.
If a quantity decreases from 250 to 200, what is the percent decrease?
40.0%
50.0%
25.0%
20.0%
Correct answer: 20.0%
The decrease is 20.0%. The quantity falls by 50, and 50 divided by the original 250 is 0.2, which is 20 percent. A figure of 25.0% divides the same 50 by the new value of 200 rather than by the starting value. A figure of 50.0% reports the raw drop of 50 units as though units were already percent. A figure of 40.0% doubles the drop to 100 before dividing by 250.
What is the value of ∣−12∣+∣7∣?
12
19
24
5
Correct answer: 19
The value is 19. Absolute value strips the sign, so negative 12 becomes 12 and 7 stays 7, and 12 plus 7 is 19. A value of 5 keeps the sign on the first term and works out negative 12 plus 7 as a subtraction. A value of 12 reports only the first absolute value and never adds the second. A value of 24 doubles that first absolute value instead of adding the 7.
Three consecutive integers add up to 48. What is the largest of the three?
21
15
19
17
Correct answer: 17
The largest is 17. Call the integers n, n plus 1 and n plus 2; their sum is 3n plus 3, so 3n is 45 and n is 15, making the three integers 15, 16 and 17. A value of 15 is the smallest of that trio rather than the largest. A value of 19 comes from adding the 3 instead of subtracting it, which gives n as 17 and pushes the trio up by two. A value of 21 comes from making that same sign slip and also stepping the terms up in twos, and 19 plus 20 plus 21 is far more than 48.
What is the slope of the line passing through the points (1,2) and (4,11)?
9
-9
-3
3
Correct answer: 3
The slope is 3. Slope is the change in y over the change in x, so 11 minus 2 is 9, 4 minus 1 is 3, and 9 divided by 3 is 3. A value of 9 reports only the rise and never divides by the run. A value of -3 subtracts the coordinates in opposite orders, taking 2 minus 11 over 4 minus 1. A value of -9 makes that reversal and also skips the division.
A coin is flipped twice. What is the probability of getting heads both times?
1/4
1/8
3/4
1/3
Correct answer: 1/4
The probability is 1/4. The flips are independent, so multiply 1/2 by 1/2, and the four equally likely results are HH, HT, TH and TT, only one of which is two heads. A probability of 1/8 multiplies three halves together and answers for three flips instead of two. A probability of 1/3 counts the results as two heads, one head and no heads, which are not equally likely. A probability of 3/4 is the chance of getting at least one head, the opposite of what is asked.
Simplify the expression: 3(2x+4)−5x.
x - 12
6x + 4
x + 12
x + 24
Correct answer: x + 12
The expression simplifies to x + 12. Distributing the 3 gives 6x + 12, and taking 5x away from 6x leaves x, so the result is x + 12. The form x - 12 carries the product of 3 and 4 across with the wrong sign. The form 6x + 4 multiplies only the 2x by 3, leaves the 4 untouched, and never subtracts the 5x. The form x + 24 multiplies the 4 by 6 rather than by 3, doubling the constant term.
A worker earns $18 per hour and gets time-and-a-half for any hours beyond 40 in a week. What is the pay for a 44-hour week?
$792
$828
$864
$756
Correct answer: $828
The pay is 828.Thefirst40hourspay40times18,whichis720,andthe4extrahourspay27anhour,whichadds108,for828intotal.Atotalof792 pays all 44 hours at the flat rate of 18 and ignores the overtime premium. A total of 864paysthe4extrahoursatdoubletherateratherthanatoneandahalftimes.Atotalof756 adds only the half-rate premium of 9 an hour for the 4 extra hours and drops their base pay.
What is 54 written as a percent?
20%
60%
80%
40%
Correct answer: 80%
The answer is 80%. Dividing 4 by 5 gives 0.8, and a decimal becomes a percent when it is multiplied by 100, so 0.8 becomes 80%. A figure of 20% is the value of 1/5 and comes from reading the fraction upside down. A figure of 40% comes from treating the denominator as 10, which turns the fraction into 4/10. A figure of 60% is the value of 3/5 and follows from miscopying the numerator as 3.
A right circular cylinder has a radius of 3 and a height of 10. What is its volume? (Use π=3.14)
188.4
94.20
28.26
282.6
Correct answer: 282.6
The volume is 282.6. Volume of a cylinder is pi times the radius squared times the height, so 3.14 times 9 times 10 gives 282.6. A value of 94.20 multiplies pi by the radius once instead of squaring it. A value of 28.26 squares the radius correctly but leaves the height out altogether. A value of 188.4 is the curved side area, found from two times pi times radius times height rather than from the squared radius.
If 7x=56, what is the value of x+4?
52
60
12
32
Correct answer: 12
The value is 12. Dividing 56 by 7 gives x as 8, and adding 4 to that 8 gives 12. A value of 60 adds the 4 to the 56 before dividing, or simply adds it to the wrong quantity. A value of 52 subtracts the 4 from the 56 instead. A value of 32 finds x correctly as 8 but multiplies it by 4 rather than adding.
What is the greatest common factor of 24 and 36?
36
12
72
24
Correct answer: 12
The greatest common factor is 12. Both numbers break down into 12 times something, since 24 is 12 times 2 and 36 is 12 times 3, and no larger number divides both. A value of 72 is the least common multiple, the smallest number both divide into, which answers the opposite question. A value of 24 divides the first number but leaves a remainder in 36. A value of 36 divides the second number but is larger than 24 and so cannot divide it.
A store marks up an item that costs $50 by 30%. What is the selling price?
$65
$35
$50
$80
Correct answer: $65
The selling price is 65.Amarkupof30percenton50adds0.30times50,whichis15,sothepricerisesto65.Apriceof80 treats the 30 as 30 dollars and adds it straight onto the cost. A price of 35subtractsthe15markupinsteadofaddingit.Apriceof50 repeats the cost and applies no markup at all.
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The quartermaster argued that the ship should carry a surplus of spare parts on long deployments. Critics countered that excess cargo wasted limited storage and slowed the vessel. The quartermaster replied that a single missing component could strand a ship for weeks, while a few extra crates cost only space. The savings of running lean, he insisted, vanished the moment a critical failure occurred far from any port.
What is the main idea of this passage?
