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136 Cards in this Set

  • Front
  • Back
  • 3rd side (hint)
Integers
Whole numbers on the number line
Consecutive Integers
Listed in order of increasing value without any integers missing in between them, such as:
• 0, 1, 2, 3, 4, 5
• -6, -5, -4, -3, -2, -1, 0
Zero
It is an integer, but it is neither positive nor negative (but it is even)
All Prime Numbers Less Than 30
2, 3, 5, 7, 11, 17, 19, 23, 29

There’s no such thing as a negative prime number or a prime fraction
Absolute Value
The absolute value of a number is equal to its distance from 0 on the number line

The absolute value of any number is always positive

ALSO: if ıxı = 4, then the value of of x is either 4 or -4.
An integer is divisible by 2 if...
if its units digit is divisible by 2.

598,447,896 is divisible by 2 because the units digit, 6, is divisible by 2
An integer is divisible by 3 if...
if the sum of its digits is divisible by 3.

2,145 is divisible by 3 because 2+1+4+5 = 12, and 12 is divisible by 3!!
An integer is divisible by 4 if...
if its last two digits form a number that’s divisible by 4

712 is divisible by 4 because 12 is divisible by 4!!!
An integer is divisible by 5 if..
if its units digit is either 0 or 5
An integer is divisible by 6 if...
its divisible by both 2 and 3
An integer is divisible by 9 if...
the sum of its digit is divisible by 9
An integer is divisible by 12 if...
If the integer is divisible by both 6 and 8
Factors
A number a is a factor of another number b if b can be divided by a without leaving a remainder.

For example, 1, 2, 3, 4, 5, 6, and 12 are all factors of 12
.2 = 20% = What Fraction?
.2 = 20% = 1/5
.4 = 40% = What Fraction?
.4 = 40% = 2/5
.6 = 60% = What Fraction?
.6 = 60% = 3/5
.8 = 80% = What Fraction?
.8 = 80% = 4/5
1/5 = What Decimal? What Percentage?
.2 = 20% = 1/5
2/5 = What Decimal? What Percentage?
.4 = 40% = 2/5
3/5 = What Decimal? What Percentage?
.6 = 60% = 3/5
4/5 = What Decimal? What Percentage?
.8 = 80% = 4/5
Percent Change Formula
(Difference/Original) x 100
How to Multiply Exponents

2^2 X 2^4 = ?
Add the exponents

2^2 + 2 ^4 = 2^6

This doesn't work for adding exponents, but won't be asked to do that.
Dividing Exponents

2^6 / 2^2 = ?
Subtract the exponents

2^6 / 2^2 = 2^6-2 = 2^4
A negative exponent should be rewritten as ....

3^-2 = ?
1/(3^2) => 1/9
Raising a number greater than 1 to a power greater than 1 results in a BIGGER or SMALLER number?

2^2 = ?
Raising a number greater than 1 to a power greater than 1 results in a BIGGER number

2^2 = 4
Raising a fraction between 0 and 1 to a power greater than 1 results in a BIGGER or SMALLER number?

(1/2) ^2 = ?
Raising a fraction between 0 and 1 to a power greater than 1 results in a SMALLER number

(1/2) ^2 = 1/4
A negative number raised to an EVEN power becomes POSITIVE or NEGATIVE?

(-2)^2 = ?
A negative number raised to an even power becomes POSITIVE

(-2)^2 = (-2)(-2) = 4
A negative number raised to an ODD power remains POSITIVE or NEGATIVE?

(-2)^3 = ?
A negative number raised to an ODD power remains NEGATIVE

(-2)^3 = (-2)(-2)(-2) = -8
A number raised to a negative power is equal to...?

2^-2 = ?
A number raised to a negative power is equal to 1 over the number raised to the positive number power.

2^-2 = 1/(2^2) = 1/4
A number raised to the 0 power is what?
A number raised to the 0 power is 1, no matter what the number is
A number raised to the first power is what?
A number raised to the first power is ALWAYS the number itself.
0 raised to the 0 power is what?
Undefined
√1 =
√1 = 1
√2 =
√2 = 1.4
√3 =
√3 = 1.7
√4 =
√4 = 2
Associative Law for Multiplication
(ab)(cd) = a(bcd)
4 X (5X8) = (4X5) X 8 = 5 X (8X4)
Distributive Law
a(b + c) = ab + ac
a(b - c) = ab - ac
Associative Law for Addition
(a + b) + (c + d) = a + (b + c + d)
4 + (5+8) = (4+5) + 8 = 5 + (4+8)
12 X 4
48
12 X 3
36
12 X 5
60
12 X 8
96
12 X 9
108
12 X 7
84
12 X 11
132
12 X 12
144
12 X 10
120
12 X 6
72
12 X 13
156
Distributive Law:

a(b + c) =
ab + ac
Distributive Law:

ab + ac
a(b + c)
Distributive Law:

a(b - c) =
ab - ac
Distributive Law:

ab - ac =
a(b - c)
Factoring:

xy + xz =
x(y + z)
Unfactoring:

x(y + z) =
xy + xz
1.4⌃2 = √?
√2
1.7⌃2 = √?
√3
Unfactor:

5(x + y)
5x + 5y
Factor:

5x + 5y
5(x + y)
Factor:

8⁷ - 8⁶
8⁶(8ⁱ - 1)
Good Plug In Numbers for Percentage Problems:
10, 100
Good Plug In Numbers for Minutes or Seconds Problems
30,120
How to solve "Must Be" problems
1. Plug in numbers
2. Eliminate answer choices
3 Plug in different numbers
What numbers to use when Plugging In to Quant Comp questions
First use "normal numbers"
Then use "weird" numbers (zero, 1, negatives, fractions, or big numbers) to disprove your first answer.

