- Only even prime
- 2 — and 1 is not prime.
- Odd × even
- Even. (Even × anything = even.)
- Odd × odd
- Odd.
- Even + even
- Even.
- Odd + odd
- Even.
- Odd + even
- Odd.
- Product of 2 consecutive integers
- Always even — one of the two is even.
- Definition of a prime number
- A whole number > 1 with exactly two factors: 1 and itself.
- Is 1 prime?
- No. 1 has only one factor.
- Smallest prime number
- 2 (also the only even prime).
- Number of factors of a perfect square
- Always odd.
- Sum of first n positive integers
- n(n + 1)/2.
- Divisibility rule for 3
- The sum of the digits is divisible by 3.
- Divisibility rule for 9
- The sum of the digits is divisible by 9.
- Divisibility rule for 4
- The last two digits form a number divisible by 4.
- Divisibility rule for 6
- Divisible by both 2 and 3.
- Divisibility rule for 8
- The last three digits form a number divisible by 8.
- GCF (greatest common factor)
- The largest integer that divides two numbers exactly.
- LCM (least common multiple)
- The smallest positive integer that is a multiple of both numbers.
- Prime factorization use
- Break a number into primes to find GCF, LCM, and factor counts.
- Units digit of 7¹, 7², 7³, 7⁴
- 7, 9, 3, 1 — then the cycle repeats (length 4).
- Units-digit cycle length of powers of 2
- 4 (2, 4, 8, 6, repeat).
- x⁰ equals
- 1 (for any nonzero x).
- xᵃ × xᵇ equals
- xa+b — add exponents when multiplying the same base.
- xᵃ ÷ xᵇ equals
- xa−b — subtract exponents when dividing the same base.
- (xᵃ)ᵇ equals
- xab — multiply exponents for a power of a power.
- x⁻ᵃ equals
- 1/xᵃ — a negative exponent is a reciprocal.
- √(ab) equals
- √a × √b (for nonnegative a, b).
- Percent change formula
- (new − original) ÷ original × 100. Always divide by the ORIGINAL.
- Percent of: 'what percent of 80 is 28?'
- 28 ÷ 80 = 0.35 = 35%.
- Convert a fraction to a percent
- Divide and multiply by 100 (e.g., 3/8 = 0.375 = 37.5%).
- Successive percent changes
- Multiply factors (×1.1 then ×0.9), do not add them.
- 50% down then 50% up
- Returns to 75% of the start, not 100% — changes multiply.
- Ratio meaning
- A comparison of quantities; scale up or down by a common factor.
- Combine a part-to-part ratio into a total
- Add the parts; each part is its share of the whole.
- Direct proportion
- As one quantity rises, the other rises by the same factor (y = kx).
- Inverse proportion
- As one rises, the other falls (xy = constant).
- work = ?
- rate × time.
- Combined work rate
- Add the individual rates (jobs per hour) — never add the times.
- Two-worker combined time
- (a × b) ÷ (a + b) for individual times a and b.
- distance = ?
- rate × time.
- Average speed for a round trip
- total distance ÷ total time (NOT the average of the two speeds).
- Simple interest
- principal × rate × time.
- Compound interest grows…
- Faster than simple interest — interest earns interest.
- Mean (arithmetic average)
- sum of values ÷ number of values.
- Median
- The middle value when data is ordered (average of the two middle values if even count).
- Mode
- The most frequently occurring value.
- Range
- largest value − smallest value.
- Mean vs. median with an outlier
- An outlier moves the mean more than the median.
- Weighted average
- Σ(value × weight) ÷ Σ(weights) — weight by each group's share.
- Standard deviation measures
- How spread out data is around the mean; larger = more dispersion.
- Quadratic standard form
- ax² + bx + c = 0.
- Quadratic formula
- x = (−b ± √(b² − 4ac)) ÷ (2a).
- Factor x² + bx + c
- Find two numbers that multiply to c and add to b.