Spare parts repay the room they fill, because a breakdown grounds a ship
Spare parts crowd the hold they fill, because a lean ship travels faster
Spare parts spark the rows they cause, because a ship crew relishes talk
Spare parts serve the brief runs they match, because a ship stays nearby
Correct answer: Spare parts repay the room they fill, because a breakdown grounds a ship
The passage argues that spare parts repay the room they fill, because a breakdown grounds a ship. The quartermaster grants that extra crates take up space, then answers that one missing component can hold a vessel for weeks far from any help, so the apparent saving disappears at the worst moment. The claim that spare parts crowd the hold a lean ship travels with is the objection the passage answers, not the point it reaches. The ship crew and its talk never appear, and the rows the two sides spark are only the setting for the argument rather than its substance. Nothing limits the case to the brief runs a ship serves while it stays nearby; the argument is strongest on the long deployments the passage describes.
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Urban beekeeping has surged in popularity over the past decade. Rooftops, balconies, and community lots that once sat empty now host hives. City flowers, drawn from a wide mix of gardens and parks, often give urban honey a more varied flavor than rural honey from a single crop. Surprisingly, studies have found that bees in some cities thrive better than their countryside counterparts, where pesticide-heavy monocultures dominate.
Which statement can be inferred from the passage?
Bees kept in a pasture meet heavier chemical loads than city bees do
Bees kept in a city travel wider daily circuits than country bees do
Bees kept in a city produce sweeter darker honey than upland bees do
Bees kept in a garden face stricter legal barriers than city bees do
Correct answer: Bees kept in a pasture meet heavier chemical loads than city bees do
The passage supports the inference that bees kept in a pasture meet heavier chemical loads than city bees do. It reports that bees in some cities do better than their countryside counterparts, where pesticide-heavy monocultures dominate, which points to the sprayed farmland as the harder place to live. Nothing in it says a city bee must travel wider daily circuits than a country bee; flight distance is never measured or compared. The passage calls urban honey more varied in flavor rather than sweeter or darker, so the claim that a city hive can produce honey to beat an upland one is not supported. It never mentions legal barriers of any kind, stricter or otherwise, and it lists a garden as one of the many places city flowers grow rather than a site where bees are kept under special rules.
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The seemingly chaotic flight of a bat is in fact a precise navigational feat. By emitting rapid bursts of sound and listening for the echoes, a bat builds a detailed map of its surroundings in total darkness. This biological sonar, called echolocation, lets the animal detect an insect the width of a human hair while weaving among branches at high speed.
As used in the passage, the word 'feat' most nearly means:
A remarkable achievement
A persistent misjudgment
A continuous disturbance
A convenient measurement
Correct answer: A remarkable achievement
In this passage the word means a remarkable achievement. The bat's flight is called precise and navigational, and the paragraph goes on to praise an animal that can pick out prey the width of a hair while weaving through branches at speed, which is admiration for a difficult act well done. A persistent misjudgment reverses that praise into failure. A continuous disturbance treats the word as a kind of noise, borrowing from the sounds the bat emits rather than from the sentence. A convenient measurement reads the word as the unit of length that sounds the same, which the sentence structure does not allow.
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The new training officer replaced the old policy of grouping all recruits into a single class. Instead, she sorted them by prior experience, giving advanced recruits harder drills while beginners reviewed fundamentals. Within a month, both groups improved faster than any class had under the old system. Even recruits who had once lagged now kept pace, because they were no longer rushed past material they had not mastered.
Why did the lagging recruits improve under the new system?
They were handed a lighter drill load to finish the week
They were placed beside a faster squad to match the pace
They were given a fair chance to master the shaky basics
They were offered a shorter course to save the idle time
Correct answer: They were given a fair chance to master the shaky basics
They improved because they were given a fair chance to master the shaky basics. The passage says beginners went back over fundamentals and that recruits who had lagged kept pace once they were no longer pushed past material they had not yet learned. It never says anyone was handed a lighter drill load or asked to finish less by the end of the week, so the workload claim is unsupported. The officer split the beginners away from the advanced recruits rather than placing them beside a faster squad to match its pace. And nobody was offered a shorter course to save idle time, because the length of the course is never mentioned.
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Mangrove forests grow where land meets sea, their tangled roots rising from salty mud. These roots trap sediment and slow incoming waves, shielding coastlines from erosion and storm surge. Beyond protecting shores, mangroves serve as nurseries for fish and store carbon at rates that rival or exceed those of tropical rainforests. Yet clearing for shrimp farms and development has destroyed vast stretches of these vital ecosystems.
Which of the following best states the author's purpose?
To show the many gifts a wetland gives and the peril ahead
To urge the case a shrimp farm makes and the ground gained
To rate the mangrove forest a poor carbon store and a risk
To trace the taste a mangrove fish has and the meal appeal
Correct answer: To show the many gifts a wetland gives and the peril ahead
The author writes to show the many gifts a wetland gives and the peril ahead. Three sentences set out how the tangled roots hold sediment, blunt waves, shelter young fish and lock away carbon, and the closing sentence warns that clearing has already wiped out huge areas. The passage treats a shrimp farm as a cause of that destruction, so it cannot be urging its case or the ground such ponds would have gained. It says these forests match or beat tropical rainforests at storing carbon, which is the reverse of rating a mangrove forest a poor carbon store or a risk. It never sets out to trace the taste a mangrove fish has, nor the appeal of any meal made from one; fish appear only as an example of what the roots shelter.
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The ship's log noted that the storm 'abated' just after midnight, and the watch officer ordered the crew to resume routine duties on deck. The seas, which had pitched the vessel violently for hours, settled into a steady swell, and the wind dropped to a moderate breeze.
As used in the passage, the word 'abated' most nearly means:
Stiffened in force
Wandered in course
Slackened in force
Persisted in force
Correct answer: Slackened in force
In this passage the word means slackened in force. Everything reported after it describes a fall: the pitching seas settle into a steady swell, the wind drops to a moderate breeze, and the watch officer judges the deck safe enough for routine duties again. Stiffened in force is the reverse of what those details show. Wandered in course describes a change of direction, while the sentence is about how hard the weather blew rather than which way. Persisted in force would mean nothing changed, which contradicts the return to normal work on deck.
