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GMAT Quant & Verbal Key Formulas & Rules

GMAT quantitative formulas, number properties, and critical reasoning structures.

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Number of Factors of

N = p_{1}^{a} p_{2}^{b} p_{3}^{c}

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Number of Factors of

N = p_{1}^{a} p_{2}^{b} p_{3}^{c}

Total positive divisors =

(a + 1) (b + 1) (c + 1)

Work-Rate Formula (2 workers)

\frac{1}{T} = \frac{1}{t _{1}} + \frac{1}{t _{2}} ⟹ T = \frac{t _{1} \cdot t _{2}}{t _{1} + t _{2}}

Average Speed for Equal Distance Trips

Harmonic mean: Avg Speed = \frac{2 v _{1} v _{2}}{v _{1} + v _{2}}

Overlapping Sets (2 sets)

∣ A \cup B ∣ = ∣ A ∣ + ∣ B ∣ - ∣ A \cap B ∣

Overlapping Sets (3 sets)

Total = A + B + C - (sum of exactly 2) - 2 (all 3) + Neither

Permutation Formula

P (n, k) = \frac{n !}{( n - k )!}

$ Order matters.

Combination Formula

C (n, k) = (k n) = \frac{n !}{k ! ( n - k )!}

$ Order does not matter.

Even and Odd Arithmetic Rules

Even \times Any = Even

;

Odd \times Odd = Odd

;

Even \pm Odd = Odd

Divisibility by 3 and 9

A number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3 (or 9).

Divisibility by 4 and 8

Divisible by 4 if the last 2 digits form a multiple of 4; by 8 if the last 3 digits form a multiple of 8.

Standard Deviation Property

Adding or subtracting a constant

k

to every term does NOT change standard deviation. Multiplying by

k

multiplies SD by

∣ k ∣

Sum of Consecutive Integers

1

n

Sum = \frac{n ( n + 1 )}{2}

Right Triangle 3-4-5 and 5-12-13 Multiples

Common Pythagorean triples:

(3, 4, 5)

(5, 12, 13)

(8, 15, 17)

(7, 24, 25)

Diagonal of a Cube of side

s

d = s 3

Compound Interest Formula

A = P (1 + \frac{r}{n})^{n t}

GMAT Sentence Correction: Subject-Verb Agreement with 'Neither/Nor'

The verb agrees with the subject closer to it: Neither the teacher nor the students were present.

GMAT CR: Assumption Definition

An unstated premise required for the conclusion to stand. Negating the correct assumption shatters the argument.

GMAT CR: Strengthen Question Strategy

Identify an additional premise that validates the author's key causal link or rules out alternative explanations.

GMAT CR: Weaken Question Strategy

Introduce new information that reveals an alternate cause, a reverse causality, or a fatal sampling flaw.

GMAT Verbal: Modifiers Placement Rule

Participial phrases at the start of a sentence must modify the immediately following grammatical subject.

GMAT Verbal: Like vs. As

Like compares nouns: She looks like her mother. As compares clauses with verbs: He solved it as he was taught.

Sum of Angles in an

n

-gon

Interior sum = (n - 2) \times 18 0^{\circ}

$ Exterior angles always sum to $360^\circ$.

Quadratic Roots: Sum and Product

For

a x^{2} + b x + c = 0

: $

Sum = - \frac{b}{a}, Product = \frac{c}{a}

Percent Increase Followed by Percent Decrease

An increase of

x %

followed by a decrease of

x %

results in an overall net loss of

(\frac{x}{10})^{2} %

Probability of Independent Events

A

and

B

P (A \cap B) = P (A) \times P (B)

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