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GMAT > Math Concepts to Memorize > Flashcards

Math Concepts to Memorize Flashcards

1
Q

Multiply Units - 10” long * 4” w * 7” h = ?

A

280 in3 (cubed)

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2
Q

Distance/Work Rate Formula

A

Rate * Time = Distance/Work or Rate = Work/Time

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3
Q

If an object moves the same distance twice at different speeds, the average will be…

A

closer to the slower speed. Pick a smart number for the distance and create a R*T=D chart for both trips. Trip 1: 4*3 = 12 Trip 2: 6*2 = 12 Aveg: ?*(3+2) = 24 ?*5=24 ?=4.8MPH

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4
Q

When two machines work together ____ the rates

A

ADD the rates. Rate A + Rate B = Rate A+B

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5
Q

2 Average Formals

A

Average = Sum/# of Terms OR Average * # of items = sum

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6
Q

Small Standard Deviation =

A

Closely clustered data

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7
Q

3 Properties of Evenly Spaced Sets

A

Arithmetic Mean = Median

Mean & Median = Avg of 1st & Last Terms

Sum of Elements = Mean * # of items

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8
Q

Formula for Counting Integers in a Set

A

Last-First + 1 OR (Last-First) / Increment + 1

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9
Q

5 Properties of Consecutive Integer Sets

A

Average First & Last Term to Find Middle

Count * of Terms (First-Last) + 1

Multiple middle term by # of terms

The average of an odd # of integers is an integer

The average of an even # of consecutive integers will never be an integer

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10
Q

To Examine Overlapping Sets

A

Create a Double Set Matrix. Use algebra.

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11
Q

To Examine 3 Overlapping Sets

A

Create A Venn Diagram. Work from Inside to Out.

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12
Q

Solving Inequalities (mult/div & add/sub)

A

When you multiply or divide by a NEGATIVE, flip the sign. You can ADD inequalities when symbols face the same way. You can NOT SUBTRACT inequalities.

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13
Q

If someone is younger ____ the difference to keep the parties equal.

A

ADD

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14
Q

Formula for distance when traveling towards each other

A

Sum of Rates * Time to Meet = Initial Separation

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15
Q

Formula for two parties working at different speeds, working together.

A

Add rates. 1/5 + 1/7 = 7/35 + 5/35 = 12/35

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16
Q

Formula for speed as two people walk towards each other at different speeds.

A

Person 1 Rate + Person 2 Rate = Rate of Travel. i.e. 5MPH + 6MPH = 11MPH

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17
Q

Setup for two different people walk towards each other but one starts 2 hours later.

A

R * T = D chart. One party will be T+2 (if time is in hours already).

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18
Q

If one party is undoing the work of the other party _____ the rates of work.

A

SUBTRACT

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19
Q

When comparing rates of work for different machines, first

A

express the rates in equivalent units. How much can it finish per second/minute/hour.

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20
Q

x*x

A

x2

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21
Q

square root 2 * square root 2

A

2

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22
Q

pull out the common factor: x2y-xy2 =

A

xy(x-y)

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23
Q

14-3(4-6) =

A

20

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24
Q

-(52)=

A

-25

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25
Q

3 x 99 - 2 x 99 - 1 x 99 =

A

0

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26
Q

(2xy)2=

A

4x2y2

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27
Q

3y + xy - 2y =

A

3y-2y+xy

(3-2)y + xy

1y + xy

(1+x)y

(x+1)y

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28
Q

12xy - (6x + 2y) =

A

12xy - 6x - 2y

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29
Q

2x2 - 4x2 - 1x2 =

A

(2-4-1)x2

(-3)x2

-3x2

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30
Q

square root 3(sq root 2 + sq root 3) =

A

square 3 * square 2 + square 3 * square 3

square 6 + 3

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31
Q

an integer is divisible by 3 if…

A

…the sume of the integer’s digits is a multiple of 3.

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32
Q

an integer is divisible by 9 if..

A

the sum of the integer’s digits is a multiple of 9.