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Many people believe that goldfish have a memory of only a few seconds, but research tells a different story. In controlled experiments, goldfish learned to push a lever for food and remembered the task months later. They can be trained to navigate mazes and even distinguish between different musical pieces. The myth of the three-second memory likely persists because it offers a convenient excuse for keeping fish in small, bare bowls.
What is the author's main point?
Goldfish adapt poorly to drills and lose a task within hours
Goldfish stick to a lesson and recall a drill long afterward
Goldfish listen to a melody and ignore a generous food plate
Goldfish come to little harm and flourish inside a bare bowl
Correct answer: Goldfish stick to a lesson and recall a drill long afterward
The author's point is that goldfish stick to a lesson and recall a drill long afterward. The passage cites controlled work in which the animals learned to push a lever for food and still had the trick months later, and adds that they run mazes and tell one piece of music from another. That same evidence shows goldfish adapt well rather than poorly to drills, and that they hold a task far longer than the hours such a claim would allow. Goldfish that listen to a melody are showing memory, not choosing a tune over a generous plate of food. And the closing sentence attacks the bare bowl as an excuse the myth props up, so it does not claim goldfish come to little harm or flourish inside one.
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The report opened with a confident summary, but the data buried in its appendix told a more cautious story. While the summary claimed the new fuel additive 'consistently' improved engine efficiency, the appendix showed gains only under laboratory conditions, with negligible effects in real-world testing. A careful reader comparing the two sections would notice the gap between the report's tone and its evidence.
Which statement is best supported by the passage?
The buried data gave a careful reader little detail
The additive lifted real engine output beyond a lab
The lab result matched a road result almost exactly
The bright preface promised a lift the tests denied
Correct answer: The bright preface promised a lift the tests denied
The passage best supports the statement that the bright preface promised a lift the tests denied. Its opening summary calls the improvement consistent, while the buried data show gains under laboratory conditions and almost nothing outside them, which is the gap a careful reader would notice. That buried data is where the meaningful detail sits, so it did not give a careful reader little to work with. Outside the lab the effects were negligible, so the additive never lifted real engine output beyond a lab bench. And because the lab result and the road result differed sharply, they cannot have matched almost exactly.
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The ancient Roman road network stretched across the empire, totaling tens of thousands of miles. These roads were engineered in layers, with a foundation of large stones topped by gravel and a paved surface that allowed water to drain. So durable was this construction that some Roman roads remain visible today, and a few still support local traffic nearly two thousand years after they were built.
Which detail from the passage supports the idea that Roman roads were exceptionally durable?
The roads crossed the whole span of a ten thousand mile empire
The roads bear the daily loads of a full twenty long centuries
The roads needed the packed bed of a sturdy gray stone footing
The roads carried the paved top of a well drained rain channel
Correct answer: The roads bear the daily loads of a full twenty long centuries
Durability is shown by the detail that the roads bear the daily loads of a full twenty long centuries. Traffic still running over a surface laid two thousand years ago is direct proof that the construction has lasted. That the roads crossed the whole span of a ten thousand mile empire measures reach, not endurance, and says nothing about how long any stretch survived. That they needed the packed bed of a sturdy gray stone footing, and that they carried a paved top that drained rain away like a channel, describe how the roads were built; a method on its own does not show the result held up. Only continued use after so long does that.
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A pilot's preflight inspection is not a formality to be rushed. Each item on the checklist guards against a specific failure that could prove catastrophic in the air. Skipping even a minor check, such as confirming the security of a fuel cap, has on rare occasions led to disaster. The discipline of the checklist exists precisely because human memory, under pressure, is unreliable.
Why, according to the passage, does the checklist discipline exist?
Because the rules a pilot obeys demand written records
Because a tense moment leaves the sharpest mind unsure
Because the daily routine gives a pilot quiet pleasure
Because the fuel cap outweighs a single plane airframe
Correct answer: Because a tense moment leaves the sharpest mind unsure
The checklist exists because a tense moment leaves the sharpest mind unsure. The final sentence gives that as the reason directly, saying the discipline is there precisely because recall fails when someone is under strain. No rules a pilot obeys are said to demand written records, and the passage treats the inspection as a real safeguard rather than a filing exercise. It never suggests the daily routine gives a pilot quiet pleasure either; it warns instead against rushing through it. The fuel cap is one example of a small item that can matter, not a part that outweighs a single plane airframe.
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When the harbor authority installed underwater microphones, it expected to record the hum of ship engines. Instead, the recordings captured an unexpected chorus: snapping shrimp, grunting fish, and the eerie songs of distant whales. The data revealed that the harbor, long thought of as a noisy industrial zone, was also a thriving acoustic community of marine life that researchers had largely overlooked.
Which statement best describes the author's tone?
Dismayed by what the instruments revealed
Annoyed by what the measurements revealed
Unimpressed by what the research revealed
Intrigued by what the soundscape revealed
Correct answer: Intrigued by what the soundscape revealed
The tone is best described as intrigued by what the soundscape revealed. The passage calls the chorus unexpected, the whale songs eerie, and the harbor a thriving acoustic community, which is the language of fascination. The author is not dismayed by what the instruments revealed, since the finding is presented as a gain rather than a loss; not annoyed by what the measurements revealed, since industrial noise is never criticized; and the detailed, wondering description rules out being unimpressed by what the research revealed.
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The debate over remote work often assumes a single right answer. In reality, the best arrangement depends on the task. Work requiring deep, uninterrupted concentration may flourish at home, while projects that thrive on spontaneous collaboration may suffer outside a shared space. Rather than choosing one model for everyone, organizations may serve their people best by matching the setting to the nature of the work.
What is the main idea of the passage?
Job type governs ideal workplace choice
Remote desks outrank crowded open space
Team projects need daily office contact
Uniform policy suits modern staff needs
Correct answer: Job type governs ideal workplace choice
The main idea is that job type governs ideal workplace choice. The passage rejects a single right answer and argues that concentration work may flourish at home while collaborative work may suffer outside a shared room. It does not hold that remote desks outrank crowded open space, since it grants that some projects fare worse away from colleagues. It does not hold that team projects need daily office contact, only that some benefit from proximity. And it directly rejects the notion that uniform policy suits modern staff needs.
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The phrase 'a watershed moment' is often used to describe a turning point after which things are never the same. The term comes from geography, where a watershed is the ridge that divides two drainage basins; rain falling on one side flows to one river, while rain on the other flows somewhere entirely different. The metaphor captures how a single decisive event can send the future in a wholly new direction.
