GMAT Reference Sheet

How to revise from this sheet

1. 1Cover the right-hand column and say the relationship out loud before reading it. Recognising a formula is not the same as recalling it, and only recall survives a timed section.
2. 2Work down a single domain at a time, then answer a few questions in that domain immediately. Recall that is never used decays fastest.
3. 3When an entry has a condition attached, rehearse the condition as part of the statement. Most exam traps are built on applying a correct formula outside its hypothesis.

GMAC describes the current GMAT as 64 questions across three 45-minute sections, for a total testing time of 2 hours 15 minutes. GMAC describes the exam's content as quantitative reasoning, verbal reasoning, and data insights.

Quantitative reasoning

A closed set of arithmetic, algebra, and word-problem relationships, drilled to instant recall.

Percent and change

$$(1 + p_1)(1 + p_2)$$

percent change = (new - old)/old; successive changes multiply, so +20% then -20% ends at 0.96 of the start

Percent change is always measured against the original value; a shifting base is the most common trap.

Ratios, rates, averages

a ratio scales by a common factor; average = sum divided by count, so sum = average times count; weighted averages lie between the parts, nearer the larger group

Converting an average back to a sum is the move that unlocks most average questions.

Distance and work

$$\frac{1}{t} = \frac{1}{t_1} + \frac{1}{t_2}$$

distance = rate x time; combined work adds rates, so two workers of times t1 and t2 finish together in 1/(1/t1 + 1/t2)

Average speed over equal distances is the harmonic mean, not the arithmetic mean of the two speeds.

Exponent rules

$$a^{m}a^{n} = a^{m+n}, \quad a^{-n} = \frac{1}{a^{n}}$$

same base multiplies by adding exponents and divides by subtracting; a power of a power multiplies; a^0 = 1 for nonzero a; a^(-n) is the reciprocal

Sums of powers do not simplify; only products and quotients do.

Algebraic identities

$$a^{2} - b^{2} = (a+b)(a-b)$$

(a + b)^2, (a - b)^2, and a^2 - b^2 = (a+b)(a-b); quadratic roots sum to -b/a and multiply to c/a

The difference of squares turns many apparently heavy computations into one line.

Number properties

even times anything is even; odd times odd is odd; a prime has exactly two positive divisors; divisibility by 3 or 9 follows from the digit sum, by 4 from the last two digits, by 8 from the last three

Zero is even, and 1 is not prime — two facts that appear in distractors far more often than in solutions.

Geometry essentials

$$1 : \sqrt{3} : 2, \qquad 1 : 1 : \sqrt{2}$$

triangle angles sum to 180; area = base x height / 2; Pythagoras and the 3-4-5, 5-12-13, 30-60-90, and 45-45-90 patterns; circle circumference 2 pi r and area pi r^2

Similar figures scale length by k, area by k squared, volume by k cubed.

Counting and probability

$$P(\text{at least one}) = 1 - P(\text{none})$$

ordered n!/(n-r)!, unordered n!/(r!(n-r)!); P(A or B) = P(A) + P(B) - P(A and B); P(at least one) = 1 - P(none)

The complement is usually the shorter route.

Statistics

mean, median, mode, range, and standard deviation; adding a constant to every value leaves the standard deviation unchanged, multiplying scales it

A symmetric set has equal mean and median; a right-skewed set has mean above median.

Verbal reasoning

Argument anatomy first; the question stem then tells you which part to attack.

Argument anatomy

premises support a conclusion; an assumption is an unstated premise the argument requires; evidence is what the premises rest on

Find the conclusion before reading the options. Conclusion indicators include therefore, thus, hence, and so.

Assumption test

negate a candidate assumption; if the argument collapses, it was necessary

A necessary assumption need not be sufficient; strengthening options are frequently offered as assumption answers.

Strengthen and weaken

strengthen by supporting the link between evidence and conclusion; weaken by attacking that link, usually with an alternative cause or a missing comparison

The strongest weakener addresses the reasoning, not the truth of a premise.

Causal reasoning flaws

correlation treated as causation, reversed causation, an omitted common cause, and unrepresentative samples

When an argument moves from an association to a cause, the answer is usually an alternative explanation.

Inference questions

an inference must follow from the stated information alone; the safest answer is the least ambitious one

Extreme qualifiers such as always, never, and only are rarely supportable by a short passage.

Reading comprehension

read for structure — claim, support, counterpoint, resolution — rather than for detail, and return to the text for every detail question

The author's attitude is usually measured, not enthusiastic; extreme tone options are commonly wrong.

Data insights

A procedure, not a body of content. The discipline is deciding sufficiency without solving.

Data sufficiency procedure

evaluate statement 1 alone, then statement 2 alone with statement 1 forgotten, then both together only if each alone was insufficient

Contaminating statement 2 with information from statement 1 is the error that produces most wrong answers on this question type.

Sufficiency means uniqueness

a statement is sufficient when it forces exactly one answer, not when it makes the problem solvable in principle

For a yes-or-no question, a consistent 'no' is sufficient; only a statement allowing both answers is insufficient.

Test the edges

before declaring sufficiency, test negative values, zero, fractions between 0 and 1, and non-integers unless the question excludes them

Assuming variables are positive integers is the single most frequent unstated assumption.

Reading data displays

read the axis labels, units, and scale before the shape; check whether a chart shows totals or rates, and whether an axis starts at zero

A truncated axis exaggerates differences; a percentage change on a small base can look large while the absolute change is trivial.

Two-part and multi-source items

identify which source answers the question before combining; each part of a two-part item is scored together, so both must be right

Time spent locating the relevant source is usually less than time spent reconciling all of them.

Rates versus totals

a rising percentage with a falling base can mean a falling count, and a group with a higher rate can contribute fewer cases

Whenever an argument mixes a proportion with a count, the answer is almost always about that mixture.

Sources

Entries drawn from a cited source list it below. Standard results and numerical constants that no source in our registry covers are given as recall material without a citation rather than attributed to a source that does not support them.

1. The GMAT Focus Edition: Exam Structure, Content & Features — GMAC. Accessed 2026-08-03. Use as a cited source for exam facts; do not imply affiliation or reproduce protected test material.
2. GMAT Exam Content — GMAC. Accessed 2026-08-07. Cited for official exam facts; do not imply affiliation or reproduce protected test material.
3. Elementary Algebra 2e, Section 6.2: Use Multiplication Properties of Exponents — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.
4. Elementary Algebra 2e, Section 3.5: Solve Uniform Motion Applications — OpenStax. Accessed 2026-08-03. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.
5. Intermediate Algebra 2e, Section 7.5: Solve Applications with Rational Equations — OpenStax. Accessed 2026-08-03. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.
6. Introductory Statistics 2e, Section 2.5: Measures of the Center of the Data — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.
7. Introductory Statistics 2e, Section 3.3: Two Basic Rules of Probability — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.
8. Introduction to Philosophy, Section 5.3: Arguments — OpenStax. Accessed 2026-08-03. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.
9. Introduction to Philosophy, Section 5.4: Types of Inferences — OpenStax. Accessed 2026-08-03. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.