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33
Q

All the primes less than 20 are…

A

2, 3, 5, 7, 11, 13, 17, 19

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34
Q

What is the factor foundation rule?

A

Every number is divisible by the factors of its factors.

Also you can multiply two factors and it will still be divisble. (If 20 is divisible by 2 & 5, it is also divisible by 2 x 5).

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35
Q

To find all the factors of a number…

A

setup a factors pairs table

1 x 30

2 x 15

3 x 10

5 x 6

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36
Q

To find all the prime factors of a number…

A

use a factors tree.

28

2 * 14

2 * 7

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37
Q

X is divisible by 10 & 17.

Is X divisible by 5?

Is X divisible by 170?

Is X divisible by 15?

A

Yes (5 is a factor of 10)

Yes (170 is the LCM of 10 * 17)

Maybe (5 is a factor but we don’t know if a 3 is present)

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38
Q

What does LCM stand for?

What is the LCM of 6 & 9?

A

Least Common Multiple

18

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39
Q

If x is divisible by A & by B then x is divisible by…

A

the LCM of A and B.

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40
Q

When you combine two factors trees of x that contain overlapping primes…

A

drop the overlap.

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41
Q

If x is divisible by 8, 12, and 45, what is the largest number that x must be divisible by?

A

Create factor trees for each number. Count the number of unique prime factors.

*8 has three 2s so include *

2 x 2 x 2

45 has two 3s and one 5

3 x 3 x 5

12 has two 2s and one 3 (but those are covered by previous factors)

add nothing

2 x 2 x 2 x 3 x 3 x 5 = 360

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42
Q

7 x 6 =

A

42

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43
Q

7 x 7 =

A

49

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44
Q

8 x 7 =

A

56

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45
Q

8 x 8 =

A

64

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46
Q

42=

A

16

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47
Q

52=

A

25

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48
Q

62=

A

36

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49
Q

72=

A

49

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50
Q

82=

A

64

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51
Q

92=

A

81

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52
Q

112=

A

121

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53
Q

122=

A

144

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54
Q

132=

A

169

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55
Q

142=

A

196

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56
Q

152=

A

225

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57
Q

202=

A

400

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58
Q

302=

A

900

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59
Q

33=

A

27

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60
Q

34=

A

81

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61
Q

53=

A

125

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62
Q

23=

A

8

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63
Q

33=

A

27

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64
Q

43=

A

64

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65
Q

53=

A

125

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66
Q

103=

A

1,000

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67
Q

23=

A

8

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68
Q

24=

A

16

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69
Q

25=

A

32

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70
Q

26=

A

64

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71
Q

27=

A

128

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72
Q

28=

A

256

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73
Q

29=

A

512

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74
Q

210=

A

1024

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75
Q

43=

A

64

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76
Q

x2 = 16

x equals ???

A

4 or -4

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77
Q

Which is larger?

(-32) or (-3)2

A

(-3)2= 9

(-32) = 3 x 3 x -1 = -9

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78
Q

To multiply exponential terms with the same base …

y(y6) =

A

add the exponents.

y1 x y6 = y7

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79
Q

When you divide exponential terms that have the same base, …

a5 / a3 =

A

subtract the exponents.

a5-3=a2

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80
Q

For any nonezero value of a,

a0=

A

1

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81
Q

2-3=

three forms of the answer

A

2-3 = 1/23 = 1/8 = 0.125

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82
Q

When you move an exponent from the top to the bottom of a fraction (or vice versa)…

_ 1 _

z-4

A

Switch the sign of the exponent. If you move the entire denominator, leave 1 behind.

_ 1_ = 1*z4 = z4

z-4 = 1 = 1

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83
Q

When you raise something that already has an exponent to another power…

(a2)4=

A

multiply the exponents together.

(a2)4= a2*4 = a8

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84
Q

When multiplying exponents with different bases….

22 x 43 x 16=

A

try breaking down the bases into prime factors.

