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