- Difference of squares
- a² − b² = (a + b)(a − b).
- (a + b)² expands to
- a² + 2ab + b².
- (a − b)² expands to
- a² − 2ab + b².
- Inequality sign flip rule
- Multiplying or dividing both sides by a negative flips < to > (and vice versa).
- Solve a system of two equations
- Substitution or elimination — combine to remove one variable.
- Absolute value |x| means
- Distance from zero; |x| = a gives x = a or x = −a.
- Slope of a line
- rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁).
- Slope-intercept form
- y = mx + b, where m is slope and b is the y-intercept.
- Function notation f(x)
- Plug the input x into the rule to get the output.
- Backsolving strategy
- Plug answer choices into the question; start with B or D.
- Picking numbers strategy
- Choose easy values (often 100 for percents) for variable problems.
- Probability of an event
- favorable outcomes ÷ total possible outcomes.
- Probability of A and B (independent)
- P(A) × P(B).
- Probability of A or B (mutually exclusive)
- P(A) + P(B).
- Probability of NOT A
- 1 − P(A).
- Permutation vs. combination
- Permutation: order matters. Combination: order doesn't.
- Combinations formula nCr
- n! ÷ (r!(n − r)!).
- Factorial n!
- n × (n−1) × … × 2 × 1; note 0! = 1.
- Counting principle
- If one event has m ways and another n ways, together m × n ways.
- Set: union vs. intersection
- Union = in either set; intersection = in both.
- Overlapping sets formula
- Total = A + B − (both) + neither.
- Is geometry on the GMAT Focus Edition?
- No — geometry was removed from the Focus Edition.
- Calculator in Quant?
- No calculator is allowed in Quantitative Reasoning.
- Quant question type (Focus Edition)
- Problem Solving only (Data Sufficiency moved to Data Insights).
- Number of Quant questions / time
- 21 questions in 45 minutes.
- Mixture problem approach
- Use a weighted average of the components' concentrations.
- Estimate to save time
- Round and approximate when answer choices are far apart.
- Two Verbal Reasoning question types
- Reading Comprehension and Critical Reasoning.
- Is sentence correction on the Focus Edition?
- No — sentence correction (grammar) was removed.
- Number of Verbal questions / time
- 23 questions in 45 minutes.
- Conclusion (in an argument)
- The main point the argument tries to establish.
- Premise / evidence
- The facts offered to support the conclusion.
- Assumption
- An unstated premise the argument needs to be valid — the missing link.
- Negation test (for assumptions)
- Deny the choice; if the argument collapses, it's the necessary assumption.
- How to weaken an argument
- Attack the assumption — offer an alternative cause or counterexample.
- How to strengthen an argument
- Confirm the assumption or rule out alternative explanations.
- Correlation vs. causation flaw
- Assuming one thing caused another just because they occur together.
- Best way to weaken a causal claim
- Provide a different cause for the same result.
- Flaw / reasoning-error question
- Name what's wrong with the logic (e.g., overgeneralizing, false analogy).
- Evaluate-the-argument question
- Find the question whose answer would most affect the conclusion.
- Resolve-the-paradox question
- Find the fact that explains how two surprising statements both hold.
- Inference (must be true)
- A conclusion that must follow from the stated facts alone.
- Inference answer rule
- Stay close to the text; reject choices needing outside assumptions.
- Main idea question
- The central point covering the WHOLE passage — not one detail.
- Reject in a main-idea question
- Choices that are too narrow or too broad.
- Detail / supporting-idea question
- Return to the exact line; don't answer from memory.
- Structure / function question
- Why a sentence or paragraph is there — its role in the argument.
- Tone / author's-attitude question
- Match the strength of the author's language; avoid extremes unless stated.
- Author's view vs. described view
- Separate what the author believes from views they cite to criticize.
- Strengthen vs. weaken (relationship)
- Mirror images — one confirms the assumption, the other breaks it.