22 x 43 x 16 = 22 x (22)3 x 24

22 x 26 x 24 =22+6+4

212

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85
Q

When you apply an exponent to a product…

(xy)3 =

(wz3)x =

A

…apply the exponent to each factor.
(xy)3 = x3y3

(wz3)x = wxz3x

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86
Q

To add or subtract exponential terms with the same base…

38 - 37 - 36=

A

pull out a common factor.

(36)(32 - 31 - 30)

36(9 - 3 - 1)

(36)(5)

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87
Q

To add or subtract exponential terms with different bases…

23 + 63=

A

break down the bases and pull out the common factor.

23 + 63=

23(1+33)

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88
Q

The square root of 16 * the square root of 16 =

A

16

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89
Q

sqr(-5)2=

A

sqr25 = 5

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90
Q

When you square a square root vs. Square-root a square

(sqr10)2 vs. sqr102

A

Get the original number vs. Get the absolute value of the original number

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91
Q

sqr2 =

A

about 1.4

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92
Q

sqr3 =

A

about 1.7

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93
Q

sqr70 is bretween what two integers?

A

sqr64 = 8

sqr81 = 9

so between 8 & 9

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94
Q

The square root of a number bigger than 1 is _______ than the original number.

The square root of a number between 0 & 1 is __________ than the original number.

A

Both are closer to 1.

SMALLER

BIGGER1

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95
Q

On the GMAT, the square root of a number is…

A

always positive.

Unlike the x2 which can be negative or positive.

96
Q

sqr722=

(two formulas)

A

sqr722 = (722)1/2 = 722/2 = 711

sqr722 = sqr711x 711 = 711

97
Q

cube root -64 =

A

-4

cube roots can be negative (unlike square roots)

98
Q

To raise a number to a fractional power…

1252/3 =

A

Apply the numerator as is and the denominator as a root in either order.

1252/3 = (cuberoot 125)2 = 52 = 25

99
Q

To mulitply and divide square roots…

A

Multiply or devide the insides, then square-root.

sqr(a) x sqr(b) = sqr(ab)

sqr a / sqr b = sqr(a/b)

100
Q

When you have a sqr of a large number…

sqr12 =

A

Pull the square factors out of the number under the radical sign.

sqr12 = sqr(4x3) = sqr4 x sqr 3 = 2sqr3

Break the number down into primes if you don’t recognize the perfect square factors.

101
Q

To add or subtract inside the root…

sqr(32+42) =

A

Do not break apart like multiplication/division!

Factor out a squre factor from the sum

sqr[310+311] = sqr[310(1+3)] = sqr[310(4)] = sqr[310] x sqr[4] = 35 x 2

OR (if small numbers)

Follow PEMDAS under the radical and then take the square root.

sqr(32+42) = sqr(9+15) = sqr(25) = 5

102
Q

56 x 54x

54

A

5(6+4x-4) = 54x+2

103
Q

-33=

A

-27

104
Q

43+43+43+43+32+32+32 =

A

Factor 43 out of the first four terms and 32 out of the last three terms.

43(1+1+1+1) + 32(1+1+1) =

43(4) + 32(3) =

44+33

105
Q

sqr[24] =

A

sqr[2*2*2*3] =

2sqr[2*3] =

2sqr[6]

106
Q

To solve sqr[352-212]

A

Pull out the great common factor 72

sqr[72(52-32)] =

sqr[72(25-9)] =

sqr[72(16)] =

square root eliminated by perfect squares

7*4 = 28

107
Q

In factions, the denominator can never equal ______.

A

zero.

108
Q

The larger the numerator, the _________ the fraction.

A

larger

109
Q

Which is larger?

3/5 or 4/7?

A

Corss-multiply from the bottom and across…

7x3 = 21 3/5 vs. 4/7 5x4=20

3/5 is larger.

110
Q

To simplify a fraction…

A

cancel out common fators from the numerator and demonminator.

18x2 = 6x * 3x = 3x

60x 6x * 10 10

111
Q

To multiply fractions…

A

first cancel any factors and then multiply the tops and bottoms together.

112
Q

The reciprocal of a negative fractions is ____________.

A

also negative.

