GRE Math Tricks Flashcards
Divide by 5
Double then divide by 10
(10k + 5)²
- k * (k + 1)
2. Append 25
k^2 –> (k - 1)²
k² - k - (k - 1)
k^2 –> (k + 1)²
k² + k + (k + 1)
quantitative comparison
estimation and part-wise comparison
compare two fractions
- cross multiply and see which side is greater (equivalent to multiplying both sides by both denominators)
- add p to numerator and q to denominator, result will move towards p/q
check if prime
check prime multiples up to square of number
average speed
do not average speeds! use d = rt formula and substitute nice distance if unknowns
counting factors of large numbers
- prime factorization
2. permutations of powers of primes
counting odd factors of large numbers
- prime factorization
2. permutations of powers of primes, ignoring factors of 2
counting even factors of large numbers
find odd factors and subtract from total factors
area of equi triangle
(√3 / 4) s²
associative property
ordering does not matter for addition and multiplication, but does matter for subtraction and division
simple interest
interest paid only on principal (initial input), linear
compound
interest paid on total current amount (initial + accrued interest)
find number of multiples between two numbers
take last multiple in range minus first multiple in range, divide by the multiple and add one
properties of n consecutive numbers
- will have at least one number that is multiple of n, n - 1, … 1
- if n is odd, sum will be a multiple of n
a² - b²
(a - b)(a + b)
note, a can also have a power (e.g. x^6 - 16 = (x^3 - 4)(x^3 + 4)
prime factorization of big numbers
if possible, use difference of two squares
e.g. 1599 = 1600 - 1 = 40² - 1² = (40 - 1)(40 + 1) = 39 * 41 = 13 * 3 * 41
simplify decimals just less than 1
if possible, use difference of two squares to get two multiples
simplify equations with fractions
multiply everything by the LCM of all denominators
solve system of equations where no coefficients are +/-1
use elimination method/linear combination
solve expression given two equations
manipulate the expressions and solve for expression using elimination method
solve three equations for three unknowns
- use elimination from 2 equations to remove one variable
- pick another 2 equations and remove the same variable
- solve the two variable, two equations
sum of 1 … n
n(n+1)/2
percentage covered 1 std dev from mean
68%
percentage covered by 2 std dev from mean
95%
rhombus properties
A = base * height
all four sides equal
min to max area of triangle given two sides
min > 0
max = right angle given neither side is hypothenuse
triangle side properties
- largest angle is opposite longest side
2. third side has to be greater than difference of two sides and smaller than sum
circle angle properties
- inscribed angles (vertex on circle) from the same arc are equal
- inscribed angles are half the central angle (vertex on center) from the same arc