As used in the passage, the phrase 'a watershed moment' most nearly means:
A pivotal juncture
A torrential storm
A watershed survey
A slight roadblock
Correct answer: A pivotal juncture
In context the phrase names a pivotal juncture. The passage defines it as a moment after which things are never the same, and the image of rain diverging on either side of a ridge shows one event sending the future in a wholly new direction. A torrential storm reads the word as weather and a watershed survey reads it as geography, both taking a figure of speech literally. A slight roadblock is far too small, since the passage stresses a wholly new direction rather than a brief obstacle.
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The shipping company switched from many small deliveries to a few large consolidated shipments. Fuel costs per item dropped sharply, and the number of trucks on the road fell. But customers complained that orders now arrived less frequently, forcing them to hold larger inventories. The company had traded one kind of cost for another, lowering its own expenses while shifting a burden onto its clients.
Which statement best captures the outcome described in the passage?
Genuine savings for the firm, plain gains for the buyers
Smaller outlay for the firm, added strain for the buyers
Costlier fuel for the firm, steady prices for the buyers
Slight upside for the firm, strong relief for the buyers
Correct answer: Smaller outlay for the firm, added strain for the buyers
The outcome is smaller outlay for the firm, added strain for the buyers. Fuel cost per item dropped sharply and trucks came off the road, while customers had to hold larger inventories because orders arrived less often. There were not genuine savings for the firm, plain gains for the buyers, since one side plainly absorbed a new cost. Costlier fuel for the firm, steady prices for the buyers reverses the passage, which says the per-item fuel cost fell. And slight upside for the firm, strong relief for the buyers inverts who came out ahead.
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For centuries, sailors prized the albatross as a sign of good fortune, believing the great bird's presence promised safe passage. Modern biologists, less concerned with omens, marvel at the albatross for a different reason: it can glide for hours, even days, without flapping its wings, using subtle differences in wind speed near the ocean surface to stay aloft with almost no effort.
How do the sailors' and biologists' views of the albatross differ?
Sailors dreaded its omen; biologists respect its instincts
Sailors trusted its luck; biologists admire its efficiency
Sailors tracked its ranges; biologists credit its fortunes
Sailors mapped its routes; biologists compute its headwind
Correct answer: Sailors trusted its luck; biologists admire its efficiency
The two views differ in that sailors trusted its luck; biologists admire its efficiency. The passage says sailors prized the bird as a sign of safe passage, while modern biologists, less concerned with omens, marvel at hours of gliding on almost no effort. Sailors dreaded its omen; biologists respect its instincts reverses the sailors' attitude, since they prized rather than feared the bird. Sailors mapped its routes; biologists compute its headwind wrongly credits both groups with studying the flight. And sailors tracked its ranges; biologists credit its fortunes hands the superstition to the wrong group.
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The young officer's first instinct was to issue orders the moment a problem arose. Over time, she learned a harder lesson: that pausing to gather information often led to faster solutions than acting at once. The crew, sensing that her decisions now rested on understanding rather than reflex, grew more willing to bring her early warnings of trouble before small issues became large ones.
Which statement can be inferred about the officer's growth?
Slow inquiry delayed crew progress
Silence replaced crew orders fully
Quick reflexes suited crew members
Measured judgment built crew trust
Correct answer: Measured judgment built crew trust
It can be inferred that measured judgment built crew trust. The crew, sensing that her decisions now rested on understanding rather than reflex, grew more willing to bring her early warnings of trouble. Silence replaced crew orders fully overstates the change, since she still decided and still directed. Quick reflexes suited crew members contradicts the passage, which shows the crew responding better to the newer and slower style. And slow inquiry delayed crew progress inverts the text, which says pausing to gather information often led to faster solutions.
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The documentary opened with sweeping shots of pristine wilderness and a narrator praising the region's untouched beauty. Only halfway through did the film reveal its purpose: to expose a proposed mining project that threatened the very landscapes the opening had celebrated. By first making viewers fall in love with the place, the filmmakers ensured that the later revelation of danger would land with greater force.
Why did the filmmakers open with images of untouched beauty?
To pad the sluggish preamble
To excuse the mining hazards
To promote the local tourism
To sharpen the eventual blow
Correct answer: To sharpen the eventual blow
The filmmakers opened with untouched beauty to sharpen the eventual blow. The passage states that by first making viewers fall in love with the place, they ensured the later revelation of danger would land with greater force. The shots were not there to pad the sluggish preamble, since they are described as a deliberate strategy. They were not there to promote the local tourism, a purpose the passage never raises. And they were not there to excuse the mining hazards, since the film exposes rather than defends the project.
Read the passage, then answer the question.
Caffeine works not by adding energy but by masking fatigue. The brain produces a chemical called adenosine that gradually builds up and signals tiredness. Caffeine blocks the receptors that detect adenosine, so the brain stops registering the fatigue signal even though the chemical is still present. When the caffeine wears off, the accumulated adenosine floods back, which is why a crash often follows.
According to the passage, why does a crash often follow caffeine use?
Ruined adenosine departs when the caffeine lands
Latent adenosine idles when the caffeine ignites
Fresh adenosine ceases when the caffeine arrives
Amassed adenosine surges when the caffeine fades
Correct answer: Amassed adenosine surges when the caffeine fades
A crash follows because amassed adenosine surges when the caffeine fades. The passage explains that caffeine only blocks the receptors while the chemical keeps building, so the whole backlog registers at once afterwards. Ruined adenosine departs when the caffeine lands is wrong because nothing is destroyed, and the passage says the chemical is still present. Latent adenosine idles when the caffeine ignites is wrong because the drug masks fatigue rather than supplying energy. And fresh adenosine ceases when the caffeine arrives is wrong because production continues throughout.
Read the passage, then answer the question.
The city's old bridge had become a bottleneck, and engineers proposed two solutions. One faction favored widening the existing structure, a cheaper option that would disrupt traffic for a year. The other pushed for a new parallel bridge, which cost far more but would keep traffic flowing during construction. The council ultimately chose the costlier path, reasoning that a year of gridlock would itself impose hidden costs on the local economy.
Why did the council choose the more expensive option?
