GMAT Quant formulas

Every formula you need for the GMAT Quantitative Reasoning section, organized by topic. Each formula comes with a one-sentence explanation of when to use it. Click a topic to practice it.

Percentages

Practice percentages →

Percent change

The old value is always the denominator.

\(\frac{\text{new} - \text{old}}{\text{old}} \times 100\)

Percent of

What portion one value is of another.

\(\frac{\text{part}}{\text{whole}} \times 100\)

Successive percent change

Each percent applies to the current value, not the original.

\((1 + r_1)(1 + r_2) - 1\)

Ratios and proportions

Practice ratios and proportions →

Ratio to fraction

The fraction of the total that belongs to part a.

\(\frac{a}{a+b}\)

Cross multiplication

Solve for an unknown in a proportion.

\(\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc\)

Rates and work

Practice rates and work →

Rate

The base formula. Everything in rates follows from it.

\(\text{rate} = \frac{\text{work}}{\text{time}}\)

Combined work rate

Rates add. Times do not.

\(\frac{1}{t_{\text{combined}}} = \frac{1}{t_1} + \frac{1}{t_2}\)

Average speed (equal distances)

The harmonic mean. Never average the speeds directly.

\(\frac{2 \times s_1 \times s_2}{s_1 + s_2}\)

Number properties

Practice number properties →

Divisibility by 3

A number is divisible by 3 if the sum of its digits is.

Sum of digits divisible by 3

Divisibility by 9

Same rule as 3 but with 9.

Sum of digits divisible by 9

GCD and LCM

When you know one, you know the other.

\(\text{GCD}(a,b) \times \text{LCM}(a,b) = a \times b\)

Algebra

Practice algebra →

Quadratic formula

Solve any quadratic equation.

\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Difference of squares

Factor quickly without long multiplication.

\(a^2 - b^2 = (a+b)(a-b)\)

Linear equation

Solve for a single variable.

\(ax + b = 0 \Rightarrow x = -\frac{b}{a}\)

Statistics

Practice statistics →

Mean

The average. Sum divided by count.

\(\frac{\sum x_i}{n}\)

Weighted average

When values have different weights or frequencies.

\(\frac{\sum w_i x_i}{\sum w_i}\)

Standard deviation

Measures spread. The GMAT rarely requires computing it by hand.

\(\sqrt{\frac{\sum(x_i - \bar{x})^2}{n}}\)

Exponents

Practice exponents →

Product rule

Add exponents when multiplying same base.

\(a^m \times a^n = a^{m+n}\)

Quotient rule

Subtract exponents when dividing same base.

\(\frac{a^m}{a^n} = a^{m-n}\)

Power rule

Multiply exponents when raising a power to a power.

\((a^m)^n = a^{mn}\)

Inequalities

Practice inequalities →

Flip on multiply

Flip the inequality when multiplying or dividing by a negative.

\(a < b, c < 0 \Rightarrow ac > bc\)

Triangle inequality

The sum of absolute values is an upper bound.

\(|a + b| \leq |a| + |b|\)

Probability

Practice probability →

Basic probability

Favorable outcomes divided by total outcomes.

\(P(A) = \frac{\text{favorable}}{\text{total}}\)

Complement rule

When it is easier to count what does not happen.

\(P(\text{not } A) = 1 - P(A)\)

Independent events

Multiply when events are independent.

\(P(A \text{ and } B) = P(A) \times P(B)\)

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