# GMAT Quantitative

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- GMAT Quantitative

**Created:**2014-05-05

**Last Modified:**2014-05-12

^{n - m}

^{n})/(x

^{m})

^{n + m}

^{n}*x

^{m}

^{n})/(y

^{n})

^{n}

^{n}

^{n}*y

^{n}

^{yz}

^{y})

^{z}

^{n})

^{-n}

^{x/y}

^{x/y }=

^{y}√a

^{x}

^{2/3}= 3√a

^{2}

^{n}

^{n }= √x

^{n}

^{n}

^{0}

^{1 }=

^{1 }= x

^{n}

^{0}= 1 or undefined

_{V}= P

_{V}(1 + i)

^{n}

_{V is }future value, P

_{V}is present value, i is the interest rate per period and n is the number of compounding periods

_{n}C

_{k}= n!/((n-k)k!)!

*n*objects

*k*objects can be selected

_{n}P

_{k}= n!/(n-k)!

*n*objects

*k*objects can be selected

(Odd)(Odd) = Odd

(Even)(Even) = Even

(Odd) ± (Odd) = Even

(Even) ± (Even) = Even

(Positive)(Negative) = Negative

(Negative)(Negative) = Positive

(Positive)/(Positive) = Positive

(Negative)/(Negative) = Positive

^{2 }where a is one side

^{2 }where a is one side

^{2 }where a is one side

^{2 }where a is one side

Area =

^{1}/

_{2}(height)(base

_{1}+ base

_{2})

_{1}+ base

_{2}are the lengths of the parallel sides

_{1}*Diagonal

_{2})

^{2}

^{x}/

_{360})πr

^{2}

- Find the area

A = π(9)^{2}= 81π - Plug into the area of a sector formula

(^{60}/_{360})81π

(^{1}/_{6})(81π)

(^{81}/_{6})π

^{degree of central angle}/

_{360})Circumference

^{x}/

_{360})2πr

- Find the circumference

C = 2π(9) = 18π - Plug into the length of an arc formula

(^{60}/_{360})(18π)

(^{1}/_{6})(18π)

3π

- All inscribed angles with the same endpoints are equal
ADB = AEB

- Inscribed Angle = (

^{1}

- /

_{2}

- )(Central Angle)
ADB = (

^{1}

- /

_{2}

- )ACB

ADB is a right angle is because central angle ACB is 180° and ADB is an inscribed angle whose endpoints are the same as ACB.

ADB = ^{1}/_{2}(ACB)

ADB = ^{1}/_{2}(180) = 90

For the above to hold true: (1) C must be the center of the circle (2) AB must be a diameter of the center

^{2}+ 4

^{2}= 5

^{2}

^{2}+ 12

^{2}= 13

^{2}

^{}

^{}

^{2}+ 15

^{2}= 17

^{2}

^{}

^{1/2}

^{1/2}-2

^{2}

^{2}+ B

^{2}= C

^{2}where A = one leg, B = the other leg, C = hypotenuse

^{3}where

*a*is the length of a side

^{2}h

SA = 2lw + 2hw + 2lh

X is Positive: x + 5 = 40

x = 35

X is Negative: x + 5 = - 40 [Make the expression opposite the absolute value negative]

x = - 45

x > 1/8

X is Negative: 10x + 8 < (-1)(9 + 2x)

x < -17/12

^{1}= 2

2

^{2}= 4

2

^{3}= 8

2

^{4}= 16

2

^{5}= 32

2

^{6}= 64

2

^{7}= 128

2

^{8}= 256

2

^{9}= 512

^{1}= 3

3

^{2}= 9

3

^{3}= 27

3

^{4}= 81

3

^{5}= 243

3

^{6}= 729

^{1}= 4

4

^{2}= 16

4

^{3}= 64

4

^{4}= 256

4

^{5}= 1,024

^{1}= 5

5

^{2}= 25

5

^{3}= 125

5

^{4}= 625

5

^{5}= 3,125

^{Even}√Positive

^{Odd}√Positive

^{Odd}√Negative

^{Even}√Negative

**/**2a

^{2}+bx+c

^{2}+bx+c

^{2}+ 2x - 8 = 0

Find two numbers whose sum is b (or 2 in this example) and whose product is c (or -8 in this example).

Two such numbers are -2 and + 4, which add to +2 and multiply to -8.

^{2}+ 2x - 8 = 0

(x - 2)(x + 4) = 0

x = +2, -4 since these two numbers make each factor equal zero.

^{2}+ bx + c = 0 to (x - a)(x - b) = 0

**f**irst,

**o**uter,

**i**nner,

**l**ast.

^{2}+ bx + c = 0) from the factored form [(x - a)(x - b) = 0]: (1) multiply the first terms, then the outer terms, then the inner terms, and finally the last terms (2) add each of the terms together and simplify.

^{2}- b

^{2}

^{2}- 4 = (x + 2)(x - 2)

a = x, b = +2

^{2}

^{2}+ 2ab + b

^{2}

a = x, b = +2

^{}

^{2}

a^{2} - 2ab + b^{2}

Example:

^{2}- 4x + 4 = (x - 2)

^{2}

a = x, b = +2

^{2}-9)/(x+3) = 0, x = ?

- Alternate Interior Angles Are Equal: K = L; O = J
- Alternate Exterior Angles Are Equal: H = M; N = I
- Corresponding Angles Are Equal: K = N; J = M; H = O; I = L
- Non-Alternate Interior Angles Are Supplementary: L + J = 180; K + O = 180

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