GRE math formulas

Slope formula

(y₂- y₁) / (x₂- x₁)

Area of Equilateral Triangle

(√3/4)side^2

percent increase

1 + P% (as a decimal) Thus, the multiplier for a 46% increase is: 1 + .46 = 1.46 Ex: An item originally cost $800. The price increased by 20%, what's the new cost? 800 x (1 + .20) = 800 x 1.20 = 960 Ex: After a 30% increase, the price of something is $78. What was the original price? x + 1.30 = 78 x = 78/1.30 original cost = $60

percent decrease

1 - P% (as a decimal) Thus, the multiplier for a 28% decrease: 1 - .28 = .72 Ex: A $170 item is discounted by 30%, what's the new price? 1 - .30 = .70 .70(170) = $119

Greatest Common Factor

1) Find the Prime Factorization of each number 2) Find the highest powers of numbers they each have in common 3) Multiply them together Ex: 360 = 6x6x10 = 2^3 x 3^2 x 5 800 = 8x10x10 = 2^5 x 5^2 GCF = 2^3x5^1 = 40

Finding the # of factors a number has

1) Find the prime factorization of N, and write it in terms of powers of the prime factors 2) Create a list of the exponents of the prime factors (remember to use 1 for a prime factor that has no exponent) 3) Add one to every number on the list, creating a new list 4) Find the product of that new list. That product is the number of factors that N has

Least Common Multiple

1) Find the two prime factorizations & the GCF 2) Now, write each number in the form (GCF) times (another factor) 3) The LCM is the product of these 3 factors Ex: 1) 24 = 6x4 = 2^3 x 3 32 = 16x2 = 4x4x2 = 2^5 2)GCF = 2^3 = 8 3) 24 = 8x3 32 = 8x4 LCM = 8x3x4 = 96

Finding the # of odd factors

1) prime factorization 2) list of exponents for odd factors 3) add one to each factor on the list 4) product of factors on new list = number of odd factors

Km

1,000 m

Fractions

1. If we start with a fraction, and add the same number to both the numerator and the denominator, that resultant fraction is closer to 1 2. If we start with a fraction, and add p to the numerator and q to the denominator, the resultant fraction is closer to p/q

Sequential Percent Changes

1. Mistake #1: an increase and a decrease by the same percent do NOT get us back to the original starting point. 2. Mistake #2: in a series of percent changes, NEVER add and subtract individual percents 3. For a series of percent changes, multiply the individual multipliers together

Fractions

1. bigger numerator -> bigger fraction 2. bigger denominator -> smaller fraction 3. multiply numerator and denominator by the same factor -> equal fractions 4. cross-multiplication comparison

Sum of Angles

180(n-2)

What's the difference between the highest and lowest number in a set?

1st number + consecutive multiple(n-1)

Prime numbers under 20

2, 3, 5, 7, 11, 13, 17, 19

Bell Curve

2.5%, 13.5%, 34%, 34%, 13.5%, 2.5%

Prime number under 60

23, 29, 31, 37, 41, 43, 47, 53, 59

Circumference of a circle

2πr or πd

Arc of a circle

2πr x (angle/360)

1 hour

3,600 seconds

Simple Interests

A mathematical fiction

Area of a triangle

A=1/2bh

Area of a Circle

A=πr^2 ​​

Divisibility Rule for 9

Add all the digits. If the sum of the digits is divisible by 9, then it's divisible by 9 (same rule for divisibility rule for 3) Ex: 1,372 ; 1+3+7+2 = 12, not divisible by 9

Adding & Subtracting Even/Odd Integers

Adding/Subtracting "likes," = we get EVEN Adding/Subtracting "unlikes," = we get ODD

Negative Integers

Both positive and negative factors

Perimeter of a Circle

C=2πr

Rebuilding the dividend

D= SQ + r

Dividing Even and Odds

E/E= E or O or not an integer at all O/O = O or not an integer at all E/O = E or not an integer at all O/E = is never an integer

Prime Factorization of Large Numbers

Ex: 1,599 = 1,600-1 = (40^2)-(1^2) = (40+1)(40-1) = (41)(39) = (41)(3x13) These are the three prime factors 2,491 = 2,500-9 = (50^2)-(3^2) = (50+3)(50-3) = (53)(47) These are the only prime numbers

