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Question 1

Least Common Denominator (LCD)

Answer 1

List the multiples of the numbers to get the LCD.

5 - 5, 10, 15, 20, 25, 30
6 - 6, 12, 18, 24, 30

LCD is 30

Question 2

Comparing Fractions

Answer 2

• Reference point (bigger than one half, smaller than one half)
• Bow tie method
• Common denominator
• Common numerator (the bigger the denominator, the smaller the fraction)

Question 3

Base Fractions and their Decimal & Percentage Approximations

Answer 3

1/2 - 0.5
1/3 - 0.333
1/4 - 0.25
1/5 - 0.2
1/5 - 0.167
1/7 - 0.143
1/8 - 0.125
1/9 - 0.111
1/10 - 0.1

Question 4

Fractions & their decimals - more complex ones

Answer 4

5/6 - 0.833

3/7 - 0.42
4/7 - 0.571
5/7 - 0.714
6/7 - 0.857

5/8 - 0.625
7/8 - 0.875

Question 5

Quadratic Identities

Answer 5

(1) (x+y)^2 = (x+y)(x+y)= x^2 + y^2 +2xy
(2) (x-y)^2 = (x-y)(x-y) = x^2+y^2-2xy
(3) (x+y)(x-y) = x^2-y^2

Question 6

Integer

Answer 6

A number that can be written without a decimal or a fractional component

Question 7

Is zero positive or negative?

Answer 7

Neither

Question 8

Whole number

Answer 8

Nonnegative integer. That is - positive integers and the number zero

Question 9

Zero properties

Answer 9

`1 - Zero x any number = zero
2 - Zero / any number = zero
3 - Any number / zero = undefined
4 - Square root of zero = zero
5 - Zero raised to any positive power = zero (0^0 is undefined and never on the GMAT)
6 - Zero is neither positive nor negative
7 - Zero is the only number equal to its opposite (0 = -0)
8 - Zero is a multiple of all numbers
9 - Zero is the only number equal to all of its multiples
10 - Zero is not a factor of any number except itself
11 - Any number to the power of zero = 1
12 - Zero is even
13 - Zero can be added or subtracted from any number without changing the value of the number

Question 10

One properties

Answer 10

1 - One is a factor of all numbers, and all numbers are multiples of 1
2 - One raised to any power is 1
3 - Multiplying or dividing any number by 1 does not change the number
4 - One is an odd number
5 - One is the number with exactly 1 factor
6 - One is not a prime number (the first prime number is 2)

Question 11

Sums and Differences of odd & evens

Answer 11

Even +- Even = Even
Odd +- Odd = Even

Even +- Odd = Odd
Odd =- Even = Odd

Question 12

Multiplication rule for evens and odds

Answer 12

Even x Even = Even
Even x Odd = Even
Odd x Even = Even
Odd x Odd = Odd

Question 13

Division rules for events and odds

Answer 13

Even/even = odd or even
even/odd = even
odd/odd = odd
odd/even - is not possible

Question 14

Absolute Value

Answer 14

Distance of the number from zero on the number line

Question 15

Prime numbers less than 10

Answer 15

2, 3, 5, 7

Question 16

Prime numbers less than 20

Answer 16

11, 13, 17, 19

Question 17

Prime numbers less than 30

Answer 17

23, 29

Question 18

Prime numbers less than 40

Answer 18

31, 37

Question 19

Prime numbers less than 50

Answer 19

41, 43, 47

Question 20

Prime numbers less than 60

Answer 20

53, 59

Question 21

Prime numbers less than 70

Answer 21

61, 67

Question 22

Prime numbers less than 80

Answer 22

71, 73, 79

Question 23

Prime numbers less than 100

Answer 23

83, 89, 97

Question 24

Remainder Equations

Answer 24

x/y = Q + r

x=QY+r

Q= (x-r)/y

r = x-Qy

Question 25

Patters in Units digits when a positive integer is raised to consecutive powers.

Answer 25

0 > 0 1 > 1 2 > 2-4-8-6 3 > 3-9-7-1 4 > 4 (odds) - 6 (evens) 5 > 5 6 > 6 7 > 7-9-3-1 8 > 8-4-2-6 9 > 9 (odd) - 1 (even)

Question 26

The product of n consecutive *even* integers is divisible by...

Answer 26

2^n * n

Question 27

Root of X^2 =

Answer 27

Absolute value of X | Even root of any number X will equal absolute value of x.

Question 28

non negative perfect cubes

Answer 28

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Question 29

Radicals (square roots of non perfect #s) - 1 to 8

Answer 29

``` sq root 2 = 1.4 sq root 3 = 1.7 sq root 5 = 2.2 sq root 6 = 2.4 sq root 7 = 2.6 sq root 8 = 2.8 ```

Question 30

2^n + 2^n = 2^n+1

Question 31

Exponents rule - If 0 < x < 1, then...

Answer 31

x^2 < x < sq root of x

Question 32

Never multiple or divide an inequality by a variable unless the sign of the variable is known

Question 33

Simple Interest

Answer 33

Principal x Rate x Time Principal - initial amount of money that was borrowed, lent, or invested Rate - simple interest rate expressed as a decimal (or fraction) Time - duration of loan or investment Units of rate & time must match. If interest rate is annual and time is 8 months - it should be added to the equation as 8/12 (and not "8") If interest rate is expressed as a variable - it should be added to the equation as x/100 Interest earned in any period on the principal invested is not factored into future amounts of interest earned.

Question 34

Inverse Variation

Answer 34

y = k/x | Direct varation y=kx

Question 35

Percent Change

Answer 35

((Final value-initial value)/Initial value)*100