- 'Most' / 'some' / 'all' in CR
- Quantifiers matter; an exception can break an 'all' statement.
- Reading for structure (RC strategy)
- Map purpose and paragraph roles first; return for details as needed.
- Necessary vs. sufficient assumption
- Necessary: required for the argument; sufficient: enough to guarantee it.
- Bold-face / argument-structure question
- Identify the role each bolded statement plays (premise, conclusion, etc.).
- Complete-the-argument question
- Choose the option that logically finishes the reasoning.
- Scope shift (CR trap)
- A choice that subtly changes the topic from the argument's actual scope.
- Extreme-language trap
- Answers with 'always/never/only' are often too strong to be supported.
- Reverse-logic trap
- A weaken choice that actually strengthens (or vice versa) — read the task.
- Data Insights — what's new
- The Focus Edition section testing data literacy; Data Sufficiency lives here now.
- Number of Data Insights questions / time
- 20 questions in 45 minutes.
- Calculator in Data Insights?
- Yes — an on-screen calculator is allowed (only in this section).
- Five Data Insights question types
- Data Sufficiency, Multi-Source Reasoning, Table Analysis, Graphics Interpretation, Two-Part Analysis.
- Data Sufficiency — your task
- Decide whether the statements give enough info to answer — not what the answer is.
- Data Sufficiency choice A
- Statement (1) alone is sufficient, but (2) alone is not.
- Data Sufficiency choice B
- Statement (2) alone is sufficient, but (1) alone is not.
- Data Sufficiency choice C
- Both statements together are sufficient, but neither alone is.
- Data Sufficiency choice D
- Each statement alone is sufficient.
- Data Sufficiency choice E
- Statements (1) and (2) together are NOT sufficient.
- Are the DS answer choices fixed?
- Yes — A–E are identical on every Data Sufficiency question. Memorize them.
- DS evaluation order
- Test (1) alone, then (2) alone, then both together only if needed.
- DS biggest time trap
- Fully solving — stop as soon as you know whether the data is enough.
- DS for a yes/no question
- Sufficient means a DEFINITE yes or a definite no — not a maybe.
- Multi-Source Reasoning
- Combine 2–3 tabbed sources (text, tables, graphics) to answer linked questions.
- Multi-Source Reasoning strategy
- Skim each tab to learn what it holds; then fetch only the data the question needs.
- Table Analysis
- Sort and read a spreadsheet-style table to judge true/false statements.
- Table Analysis tip
- Sort by the relevant column first to evaluate statements quickly.
- Graphics Interpretation
- Read a chart or graph and complete statements via drop-down menus.
- Graphics Interpretation tip
- Check axis labels, units, and scale before answering.
- Two-Part Analysis
- Choose one answer in each of two related columns from a shared option set.
- Two-Part Analysis tip
- The two parts are related — one choice often constrains the other.
- Why Data Insights matters
- It's weighted equally with Quant and Verbal — don't under-prepare it.
- Reading a scatter plot
- Each point is a paired (x, y) value; look for an upward/downward trend.
- Reading a bar chart
- Compare category heights; check the axis scale for the true difference.
- Reading a line graph
- Track change over time; the slope shows the rate of change.
- Pie chart values
- Each slice is a percent of the whole; the slices sum to 100%.
- Cumulative vs. frequency table
- Frequency = count per category; cumulative = running total.
- Median from a frequency table
- Find the middle data point by counting up the frequencies.
- Percentile meaning
- The percent of values at or below a given value.
- Interpreting a trend line
- Shows the overall direction; individual points may vary around it.
- GMAT total score scale
- 205–805, in 10-point increments (always ends in 5).
- GMAT section score range
- 60–90 for each of the three sections.
- How the total score is built
- Three section scores, equally weighted, combine into the 205–805 total.
- GMAT mean total score
- Roughly 545 on the Focus scale.
- GMAT total questions / time
- 64 questions in 2 hours 15 minutes (45 min per section).
