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)