Parallel spans would undercut the prices
Broader decks would defeat the engineers
New crossings would avoid the earthworks
Prolonged jams would sap the marketplace
Correct answer: Prolonged jams would sap the marketplace
The council paid more because prolonged jams would sap the marketplace. The passage says the members reasoned that a year of gridlock would itself impose hidden costs on the local economy. Parallel spans would undercut the prices is wrong because the parallel bridge was the far more expensive of the two proposals. Broader decks would defeat the engineers is wrong because widening was presented as a workable and cheaper option. And new crossings would avoid the earthworks is wrong because the second bridge still had to be built, only without halting traffic.
Read the passage, then answer the question.
The essay argued that silence is a skill as important as speech. A leader who fills every pause with words, the author wrote, may seem confident but often misses what others are trying to say. By contrast, a leader comfortable with silence invites quieter members of a team to speak and signals that their contributions are genuinely wanted. The most persuasive voice, the essay concluded, sometimes belongs to the one who knows when not to use it.
What is the central message of the essay?
The central message is that timely quiet strengthens leader impact. The essay says a leader comfortable with silence invites quieter members to speak, and that the most persuasive voice sometimes belongs to the one who knows when not to use it. Endless talk signals leader confidence is the very position the essay rejects, since filling every pause makes a leader miss what others are trying to say. Sheer volume decides leader persuasion misreads an argument about restraint. And withdrawn staff waste leader attention reverses the essay's respect for quieter contributors.
Read the passage, then answer the question.
The explorer's journal grew increasingly terse as the expedition wore on. Early entries ran for pages, rich with descriptions of landscapes and wildlife. By the final weeks, each day merited only a few clipped words: distances marched, rations remaining, weather endured. The shrinking entries, more than any single statement, conveyed how exhaustion had stripped the journey down to bare survival.
What does the change in the journal entries suggest?
Grinding fatigue left mere subsistence
Sagging interest ended idle authorship
Dulling scenery halted lavish accounts
Dwindling paper forced cramped entries
Correct answer: Grinding fatigue left mere subsistence
The shrinking entries suggest that grinding fatigue left mere subsistence. The passage says the late entries recorded only distances marched, rations remaining and weather endured, and that this conveyed how exhaustion stripped the journey down. Sagging interest ended idle authorship is wrong because the change tracks physical strain rather than a lapsed hobby. Dulling scenery halted lavish accounts is wrong because nothing suggests the country grew less remarkable. And dwindling paper forced cramped entries invents a shortage the passage never mentions.
A worker carries a heavy bucket on the end of a uniform horizontal plank that rests on two supports. To reduce the load felt by the support nearest the bucket, the worker should:
Slide the bucket toward the far support
Anchor the bucket nearer the plank edge
Center the bucket atop the near support
Double the bucket load beside the plank
Correct answer: Slide the bucket toward the far support
The worker should slide the bucket toward the far support. Each support carries a share of the load in proportion to the load's distance from the other support, so lengthening the bucket's arm about the far support shortens it about the near one and the near support bears less. Center the bucket atop the near support does the opposite and throws almost the whole weight onto it. Anchor the bucket nearer the plank edge leaves the weight at the same end the near support already carries. And double the bucket load beside the plank adds weight instead of moving it.
A vehicle climbs a steep hill in low gear rather than high gear. Low gear helps because it:
Lifts the torque while doubling the tempo
Raises the torque while cutting the speed
Blunts the torque while trimming the rate
Reduces the torque while raising the pace
Correct answer: Raises the torque while cutting the speed
Low gear raises the torque while cutting the speed. A low gear is a large reduction, so the wheels turn more slowly than the engine but with multiplied turning force, which is exactly what a climb demands. Lifts the torque while doubling the tempo cannot happen, because a gear train trades one for the other rather than raising both. Reduces the torque while raising the pace describes high gear, the wrong choice for a hill. And blunts the torque while trimming the rate would leave the vehicle worse off in every respect.
A 100-pound load is lifted using an inclined plane 12 feet long that rises 3 feet. Ignoring friction, the ideal effort needed to slide the load up the ramp is about:
Twenty-five pounds
Seventy-five pounds
Four hundred pounds
Thirty-three pounds
Correct answer: Twenty-five pounds
The ideal effort is twenty-five pounds. A ramp's ideal mechanical advantage is its length divided by its rise, twelve over three, or four, and the hundred-pound load divided by four leaves twenty-five pounds. Seventy-five pounds subtracts that result from the load instead of reporting it. Four hundred pounds multiplies by the advantage instead of dividing by it. And thirty-three pounds divides by the three-foot rise alone, ignoring the length of the ramp that creates the advantage.
Two pipes of different diameters carry the same steady volume of water per second. Compared with the wide pipe, water in the narrow pipe moves:
Sluggish
Unvaried
Speedier
Rearward
Correct answer: Speedier
Water in the narrow pipe is speedier. Steady flow means the same volume must pass every cross-section each second, so where the bore is smaller the water has to hurry to carry that volume through. Sluggish reverses the continuity rule and would leave water piling up at the constriction. Unvaried is wrong because two pipes of different bore cannot carry the same volume at one rate. And rearward is impossible, since the flow is driven one way along the line.
A spinning bicycle wheel resists being tilted to a new orientation and tends to keep its axis pointed the same way. This stabilizing behavior of a spinning mass is called:
The Bernoulli theorem
The gyroscopic effect
The centrifugal force
The thermal expansion
Correct answer: The gyroscopic effect
The behavior is called the gyroscopic effect. A rapidly spinning wheel carries angular momentum that resists any change in the direction of its spin axis, the same rigidity a spinning top and a gyrocompass both rely on. The Bernoulli theorem concerns pressure in a moving fluid rather than a spinning solid. The centrifugal force is the outward tendency felt in a turn and does nothing to hold an axis steady. And the thermal expansion simply describes how materials grow when heated.
A nut is being tightened with a wrench. Compared with pushing straight along the handle toward the bolt, applying the same force perpendicular to the handle produces:
Extra torque on the nut
Equal torque on the nut
Faint torque on the nut
Lower torque on the nut
Correct answer: Extra torque on the nut
A perpendicular push produces extra torque on the nut. Torque depends on the component of force acting at right angles to the handle, so a square push uses the whole lever arm. Lower torque on the nut is backwards, because the push aimed along the handle is the weaker of the two. Equal torque on the nut ignores the angle altogether. And faint torque on the nut describes the push driven straight at the bolt, which has almost no lever arm to work with.