- GMAT section order
- Flexible — you choose any of the six possible orders.
- GMAT optional break
- One 10-minute break, after the first or second section.
- Question Review & Edit tool
- Bookmark any question; change up to 3 answers per section before time ends.
- GMAT adaptivity
- Section-adaptive — difficulty adjusts to your performance within each section.
- Is there an essay (AWA) on the Focus Edition?
- No — the Analytical Writing Assessment was removed.
- GMAT score validity
- Scores are valid for 5 years.
- GMAT exam fee (approx.)
- About $275 at a test center, $300 online (excluding tax).
- Free score sends with registration
- Up to 5 programs at the time of registration.
- Convert a percent to a decimal
- Divide by 100 (e.g., 35% = 0.35).
- Convert a decimal to a percent
- Multiply by 100 (e.g., 0.4 = 40%).
- 10% of a number (quick)
- Move the decimal one place left.
- 1% of a number (quick)
- Move the decimal two places left.
- Find a number when you know a percent of it
- Divide the part by the decimal form of the percent.
- Percent increase of 50 → 60
- (60 − 50) ÷ 50 = 20% increase.
- Percent decrease of 250 → 200
- (250 − 200) ÷ 250 = 20% decrease.
- Markup vs. margin
- Markup is over cost; margin is over selling price.
- Profit
- selling price − cost.
- Fraction comparison trick
- Cross-multiply: a/b vs c/d → compare a·d with b·c.
- Adding fractions
- Use a common denominator, then add numerators.
- Multiplying fractions
- Multiply numerators and denominators straight across.
- Dividing fractions
- Multiply by the reciprocal of the second fraction.
- Reciprocal of a/b
- b/a.
- Improper fraction to mixed number
- Divide; the quotient is the whole part, remainder over divisor is the fraction.
- √(a/b) equals
- √a ÷ √b — the root distributes over a quotient.
- Perfect squares 1–15
- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
- Cube of 2, 3, 4, 5
- 8, 27, 64, 125.
- √2 ≈ ?
- 1.41.
- √3 ≈ ?
- 1.73.
- Estimate √50
- Between 7 and 8 (closer to 7, since 7² = 49).
- Negative × negative
- Positive.
- Negative × positive
- Negative.
- Even root of a negative number
- Not a real number.
- Order of operations (PEMDAS)
- Parentheses, Exponents, Multiply/Divide, Add/Subtract — left to right.
- Distributive property
- a(b + c) = ab + ac.
- Solve a linear equation
- Isolate the variable using inverse operations on both sides.
- Cross-multiply to solve a proportion
- a/b = c/d → a·d = b·c.
- Consecutive even/odd integers
- Differ by 2: x, x+2, x+4, …
- Average of consecutive integers
- Equals the median (the middle value).
- Sum of an evenly spaced set
- average × number of terms.
- Number of integers from a to b inclusive
- b − a + 1.
- Remainder concept
- What's left after division; remainder < divisor.
- A number divisible by 10
- Ends in 0.
- A number divisible by 5
- Ends in 0 or 5.
- A number divisible by 2
- Ends in an even digit (0, 2, 4, 6, 8).
- Exponent of 0 base
- 0ⁿ = 0 for n > 0; 0⁰ is undefined on the GMAT.
- Fractional exponent x1/2
- Equal to √x (a one-half power is a root).
- Scientific notation
- A number as a × 10ⁿ with 1 ≤ a < 10.
- Average rate when distances are equal
- Use total distance ÷ total time, never the mean of the rates.
- Ratio word problem setup
- Let the parts be multiples of a variable (e.g., 2x and 3x).
- Mixture: stronger + weaker solution
- Resulting concentration is the weighted average of the two.
- Interest: which grows more, simple or compound?
- Compound, because it earns interest on interest.
- Percent of a percent
- Multiply the decimals (e.g., 20% of 30% = 0.06 = 6%).
