The GRE does not give you a formula sheet. These formulas cover more than 90% of what appears in Quantitative Reasoning, memorize them, then practice applying them under time pressure.
Arithmetic & Number Properties
Even ± even
even; odd ± odd = even; even ± odd = odd
Even × any integer
even
Odd × odd
odd
Divisibility by 3
sum of digits divisible by 3
Divisibility by 4
last two digits divisible by 4
Divisibility by 9
sum of digits divisible by 9
Number of factors
if n = aᵖ·bᵠ, factors = (p+1)(q+1)
GCD × LCM
= a × b
Remainder
n = qd + r, 0 ≤ r < d
Percent change
(new − old) / old × 100
Successive % changes
(1 + a)(1 + b) − 1
Simple interest
I = P·r·t
Compound interest
A = P(1 + r/n)ⁿᵗ
Sum 1…n
n(n+1)/2
Consecutive integers count
last − first + 1
Algebra & Exponents
aᵐ · aⁿ
aᵐ⁺ⁿ
aᵐ / aⁿ
aᵐ⁻ⁿ
(aᵐ)ⁿ
aᵐⁿ
a⁰
1 (a ≠ 0)
a⁻ⁿ
1/aⁿ
a^(1/n)
ⁿ√a
(ab)ⁿ
aⁿbⁿ
√a · √b
√(ab)
(a + b)²
a² + 2ab + b²
(a − b)²
a² − 2ab + b²
a² − b²
(a + b)(a − b)
(a + b)³
a³ + 3a²b + 3ab² + b³
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Sum of roots
−b/a
Product of roots
c/a
Discriminant
b² − 4ac (>0: 2 roots, 0: 1, <0: none)
|x| < a
−a < x < a
|x| > a
x > a or x < −a
Direct variation
y = kx
Inverse variation
y = k/x
Rates, Work & Mixtures
Distance
d = r · t
Average speed
total distance / total time
Combined work
1/T = 1/A + 1/B
Work
work = rate × time
Mixture
c₁v₁ + c₂v₂ = c(v₁ + v₂)
Weighted average
(w₁x₁ + w₂x₂)/(w₁ + w₂)
Relative speed (opposite)
r₁ + r₂
Relative speed (same dir.)
|r₁ − r₂|
Profit
revenue − cost
Ratio parts
a:b → a/(a+b) of total
Geometry
Triangle angles
sum = 180°
Triangle area
½ · b · h
Pythagorean theorem
a² + b² = c²
Common triples
3-4-5, 5-12-13, 8-15-17, 7-24-25
45-45-90
x : x : x√2
30-60-90
x : x√3 : 2x
Equilateral area
(√3/4) · s²
Triangle inequality
|a − b| < c < a + b
Polygon interior sum
(n − 2) · 180°
Regular polygon angle
(n − 2) · 180° / n
Exterior angles
sum = 360°
Rectangle area
l · w
Parallelogram area
b · h
Trapezoid area
½(b₁ + b₂) · h
Rhombus area
½ · d₁ · d₂
Circle area
πr²
Circumference
2πr
Arc length
(θ/360) · 2πr
Sector area
(θ/360) · πr²
Inscribed angle
½ central angle
Diameter triangle
triangle on a diameter is right-angled
Box volume
l · w · h
Box surface
2(lw + wh + lh)
Box diagonal
√(l² + w² + h²)
Cube volume
s³
Cylinder volume
πr²h
Cylinder surface
2πr² + 2πrh
Similar figures
area ratio = k², volume ratio = k³
Coordinate Geometry
Slope
m = (y₂ − y₁)/(x₂ − x₁)
Line
y = mx + b
Point-slope
y − y₁ = m(x − x₁)
Distance
√((x₂ − x₁)² + (y₂ − y₁)²)
Midpoint
((x₁ + x₂)/2, (y₁ + y₂)/2)
Parallel lines
equal slopes
Perpendicular lines
m₁ · m₂ = −1
Circle
(x − h)² + (y − k)² = r²
x-intercept
set y = 0
Parabola vertex
x = −b/2a
Statistics
Mean
sum / count
Median
middle value (sorted)
Mode
most frequent value
Range
max − min
Sum from mean
sum = mean × count
Std. deviation
spread around mean; unchanged when adding a constant
Scaling data
multiply by k → SD × k
Normal: ±1 SD
≈ 68%
Normal: ±2 SD
≈ 95%
Interquartile range
Q3 − Q1
Counting & Probability
Fundamental counting
m × n ways
Factorial
n! = n(n−1)…1
Permutations
nPr = n!/(n−r)!
Combinations
nCr = n!/(r!(n−r)!)
Arrangements w/ repeats
n!/(a!·b!…)
Circular arrangements
(n − 1)!
Probability
favorable / total
Complement
P(not A) = 1 − P(A)
Independent AND
P(A)·P(B)
OR
P(A) + P(B) − P(A and B)
Mutually exclusive OR
P(A) + P(B)
At least one
1 − P(none)
Put it into practice
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