A wheel and axle is used to raise a bucket from a well. To make raising the bucket easier with less effort, you should:
Fit a small wheel onto a thickened axle
Fit a broader wheel onto a thinner axle
Fit a weighted wheel onto a smooth axle
Fit a wooden wheel onto a polished axle
Correct answer: Fit a broader wheel onto a thinner axle
You should fit a broader wheel onto a thinner axle. Mechanical advantage here is the wheel's radius divided by the axle's radius, so widening the wheel and slimming the axle multiplies whatever effort you apply. Fit a small wheel onto a thickened axle drives that ratio below one and makes the lift harder. Fit a weighted wheel onto a smooth axle adds mass without touching the ratio. And fit a wooden wheel onto a polished axle only trims friction, leaving the advantage exactly where it was.
Two boxes slide down identical frictionless ramps. Box A weighs twice as much as box B. When they reach the bottom, their speeds are:
Box A doubles box B easily
Box A equals box B exactly
Box B outpaces box A twice
Box A beats box B fourfold
Correct answer: Box A equals box B exactly
At the bottom, box A equals box B exactly. On a frictionless ramp the speed gained depends on the vertical drop alone and not on mass, so the two boxes accelerate alike and arrive together. Box A doubles box B easily assumes that weight adds speed, which it does not. Box B outpaces box A twice assumes that lightness adds speed, which it also does not. And box A beats box B fourfold compounds the same mistake.
A belt connects a small pulley on a motor to a large pulley on a fan. As the belt runs, the large fan pulley turns:
Faster than a smaller pulley
Level with the driver pulley
Slower than the drive pulley
Opposite to the motor pulley
Correct answer: Slower than the drive pulley
The large fan pulley turns slower than the motor pulley. A belt drags the rims of both wheels along at one linear speed, so the bigger circumference swallows more belt per turn and completes fewer turns each minute. Faster than a smaller pulley reverses that relationship. Level with the driver pulley would hold only if the two wheels were the same size. And opposite to the motor pulley is wrong because an ordinary open belt drives both wheels the same way round.
A solid steel ball and a hollow steel ball have the same outside diameter. Dropped together in a vacuum, they will:
The balls arrive dead level
The hollow ball lands early
The balls hang frozen aloft
The solid ball lands sooner
Correct answer: The balls arrive dead level
Dropped in a vacuum, the balls arrive dead level. With no air to resist them, gravity accelerates every object at the same rate whatever its mass, so the solid and the hollow sphere fall side by side. The solid ball lands sooner assumes that heavier means quicker, which holds only where air resistance is in play. The hollow ball lands early makes the opposite mistake. And the balls hang frozen aloft confuses the absence of air with the absence of gravity.
A 200-pound load hangs from a system using one fixed pulley and one movable pulley, giving two supporting rope segments. Ignoring friction, the effort needed to hold the load is about:
One fourth of the load
One third of the load
One half of the load
One eighth of the load
Correct answer: One half of the load
The effort needed is one half of the load, about a hundred pounds. Two rope segments support the movable pulley, so they share the weight between them and the mechanical advantage is two. One third of the load would follow from counting three supporting segments instead of two. One fourth of the load counts four segments. And one eighth of the load counts eight, an advantage no single movable pulley can supply.
Antifreeze is added to a car's radiator water mainly because the mixture, compared with plain water:
Boils at a chillier point
Freezes at a colder point
Congeals at a tepid point
Vaporizes at a mild point
Correct answer: Freezes at a colder point
The mixture freezes at a colder point. Blending antifreeze into the water pushes the freezing point well below that of pure water, so the coolant will not turn to ice and crack the block in winter. Boils at a chillier point is the reverse of the truth, since the mixture also raises the boiling point. Congeals at a tepid point would leave the coolant useless in ordinary weather. And vaporizes at a mild point would drive the coolant out of the system rather than protect it.
A diver swims deeper underwater and feels increasing pressure on the ears. Water pressure increases with depth because:
The chill of the depths concentrates
The rumble of the ocean reverberates
The weight of the column accumulates
The salt of the shoreline evaporates
Correct answer: The weight of the column accumulates
Pressure grows with depth because the weight of the column accumulates. Every layer of water presses on the layers beneath it, so the deeper the diver goes the taller the column overhead and the harder the squeeze on the ears. The chill of the depths concentrates is wrong because the tiny density change with temperature is nowhere near the effect felt. The rumble of the ocean reverberates confuses sound with static pressure. And the salt of the shoreline evaporates has nothing to do with depth at all.
A small electric motor spins too fast and with too little turning force for a task. A gear reduction is added to its output shaft. The reduction will:
Push the speed and grow the torque
Trim the speed and sink the torque
Hold the speed and keep the torque
Drop the speed and lift the torque
Correct answer: Drop the speed and lift the torque
The reduction will drop the speed and lift the torque. Gearing down trades rotation for force, so the output shaft turns more slowly than the motor while delivering the greater turning effort the task needs. Push the speed and grow the torque cannot happen, since a gear train has no way to create both at once. Trim the speed and sink the torque would leave the shaft weaker as well as slower. And hold the speed and keep the torque describes no reduction at all.
To pry the lid off a paint can with a flat bar resting on the can's rim, the rim acts as the:
The effort hand
The pivot point
The load itself
The pointed tip
Correct answer: The pivot point
The rim acts as the pivot point. The bar is a lever: your hand supplies the effort at one end, the lid is the resistance raised at the other, and the rim is the fixed place the bar turns about. The effort hand names where you push rather than where the bar bears. The load itself names the lid being lifted. And the pointed tip names the working end of the bar, not the fixed point that supports it.
A car rounds a flat curve at steady speed. The force that actually keeps the car turning along the curve is supplied by:
Traction between the tires and the road
Thrust between the engine and the wheel
Pressure between the wind and the glass
Weight between the cabin and the riders
Correct answer: Traction between the tires and the road
The turning force is traction between the tires and the road. Rounding a curve needs a force aimed at the center of the turn, and on a flat road only the grip of the rubber can supply it. Thrust between the engine and the wheel drives the car forward along its path rather than sideways into the curve. Pressure between the wind and the glass is far too small and points the wrong way. And weight between the cabin and the riders acts straight down.