- Solve for a variable in a formula
- Treat other letters as constants; isolate the target variable.
- Inequalities with a variable denominator
- Be careful — the sign of the denominator affects the direction.
- Quadratic with no real solution
- Discriminant b² − 4ac < 0.
- Sum/product of quadratic roots
- Sum = −b/a; product = c/a.
- Function composition f(g(x))
- Apply g first, then f to the result.
- Reading Comprehension passage length
- Short to medium business, science, or social-science passages with several questions.
- First read of an RC passage
- Skim for the main point and structure, not every fact.
- Where RC answers come from
- The passage only — never outside knowledge.
- 'EXCEPT' question
- Four choices are true/supported; the answer is the one that is NOT.
- Primary purpose vs. main idea
- Purpose = why the author wrote it; main idea = what it says overall.
- Identify the argument's parts (CR)
- Find the conclusion, the evidence, and the assumption linking them.
- Signal words for a conclusion
- Therefore, thus, so, hence, clearly.
- Signal words for evidence
- Because, since, for, as, given that.
- Assumption family questions
- Assumption, strengthen, weaken, evaluate, flaw — all turn on the gap.
- Sampling flaw
- Generalizing from an unrepresentative or too-small sample.
- Survey / self-report flaw
- Respondents may be biased or untruthful.
- Percent vs. number flaw
- A higher percent doesn't mean a higher absolute number (and vice versa).
- Ad hominem in CR
- Attacking the source rather than the argument — a reasoning flaw.
- Circular reasoning
- Using the conclusion as its own evidence.
- False analogy
- Treating two unlike situations as comparable.
- Equivocation
- Using one word in two different senses within the argument.
- Plan / proposal question
- Evaluate whether a proposed action will achieve its goal.
- Strengthen a plan
- Show the plan addresses the real obstacle to the goal.
- Weaken a plan
- Show an obstacle or side effect that defeats the goal.
- Inference vs. assumption
- Inference follows FROM the argument; assumption is needed BY it.
- Trap: out-of-scope choice
- Introduces information irrelevant to the argument.
- Trap: opposite answer
- Does the reverse of what the question asks (e.g., strengthens a weaken).
- Predict before reading choices (CR)
- Anticipate the answer's role, then match — it speeds elimination.
- Read the question stem first?
- In CR, yes — knowing the task focuses your read of the argument.
- DS: 'C trap'
- Picking 'both together' before checking each statement alone.
- DS: statements never contradict
- Both statements are always true; they just may or may not be sufficient.
- DS value question
- Sufficient means the statements pin down ONE exact value.
- DS: rephrase the question first
- Simplify what you actually need before testing the statements.
- Multi-Source Reasoning question format
- Often several questions (some yes/no, some multiple choice) per prompt.
- Table Analysis answer format
- A set of true/false (or yes/no) statements to evaluate from the table.
- Graphics Interpretation answer format
- Drop-down menus that complete sentences about the graphic.
- Two-Part Analysis answer format
- A grid: pick one option for each of two columns.
- Reading a histogram
- Bars show frequency over value ranges (bins); look at shape and center.
- Skewed-right distribution
- A long right tail; mean > median.
- Skewed-left distribution
- A long left tail; mean < median.
- Symmetric distribution
- Mean ≈ median ≈ mode.
- Correlation in a scatter plot
- Points trending up = positive; trending down = negative.
- Correlation does not imply…
- Causation — a Data Insights and CR theme alike.
- Rate from a graph
- The slope between two points = change in y ÷ change in x.
- Weighted data in a table
- Account for group sizes when combining averages.
- Two-way (contingency) table
- Rows and columns of counts; read joint and marginal totals.
- Marginal total
- A row or column total (the 'margin') of a two-way table.
- Reading units carefully (DI)
- Thousands vs. millions and % vs. count change the answer.
- Budget time across DI
- ~2.25 minutes per question on average; don't sink time in one source.
