GRE Math

Time

(distance)/(rate) d/r

Distance

(rate)(time) d=rt

-3³

-27

3 is the opposite of

-3

X is the opposite of

-X

If a>b then

-a<-b

1ⁿ

1

The product of any number x and its reciprocal

1

b¹

1

Probability of E not occurring:

1 - P(E)

1/2 divided by 3/7 is the same as

1/2 times 7/3

The reciprocal of any non-zero #x is

1/x

The reciprocal of any non-zero number is

1/x

Number of degrees in a triangle

180

If a pair of parallel lines is cut by a transversal that's not perpendicular, the sum of any acute angle and any obtuse angle is

180 Acute Angle an angle that is less than 90° Obtuse Angle:angle that is greater than 90° but less than 180°

Circumference of a circle

2(pi)r

20<all primes<30

23, 29

2⁵/2³

2²

(2²)³

2⁶

2⁵+2³

2⁸

30 60 90

3, 4, 5

The sum of all angles around a point

360°

25^(1/2) or sqrt. 25 =

5 OR -5

30 60 90

5, 12, 13

50 < all primes< 60

53, 59

The percent decrease of a quantity

= (actual decrease/Original amount) x 100%

If a lamp increases from $80 to $100, what is the percent increase?

= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

∅ is

A multiple of every integer

Area of a Parallelogram:

A=(base)(height)

What are the integers?

All numbers multiples of 1.

What are the rational numbers?

All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2, 1, .25, 1/2)

What are the irrational numbers?

All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3)

THE DENOMINATOR CAN NEVER

BE ZERO! 1/∅=null

For any number x

Can be negative, zero, or positive

How do you solve proportions? a/b=c/d

Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60

∅ Is

EVEN

∅ is

Even

2 is the only

Even prime number

∅ is a multiple of

Every number

One is (a prime or not?)

NOT A PRIME

Slope of any line that goes down as you move from left to right is

Negative

The product of odd number of negative numbers

Negative

7 divided by ∅

Null

1 is an

ODD number

If E is certain

P(E) = 1/1 = 1

Probability of an Event

P(E) = number of favorable outcomes/total number of possible outcomes

If Event is impossible

P(E) = ø

The Perimeter of a rectangle

P=2(l+w)

The Perimeter of a Square

P=4s (s=side)

If a is positive, aⁿ is

Positive

Slope of any line that goes up from left to right

Positive

∅ Is neither

Positive or Negative

Positive integers that have exactly 2 positive divisors are

Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)

Dividing by a number is the same as multiplying it by its

Reciprocal

If a<b, then

a+c<b+c

a<b then a - b is positive or negative?

a-b is negative

a>b then a - b is positive or negative?

a-b is positive

a(b+c)

ab+ac

a(b-c)

ab-ac

If a is negative and n is even then aⁿ is (positive or negative?)

aⁿ is positive

bⁿ

b∧b∧b (where b is used as a factor n times)

Rate

d/t (distance)/(time)

formula for distance problems

distance=rate×time or d=rt

Volume of a cube

edge³

To decrease a number by x%

multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

Circumference of a circle

pi(diameter)

1 is the

smallest positive integer

A number is divisible by 9 if...

the sum of digits is divisible by 9.

A number is divisible by 3 if ...

the sum of its digits is divisible by 3.

30 60 90

x, x(SR3), 2x

Consecutive integers

x, x+1, x+2

(x-y)²

x²-2xy+y²

(x-y)(x+y)

x²-y²

Slope

y₂-y₁/x₂-x₁

Any Horizontal line slope

zero

If a product of two numbers is ∅, one number must be

∅

Product of any number and ∅ is

∅

∅ divided by 7

∅

∅²

∅

The only number that is equal to its opposite

∅ ∅=∅

Probability of Event all cases

∅≤P(E)≤1

2³×7³

(2x7)³

Volume of a rectangular solid

(length)(width)(height)

Area of a circle

(pi)r²

10<all primes<20

11, 13, 17, 19

30< all primes<40

31, 37

30 60 90

3x, 4x, 5x

40 < all primes<50

41, 43, 47

-3²

9

If a lamp decreases to $80, from $100, what is the decrease in price?

= (actual decrease/Original amount) x100% = 20/100x100% = 20%

What are the real numbers?

All the numbers on the number line (negative, rational, irrational, decimal, integer). All the numbers on the GRE are real. (-2, 1, .25, 1/2, pi)

Vertical lines

Do not have slopes!

a/∅

Null

An Angle that's 180°

Straight Angle

∅ is a multiple of

Two (∅×2=∅)

1 is a divisor of

every number

A number is divisible by 6 if...

its divisible by 2 and by 3.

A number is divisible by 4 is...

its last two digits are divisible by 4.

To increase a number by x%

multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

(x+y)²

x²+2xy+y²