A thermometer's liquid rises in its thin tube when warmed because the liquid:
Hardens and sinks deeper down
Evaporates and forms thin gas
Expands and claims extra room
Lightens and drops raw weight
Correct answer: Expands and claims extra room
The liquid expands and claims extra room. Heating makes the fluid swell, and because the bore is so narrow even a tiny gain in volume drives the column noticeably higher, which is what the scale reads. Hardens and sinks deeper down is the reverse of what warming does. Evaporates and forms thin gas would wreck the instrument rather than move the column. And lightens and drops raw weight confuses mass, which does not change, with volume, which does.
A heavy crate must be slid across a rough floor. Placing several round pipes under the crate and rolling it makes the job easier mainly by:
Shedding solid mass for lighter freight
Spreading wider load for firmer footing
Nullifying downward pull for free float
Trading sliding drag for roller contact
Correct answer: Trading sliding drag for roller contact
The pipes help mainly by trading sliding drag for roller contact. Rolling resistance is a small fraction of sliding resistance, so the same crate needs far less push once it rides on pipes. Shedding solid mass for lighter freight is wrong because the crate weighs exactly what it weighed before. Spreading wider load for firmer footing is wrong because a larger contact patch does not by itself lower the resistance. And nullifying downward pull for free float is impossible, since gravity still acts on the crate.
A simple pendulum is shortened to half its original length. Its swing will become:
Unchanged, with a fixed period
Sluggish, with a longer period
Quicker, with a briefer period
Frozen, with a vanished period
Correct answer: Quicker, with a briefer period
The swing becomes quicker, with a briefer period. A pendulum's period depends on its length, so halving the length shortens the time each swing takes. Sluggish, with a longer period reverses that relationship. Unchanged, with a fixed period is wrong because mass is the thing that does not matter here, while length very much does. And frozen, with a vanished period would require the restoring force to disappear, which shortening the pendulum cannot do.
Pressing the brake pedal in a car forces fluid through lines to squeeze the brake pads. The fluid transmits the force well because liquids are:
Markedly compressible
Almost incompressible
Extremely lightweight
Thoroughly insulative
Correct answer: Almost incompressible
Brake fluid works because liquids are almost incompressible. Since the fluid barely changes volume under pressure, a push on the pedal travels nearly instantly down the lines to the pads. Markedly compressible is the reverse of the truth and would leave the pedal feeling spongy. Extremely lightweight has nothing to do with transmitting a force. And thoroughly insulative describes an electrical property that plays no part in a hydraulic circuit.
A counterweight is attached to a drawbridge so a small motor can raise the heavy span. The counterweight helps mainly by:
Enlarging the entire burden at the engine
Increasing the grinding drag at the joint
Reducing the actual tonnage at the bridge
Offsetting the girder torque at the hinge
Correct answer: Offsetting the girder torque at the hinge
The counterweight helps mainly by offsetting the girder torque at the hinge. It produces a turning effect opposite to that of the heavy span, so the two nearly cancel and only a small extra force is needed to swing the bridge up. Enlarging the entire burden at the engine is the opposite of what a counterweight achieves. Increasing the grinding drag at the joint would make the motor's task harder. And reducing the actual tonnage at the bridge is impossible, since the counterweight adds mass rather than removing it.
Two identical springs are joined end to end in a single line and then stretched by a hanging weight. Compared with one spring alone, this end-to-end pair will stretch:
Extends halfway under one hanging weight
Sits unyielding under one hanging weight
Elongates twice under one hanging weight
Moves unaltered under one hanging weight
Correct answer: Elongates twice under one hanging weight
Joined in series, the pair elongates twice under one hanging weight. Each spring carries the full load and stretches by its own amount, so the two extensions add and the total is double that of a single spring. Extends halfway under one hanging weight describes springs placed side by side rather than end to end. Moves unaltered under one hanging weight ignores the second spring altogether. And sits unyielding under one hanging weight would need a spring that does not stretch at all.
In a four-stroke engine, the stroke during which the piston moves up and squeezes the fuel-air mixture before ignition is the:
The full compression stroke
The induction intake stroke
The combustion power stroke
The expelled exhaust stroke
Correct answer: The full compression stroke
The stroke described is the full compression stroke. Once the charge has been drawn in, the piston rises with both valves shut and squeezes the mixture into a small space, raising its pressure so that it burns fiercely when the spark arrives. The induction intake stroke is the one before it, when the charge is drawn into the cylinder. The combustion power stroke follows ignition and drives the piston back down. And the expelled exhaust stroke clears the burned gases afterward.
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When a moving car suddenly stops, passengers lurch forward due to:
Pick an answer to see the explanation
Click Start Test above to launch a full-length OAR practice test weighted like the real ASTB-E academic portion, or drill a single subtest — Math Skills, Reading Comprehension, or Mechanical Comprehension. Every question includes a clear explanation so you learn the reasoning, not just the answer.
The OAR (Officer Aptitude Rating) is the academic portion of the U.S. Navy's Aviation Selection Test Battery (ASTB-E). It is the score used to screen candidates for non-aviation officer programs.
[1][2] The OAR is built from three ASTB-E subtests: Math Skills, Reading Comprehension, and Mechanical Comprehension. Aviation applicants take additional subtests, but non-aviation officer candidates are scored on these three.
Aviation Selection Test Battery, Series E (ASTB-E)
Subtests
Math Skills Test (MST), Reading Comprehension Test (RCT), Mechanical Comprehension Test (MCT)
Questions
87 on the official fixed-form OAR (MST 30 / RCT 27 / MCT 30); the live exam is computer-adaptive with a variable item count
Format
Computer-adaptive, proctored (APEX/Pearson VUE / Navy sites)
Score Range
Scaled t-score 20–80 (40 ≈ average); not pass/fail
Passing Score
Varies by officer program (often 35–50+)
Time
65 minutes total on the fixed form (MST 25 / RCT 25 / MCT 15), each subtest timed separately
Retakes
Up to 3 lifetime attempts; 31- and 91-day waits
What Is on the OAR?
The OAR is built from three ASTB-E subtests: Math Skills, Reading Comprehension, and Mechanical Comprehension.[2]
Math Skills covers arithmetic, algebra, and geometry; Reading Comprehension tests your ability to draw conclusions from passages; and Mechanical Comprehension applies basic physics and mechanical principles.
