Reference · Cheat sheet
The quant formula cheat sheet
Every formula the GMAT and GRE can test fits on one page. Memorize the ones you use weekly, and drill the rest until they are reflexes. Formulas do not solve questions by themselves, but not knowing them guarantees you will not.
Bookmark this sheet and pair it with the drills in theGMAT GRE Prep practice bank. Each section below links to a worked example where the formula earns its keep.
Arithmetic and percents
- Percent change
- (new − old) / old × 100%
- Successive changes
- Multiply factors: +20% then −20% is 1.2 × 0.8 = 0.96
- Simple interest
- I = P × r × t (see the worked example)
- Compound interest
- A = P(1 + r/n)^(nt)
- Ratio setup
- a : b = ak : bk; keep the multiplier k (see this question)
Exponents and roots
- Product rule
- a^m × a^n = a^(m+n)
- Quotient rule
- a^m / a^n = a^(m−n)
- Power of a power
- (a^m)^n = a^(mn)
- Negative exponent
- a^(−n) = 1 / a^n
- Fractional exponent
- a^(1/n) = the nth root of a
- Same terms added
- a^n + a^n = 2·a^n (see this question)
Algebra
- Difference of squares
- a² − b² = (a − b)(a + b)
- Perfect squares
- (a ± b)² = a² ± 2ab + b²
- Quadratic formula
- x = (−b ± √(b² − 4ac)) / 2a
- Absolute value inequality
- |x − c| < d means c − d < x < c + d
- Distance between points
- √((x₂ − x₁)² + (y₂ − y₁)²)
- Slope
- m = (y₂ − y₁) / (x₂ − x₁)
Geometry
- Triangle area
- (1/2) × base × height (legs in a right triangle)
- Pythagorean theorem
- a² + b² = c²; memorize 3-4-5, 5-12-13, 8-15-17
- Circle area and circumference
- A = πr², C = 2πr
- Rectangle and square
- A = lw; square diagonal = s√2
- Triangle angle sum
- 180°; exterior angle = sum of remote interiors
- Cube and cylinder volume
- V = s³; V = πr²h
Rates and work
- Distance
- d = r × t
- Combined work
- Add rates: 1/a + 1/b = 1/together (see this question)
- Average speed
- total distance / total time, never the average of speeds
- Consecutive integers
- n, n+1, n+2 …; sum of n terms = n × median
Statistics
- Mean
- sum / count; work with sums to undo it (example)
- Median
- Middle value of an ordered list; average the middle two if count is even
- Weighted average
- (w₁x₁ + w₂x₂) / (w₁ + w₂)
- Range
- max − min
- Standard deviation (concept)
- How spread out values are; you compare spreads, you never compute it
Counting and probability
- Combinations
- C(n,k) = n! / (k!(n−k)!) (see this question)
- Permutations
- P(n,k) = n! / (n−k)!
- At least one
- 1 − P(none); complement first
- Probability
- favorable / total equally likely outcomes (example)
- Independent events
- P(A and B) = P(A) × P(B)
- Mutually exclusive events
- P(A or B) = P(A) + P(B)
How to actually memorize these
- Recall, do not reread. Cover the formula column and reproduce it from memory. Rereading feels fluent and is nearly useless.
- Attach each formula to one question. The links above exist for this: a formula tied to a solved problem sticks far better than a formula on a list.
- Spaced review. Ten minutes at the start of every study session, from week 2 of the 8-week plan onward.