Greatest Prime factor

Ex: 144 = 2x72 = 2x2x36 = 2x2x6x6 = 2x2x2x3x2x3 --> 3 is greatest prime factor and 96 = 3x32 = 3x8x4 = 3x4x2x2x2 = 3x2x2x2x2x2 --> 3 is greatest prime factor **be aware of equal divisible numbers (ex: 40,002 and 80,004) *** answer would be, they're both equal

Multiplying Evens and Odds

ExE=E OxO=O ExO=E As long as there is at least one even factor in a product, the product will be even. The only way a product can be odd is if every single factor is odd

Quadrilateral

Inside angles will always = 360 Outside angles will also always = 360

GCD-LCM Formula

LCM = PxQ/GCF

All positive factors for #'s under 100

List all the pairs Ex: 36 1, 36 ; 2, 18 ; 3, 12 ; 4,9 ; 6,6

Divisibility Rules for 4

Look at the 10's place and the 1's place If the last 2 digits form a two-digit number that's divisible by 4, then the entire number is divisible by 4 Ex: 262,584,2'96'

Parallelogram angles

Opposite Angles are Congruent. Consecutive Angles are Supplementary.

Probability Formula for 'or'

P(A or B) = P(A) + P(B) - P(A and B)

Probably of (A or B)

P(A) + P(B) - P(A and B)

Probably of (A and B)

P(A) + P(B) - P(A or B)

Does a point lie on line 'x'

Plug in the numbers in the parenthesis into the slope equation, if it does lie on the line both sides of the equation will equal each other

Mean of N numbers,

Sum of the numbers is nxm

Least Common Multiple (LCM)

The least number that is a common multiple of two or more numbers.

Circumference/Diameter

The ratio of the circumference to the diameter of any circle of any size is always π. If k has a value k/3=π, then this the value of the circumference-to-diameter ratio in both circles.

We CAN subtract inequalities with opposite signs

Think about it, If a > b and d < c, then (a-d) > (b-c)

Divisibility Rule for 6

This rule is a combination of a couple of other rules. In order for it to be divisible by 6, a number must be: a) divisible by 2, and b) divisible by 3 We check divisibility by 2 by looking at the last digit, we check divisibility by 3 by finding the sum of the digits

Volume of Cube

V=s^3

Volume of a Cylinder

V=πr2h

Divisibility Rules for 3

We add up all the digits of the number: if the sum of the digits is divisible by 3, then the number is divisible by 3, and if the sum of the digits is not divisible by 3, then the number isn't divisible by 3 Ex: 102,334,155 ; 1+0+2+3+3+4+1+5+5=24, which is divisible by 3

We have no direct way to calculate the number of even factors

We have to calculate (a) the total number of factors, and (b) the number of odd factors, and then subtract

No Solutions

When one side of the equation is zero and equals a different number. Or when one side of the equation doesn't equal the other side of the equation (ex: 15=8)

Infinite Solutions

When two sides of the equations equal each other.

We CAN add inequalities in the same direction

a < b and c < d , then (a+c) < (b+d)

Isoceles Right Triangle

a = x b = x c = x√2 ex: 45, 45, 90

Scalene Right Triangle

a = x b = x√3 c = 2x ex: 30, 60, 90

A negative number raised to the power of an even number =

a positive number

Equaliateral Triangle

all sides = x

Pythagorean Theorem

a²+b²=c²

Time Formula

distance/speed

Finding the percent of decrease

m = new price/old price Ex: The price of an item decreases from $250 to $200. What was the percent decrease? 200/250 = 20/25 = 80/100 = .80 = 20% decrease

Finding the percent of increase

m = new price/old price Ex: The price of an item increases from $60 to $102. What was the percent increase? 102/60 = 1.7 = (1 +.70) 70% increase

y = mx+b

m = slope (rise/run) b = y-intercept

Sum of Integers Formula

n(n+1)/2

Number of integers from n to m inclusive

n-m+1

percent

part/whole x 100

Substitution Method

replace one variable with an expression containing the remaining variable

square root

taking the square root of something is the same thing as raising it to the power of 1/2

Negative exponent

the number flips

If m is the mean of n numbers,

then the sum of those numbers is mn

Elimination Method

when you add or subtract two equations to eliminate one of the variables

Area of equilateral triangle

√3)/4 x (side^2)