- Express 'is' and 'of' in percent problems
- 'is' → equals (=); 'of' → multiply (×).
- Translate 'x is 25% greater than y'
- x = 1.25y.
- Translate 'x is 30% less than y'
- x = 0.70y.
- Doubling time idea
- How long for a quantity to double under repeated growth.
- Greatest common factor of primes p, q
- 1 (distinct primes share no common factor > 1).
- Sum of interior digits divisible by 3 means
- The whole number is divisible by 3.
- Median of an even-sized set
- Average the two middle values.
- Effect of adding the mean to a data set
- The mean stays the same; the standard deviation decreases.
- Effect of multiplying all values by k
- Mean, median, and SD all scale by k.
- Set with the smallest standard deviation
- The one whose values are closest together.
- Solve |x − 3| = 5
- x − 3 = 5 or x − 3 = −5 → x = 8 or x = −2.
- Number of diagonals (not tested?)
- Geometry is not on the Focus Edition — skip pure geometry formulas.
- Translate 'product' and 'quotient'
- Product = multiply; quotient = divide.
- Translate 'sum' and 'difference'
- Sum = add; difference = subtract.
- Percent profit on cost
- (selling − cost) ÷ cost × 100.
- Ratio 3:4 as a fraction of the whole
- 3/7 and 4/7 (parts over the sum of parts).
- Average speed: 60 mi at 30 mph, 60 mi at 60 mph
- 120 ÷ (2 + 1) = 40 mph (not 45).
- When to pick 100
- Percent problems with unknown starting amounts.
- Check answer reasonableness
- Estimate magnitude; reject choices that are obviously too big/small.
- Even number of negative factors
- Product is positive; odd number of negatives → negative.
- Conclusion location in an argument
- Anywhere — beginning, middle, or end; find it by meaning, not position.
- 'Which best supports' question
- A strengthen question — add evidence for the conclusion.
- 'Which most undermines' question
- A weaken question — break the link to the conclusion.
- 'Properly drawn conclusion' question
- An inference — must be fully supported by the stated facts.
- Author tone: most common GMAT range
- Usually measured/objective — extreme tones are rare and often traps.
- Main-idea trap: a true detail
- A true statement that's too narrow to be the main idea.
- Critical Reasoning argument length
- Short — usually a few sentences; read precisely.
- Strengthen by eliminating an alternative
- Rule out another possible cause of the result.
- Identify the issue in 'evaluate' questions
- Pinpoint the assumption the question would test.
- Inference question: avoid
- Choices that go beyond or distort what the passage states.
- RC: tracking a contrast
- Watch 'but, however, although' — they often signal the main point.
- RC: a 'function' question asks
- The role a detail plays, not whether it's true.
- DS: yes/no, statement gives 'always yes'
- Sufficient (a definite answer).
- DS: statement gives 'sometimes yes, sometimes no'
- Insufficient.
- DS: combine statements
- Only if neither alone is sufficient; then test both together.
- DS: don't carry info between statements
- Evaluate (1) and (2) independently before combining.
- Multi-Source: yes/no sub-question scoring
- All parts of a single MSR item must be correct to earn credit.
- Table Analysis: most efficient first step
- Sort the table by the column the statement is about.
- Graphics: read the legend
- Identify what each color/series represents before answering.
- Two-Part: when parts are 'min' and 'max'
- Find values satisfying the shared constraint at each extreme.
- DI calculator best use
- Heavy arithmetic; still reason first to avoid wasted keystrokes.
- Percent change from a chart
- (later − earlier) ÷ earlier × 100, read off the axis values.
- Reading stacked bar charts
- Each segment adds to the total bar; compare segments and totals.
- Outlier on a scatter plot
- A point far from the trend; note its effect on any average.
- DI question mix
- Quantitative, verbal, or both — the section is intentionally blended.
- Time management across all of DI
- 20 questions, 45 minutes — protect time for multi-part prompts.