GRE Math Tricks

Question 1

Divide by 5

Answer 1

Double then divide by 10

Question 2

(10k + 5)²

Answer 2

1. k * (k + 1)

2. Append 25

Question 3

k^2 –> (k - 1)²

Answer 3

k² - k - (k - 1)

Question 4

k^2 –> (k + 1)²

Answer 4

k² + k + (k + 1)

Question 5

quantitative comparison

Answer 5

estimation and part-wise comparison

Question 6

compare two fractions

Answer 6

1. cross multiply and see which side is greater (equivalent to multiplying both sides by both denominators)
2. add p to numerator and q to denominator, result will move towards p/q

Question 7

check if prime

Answer 7

check prime multiples up to square of number

Question 8

average speed

Answer 8

do not average speeds! use d = rt formula and substitute nice distance if unknowns

Question 9

counting factors of large numbers

Answer 9

1. prime factorization

2. permutations of powers of primes

Question 10

counting odd factors of large numbers

Answer 10

1. prime factorization

2. permutations of powers of primes, ignoring factors of 2

Question 11

counting even factors of large numbers

Answer 11

find odd factors and subtract from total factors

Question 12

area of equi triangle

Answer 12

(√3 / 4) s²

Question 13

associative property

Answer 13

ordering does not matter for addition and multiplication, but does matter for subtraction and division

Question 14

simple interest

Answer 14

interest paid only on principal (initial input), linear

Question 15

compound

Answer 15

interest paid on total current amount (initial + accrued interest)

Question 16

find number of multiples between two numbers

Answer 16

take last multiple in range minus first multiple in range, divide by the multiple and add one

Question 17

properties of n consecutive numbers

Answer 17

1. will have at least one number that is multiple of n, n - 1, … 1
2. if n is odd, sum will be a multiple of n

Question 18

a² - b²

Answer 18

(a - b)(a + b)

note, a can also have a power (e.g. x^6 - 16 = (x^3 - 4)(x^3 + 4)

Question 19

prime factorization of big numbers

Answer 19

if possible, use difference of two squares

e.g. 1599 = 1600 - 1 = 40² - 1² = (40 - 1)(40 + 1) = 39 * 41 = 13 * 3 * 41

Question 20

simplify decimals just less than 1

Answer 20

if possible, use difference of two squares to get two multiples

Question 21

simplify equations with fractions

Answer 21

multiply everything by the LCM of all denominators

Question 22

solve system of equations where no coefficients are +/-1

Answer 22

use elimination method/linear combination

Question 23

solve expression given two equations

Answer 23

manipulate the expressions and solve for expression using elimination method

Question 24

solve three equations for three unknowns

Answer 24

1. use elimination from 2 equations to remove one variable
2. pick another 2 equations and remove the same variable
3. solve the two variable, two equations

Question 25

sum of 1 … n

Answer 25

n(n+1)/2

Question 26

percentage covered 1 std dev from mean

Answer 26

68%

Question 27

percentage covered by 2 std dev from mean

Answer 27

95%

Question 28

rhombus properties

Answer 28

A = base * height

all four sides equal

Question 29

min to max area of triangle given two sides

Answer 29

min > 0

max = right angle given neither side is hypothenuse

Question 30

triangle side properties

Answer 30

1. largest angle is opposite longest side

2. third side has to be greater than difference of two sides and smaller than sum

Question 31

circle angle properties

Answer 31

1. inscribed angles (vertex on circle) from the same arc are equal
2. inscribed angles are half the central angle (vertex on center) from the same arc