The live ASTB-E is computer-adaptive, so the exact number of items varies by administration and answers cannot be changed. Our full practice test simulates the official fixed-form OAR — 87 questions split MST 30 / RCT 27 / MCT 30 — which is the most representative published form:
OAR practice weighting by subtest (official fixed-form OAR, 87 items)
Math Skills Test (MST)34% · 30 Qs
Mechanical Comprehension Test (MCT)34% · 30 Qs
Reading Comprehension Test (RCT)31% · 27 Qs
Practice Questions by Subtest
Use Start Test for a full weighted OAR simulation, or open the hub and pick a single subtest to drill your weak spot. After each full exam, your results show a per-subtest breakdown so you know exactly where to focus your remaining study time.
Who Is Eligible to Take the OAR?
You take the OAR as part of applying to a Navy officer program such as Officer Candidate School (OCS) or NROTC, so OAR eligibility tracks with officer-program eligibility.
[4][6] Officer candidates are generally U.S. citizens who hold or are completing a bachelor's degree and meet the program's age and physical standards. There is no separate prerequisite to sit for the OAR itself beyond being a qualified applicant.
[5] Your recruiter or ROTC unit schedules your test once you are in the application pipeline.
How Do You Register for the OAR?
You do not register for the OAR independently — you schedule it through your Navy recruiter, NROTC unit, or an Officer Recruiting Station, which authorizes your seat via APEX/Pearson VUE.
[3] The test is delivered at Navy recruiting districts, NROTC units, Military Entrance Processing Stations, and approved Pearson VUE centers. There is no exam fee for applicants in the official pipeline.
Confirm your testing location, allowed waiting periods, and current requirements with your recruiter, since policies can change.
How Is the OAR Scored?
The OAR is reported as a single scaled score from 20 to 80, combining your performance on the three academic subtests. A score of 40 is roughly the population average.
[2][5] There is no universal passing score — the minimum you need depends on the officer program you are applying to. Many non-aviation pipelines look for at least a 35–40, while competitive boards favor 50 and above.
Because the ASTB-E is computer-adaptive, question difficulty adjusts to your answers, and your scaled score reflects that difficulty rather than a fixed percentage correct.
How Hard Is the OAR?
The Navy does not publish a single official OAR pass rate, partly because the required score varies by program rather than a fixed cutoff.
The OAR is moderately challenging because of its breadth and timing — you move quickly across algebra and geometry, dense reading passages, and applied mechanical physics, each under its own clock.
The difficulty comes from speed and range rather than deep specialization. Strong, timed practice across all three subtests is what separates competitive scores from average ones.
20–80
Scaled score range
40 ≈ average
3
Academic subtests
math, reading, mechanical
3
Lifetime attempts
with mandatory waits
The takeaway: candidates often arrive strong in one area — math, reading, or mechanical — but competitive OAR scores require deliberately raising your weakest subtest under realistic time pressure.
What to Expect on Exam Day
The OAR is a proctored, computer-adaptive test delivered at a Navy recruiting site or Pearson VUE center.[3] Arrive early to check in and bring a valid, unexpired government-issued photo ID. Personal items are stored away; no notes or calculators beyond what the test provides are allowed.
Each subtest is separately timed, so you cannot bank extra minutes from one section to another. Pace yourself, answer what you can quickly, and keep moving — the adaptive engine rewards steady, accurate work.
The Navy processes your results and provides your scaled OAR score. Having simulated the timed, three-subtest format with practice tests makes test day feel routine.
How to Use This OAR Practice Test
Recreate exam conditions. Take the full test timed, with no notes.
Diagnose, then drill. Use a full OAR simulation to find your weakest subtest, then drill it.
Build speed. The OAR rewards quick, accurate work across math, reading, and mechanical.
Review the mechanics. Mechanical Comprehension trips up many candidates — practice the physics basics.
Learn the why. Read every explanation — understanding beats memorizing.
Why Take the OAR?
The OAR is the gateway to commissioning as a U.S. Navy officer through non-aviation programs like OCS and NROTC. A competitive score strengthens your selection board package and opens more program options.[1][4] These free OAR practice tests are the most efficient way to get exam-ready.
Conclusion
A strong OAR comes down to building speed and accuracy across all three subtests rather than leaning on your strongest one. Use this free OAR practice test to find your weak subtest, drill it to mastery, and reinforce it with our study guide, flashcards, and cheat sheet so you walk in confident on test day.
OAR Practice Test FAQ
The OAR (Officer Aptitude Rating) is the academic portion of the U.S. Navy's Aviation Selection Test Battery (ASTB-E). It is administered by the Navy through Pearson VUE and at Navy recruiting and ROTC sites, and it screens candidates for non-aviation officer programs such as Officer Candidate School.
The OAR is built from three ASTB-E subtests: the Math Skills Test (MST), the Reading Comprehension Test (RCT, also called the Reading Skills Test), and the Mechanical Comprehension Test (MCT). Aviation applicants take additional subtests, but non-aviation officer candidates are scored only on these three.
The OAR is reported on a scaled score from 20 to 80, with 40 as the rough average. There is no universal passing score — the minimum you need depends on the officer program you are applying to, with many programs requiring a 35 to 50 or higher.
Minimum OAR scores vary by program. Many non-aviation officer pipelines look for at least a 35 to 40, while competitive programs and selection boards favor scores of 50 and above, so confirm the current requirement with your recruiter.
On the official fixed-form OAR, the three subtests total 87 questions in 65 minutes — Math Skills (30 items / 25 min), Reading Comprehension (27 / 25 min), and Mechanical Comprehension (30 / 15 min). The live ASTB-E is computer-adaptive, so the exact number of items varies by administration.
Yes. You may retake the ASTB-E, but the Navy limits attempts and enforces waiting periods between them — generally a 31-day wait before a second attempt and 91 days before a third, with three lifetime attempts. Plan to be ready, since scores follow you.
No. The ASVAB is the enlistment aptitude battery, while the OAR is the academic component of the officer-focused ASTB-E. They are separate tests used for different commissioning and enlistment paths.
Candidates pursuing non-aviation Navy officer roles — through Officer Candidate School, NROTC, or similar programs — take the OAR. Applicants seeking aviation roles take the full ASTB-E, which includes the OAR subtests plus aviation-specific sections.
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