GRE Study Quant

Percent

(part/base) * 100

Percent Change

(Amount of Change / Initial Base)

Successive Change

New Value = (Original)(1 ± %change)(1 ± %change)…

Quadratic Formula

How to Factor

ax² + bx + c, find numbers with product ac and sum b → ax² + s₁x + s₂x + c =0. Solve by grouping.

Interest Variables

P = investment, n = how many times in a year, t = time, r = rate, V = final total

Simple Interest

V = P(1 + rt/100)

Compound Interest

V = P( 1 + r/100n)^nt

Distance Over Time

dist = rate(time)

Work by Multiple Parties

1/r₁ + 1/r₂ = 1/x

Distance Formula

Circle Formula

(x-a)² + (y-b)² = r², (a,b) is center, r is radius.

Sum of Interior Angles

(n-2) * 180°

Common Triangle Ratios

45° - 45° - 90°: 1:1:√2
30° - 60° - 90°: 1: √3: 2

Trapezoid Area Formula

A = 1/2(b₁+b₂)h

Circle: Circumference + Area

C = 2πr
A = πr²

Circle: Arc Length

(n/360)*2πr

Circle: Sector Area

(n/360)*πr²

Rectangular Prism: Volume + Surface Area

V = lwh
SA = 2(lw + lh + wh)

Cylinder: Volume + Surface Area

V = πr²h
SA = 2(πr²) + 2πrh

Standard Deviation

SD = (x̄ -x₁)², (x̄-x₂)², (x̄-x₃)²; find average, take square root.

Z value

z* = (x₁ - x̄)/SD

|A U B|

|A| + |B| - |A ∩ B|

Permutation

Order Matters
_nP_k = n!/(n-k)!

Combination

Order Doesn’t Matter
_nC_k = n!/k!(n-k)!

P(E or F) (independent)

P(E) + P(F)

P(E or F) (dependent)

P(E) + P(F) - P(E and F)

P(E and F) (independent)

P(E) * P(F)

P(E and F) (dependent)

P(E) * P(F|E)
or
P(F) * P(E|F)

Bayes Rule

P(A|B) = (P(A) * P(B|A)) / P(B)

Range of the Third Side of a Triangle

∣a−b∣ < x < a+b