If different numbers give you different answers, you've proved answer is D
When Plugging In answer choices, which answer choice should you start with
The one in the middle
When is answer D eliminated with Quant Comp questions?
When the question contains only numbers.
Dividing Fractions:
Dividing Fractions: Multiply the first fraction by the reciprocal of second fraction

*Cross Reduce before you multiply
⅔ ÷ ⅘
2/3 ÷ 4/5 =
2/3 X 5/4 =Then Cross-Reduce
1/3 X 5 /2 = 5/6
Bowtie
Multiply denominators together to get the new denominator, and multiply diagonally up to get the new numerators

2/3 - 3/4 = 8/3 -9/4 =

8/12 - 9/12 = -1/12
When to Bowtie
When adding or subtracting fractions with different denominators

When comparing fractions with different denominators
1/5 = x%
20%
1/4 = x%
25%
4/5 = x%
80%
2/5 = x%
40%
3/5 = x%
60%
2x⁴ X 2x⁵
2x⁹
When do you use weird numbers?
Second round of Pluggin In on quant comps

(0, 1, negatives, fractions, or really big numbers)
Whenever the answer choices are far apart in value you can...
ESTIMATE/BALLPARK
Whenever you see the word APPROXIMATELY in a question you can...
Ballpark!/Estimate!
Formula for Averages:
Total
______
# of things
RANGE
Difference between highest and lowest numbers in your set

(2, 6, 13, 3, 15, 4, 9) range: 15-2, or 13
STANDARD DEVIATION
How much the numbers in a set vary from the mean of the set
A large standard deviation means...
the numbers in the set are spread far from the mean
A small standard means the values in the set are...
clustered closely around the average
RATE
Distance or Amount
_________________
Time X Rate
Ratio Table
Part Part Total
Ratio

Multiply by

Real
PROBABILITY
Number of possible outcomes that satisfy the condition
_________________________
Number of total possible outcomes
To find the probability of a series of events in a row
Multiply the probabilities of the individual events
To find the probability of either one event OR another event happening
Add the probabilities
The probability of an event happening and the probability of an event NOT happening....
Must add up to 1
Factorial
That number times every positive whole number smaller than itself, down to 1

6 = 6 X 5 X 4 X 3 X 2 X 1= 720
Symbol for a Factorial
!
0!
1
When factorials show up in GRE...
Look for a shortcut like canceling or factoring
12!
___
11!
12 X 11 X 10 X 9 X 8 X 7 6 X 5 X 4 X 3 X 2 X 1
_________________________
11 X 10 X 9 X 8 X 7 6 X 5 X 4 X 3 X 2 X 1

12!/11! = 12
4!
___
2!
4 X 3 X 2 X 1
___________
2 X 1

4!/2! = 12
Permutation
Arrangement of things in a particular order
To solve a permutation
Figure out how many slots you have, write down number of options for each slot, and then multiply
Combination
A group, and the order of elements within the group doesn't matter
To solve a combination
Figure out how many slots you have, fill in the slots like a permutation, then divide by the factorial of the number of slots

*denominator will always cancel out completely
Given events A and B, the probability of events A AND B=
(Probability of A) x (Probability of B)
Given events A and B, the probability of events A OR B =
(Probability of A) + (Probability of B)
Given event A: Probability that A happens + Probability that A does NOT happen =
1
Unfactor:
x^2 - y^2
(x + y)(x - y)
Factor:
(x + y)(x - y)
X^2 - y^2
Unfactor:
X^2 + 2xy + y^2
(x + y)(x + y)
Factor:
(x + y)(x + y)
X^2 + 2xy + y^2
Unfactor:
(x - y)^2
x^2 - 2xy + y^2
Factor:
x^2 - 2xy + y^2
(x - y)^2
When two lines intersect, four angles are formed; what is the sum of these angles?
360 degrees
The three angles inside a triangle add up to...
180 degrees
The four angles inside any four sided figure add up to...
360 degrees
When two parallel lines are intersected by a third line, all the big angles are...
Equal
When two parallel lines are intersected by a third line, all the small angles are...
Equal
When two parallel lines are intersected by a third line, the sum of any big and any small angle is always...
180 degrees
Degrees of a right triangle
30, 30, 60
Degrees of an equilateral triangle
60, 60, 60
Isosceles Triangles
40, 70,70
The length of any side of a triangle must be ___________ than the sum of the other two sides and ________ than the difference between the other two sides.
The length of any side of a triangle must be LESS than the sum of the other two sides and LARGER than the difference between the other two sides.
Area of a Triangle
Height multiplied by the base, divided by 2

A = (1/2)BH
Pythagorean Theorem
a^2 + b^2 = c^2

Only works with right angles
Degrees of Isosceles Right Triangle
45, 45, 90
The ratio between the length of sides in a _______ (degrees) triangle is constant.
30, 60, 90
If you know the length of any sides in a ______ (degrees) triangle, you find the length of any of the others
If you know the length of any sides in a 30, 60, 90 triangle, you find the length of any of the others
In an isosceles right triangle, the two non-hypotenuse sides are...
Equal
In an isosceles right triangle, the length of each short leg is x, then the length of the hypotenuse is...
x√2
Circumference of a Circle
∏d

2∏r
Area of a Circle
πr^2
Slope
y = mx + b

x and y are points on the line
b stands for the y-intercept
Slope
rise/run
Volume
LWH
length x width x height
Volume of Circular Cylinder
∏r^2h
Finding the Length of a Diagonal Line inside a Three Dimensional Rectangular Box
a^2 + b^2 + c^2 = d^2

a, b, c = dimensions of the figure
Surface Area of a Rectangular Box
Sum of the areas of all its sides