113
Q

To divide by a fraction…

A

multiply by the reciprocal.

114
Q

If you have addition or subtraction in the numberator of a fraction…

9x - 6

3x

A

Pull out a factor form the entire numorator and cancel that factor with one in the denominator.

9x - 6 = 3(3x-2) = 3x-2

3x = 3x x

115
Q

If you have addition or subtraction in the numerator, you can rewrite…

A

the fraction as the sum of two fractions.

9x - 6 = 3(3x-2) = 3x-3 = 3x - 2 = 3 - 2

3x 3x x x x x

116
Q

If you have addition or subraction in the denominator ___________.

A

NEVER split a fraction in two.

Look for a common factor on the top and bottom to simpilfy out.

117
Q

To compute “nasty” fractions…

A

put parentheses around the nasty numerators and denominators and then proceed normally.

118
Q

If you encounter a fraction within a fraction…

A

work your way out from the deepest level inside.

119
Q

To simplify sqr[18]…

A

look for the perfect squares.

sqr[2*3*3] = 3sqr[2]

120
Q

Another word for ratio is _________

A

proporation.

121
Q

To convert a percent to a fraction….

A

write the percent “over one hundred”.

45% = 45/100

122
Q

5/8 = 0.?? = ??%

A

5/8 = 0.625 = 62.5%

123
Q

7/8 = 0.?? = ??%

A

7/8 = 0.875 = 87.5%

124
Q

6/5 = ??? = ??%

A

6/5 = 1.2 = 120%

125
Q

3/8 = ??? = ???%

A

3/8 = 0.375 = 37.5%

126
Q

To calculate 0.004 * 10-3 =

A

Change teh negative power to postiive and divide instead of mutliply.

  1. 004 * 10-3 =
  2. 004 / 103 =

.000004

127
Q

To multiply a decimal and a big number….

4,000,000 * 0.0003 =

A

Move the decimal to the right in the small number and to the left in the large number.

4,000,000 * 0.0003 =

400 x 3 = 120

128
Q

To divide two decimals…

300 / 0.05

A

move points in the SAME direction until you kill the decimals.

300 / 0.05 =

30,000 / 5 =

6,000

129
Q

When the GMAT says “what percent of”, you should…

What percent of 200 is 60?

A

Turn “what percent” into x/100, then multiply.

x/100 * 200 = 60

130
Q

To find percent change…

If the price increases from $200 to $230, what perecent does it change?

A

divide the change in value by the original value.

$30/$200 = 15%

131
Q

To find the new value after a percent change has been applied…

The $60 purse was marked up by 25%

A

Find the new percent (100% + 25%), convert to a fraction (5/4) and multiply by the original value.

(5/4) * $60 = $75

132
Q

To find the percent more/less than..

$200 is what percent more than $150?

A

Divide the change in value by the original value.

$50/$200 = 25%

133
Q

When you have successive percent changes…

What is 120% of 150% of 30?

A

multiply the origianl value by the new percents for both percent changes.

(using fractions might allow you to cancel)

6/5 * 3/2 * 30 = 54

134
Q

If you have a ratio, write it out as ________ to compute the whole.

For every 2 girls in the class there are 3 boys.

A

Part : Part : Whole

2 girls : 3 boys : 7 students

135
Q

How are expressions and equations different?

A

Expressions don’t have equal signs.

136
Q

4 ways to simplify expressions.

A

Combine like terms. 3x + 4x -> 7x

Find a common denominator and then combine. 3/5 + 4/10 ->10/10

Pull out a common factor. x + xy -> x(1+y)

Cancel common factors. 3x2 / 6x -> x/2

Simplifying the expression NEVER changes its value.

137
Q

What is the order of operations?

A

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

138
Q

What are two things you can do to one side of the equation but not the other?

A

Simplify the expression on one side OR

Evaluate the expression on one side.

You may NEVER change one expression without changing the other.

139
Q

When changing one side of an equation by multiplying, dividing, squaring or taking the square root, you must….

x + 4 = x/2

A

Put parenthesis on the other side of the equation to perform the same action to the ENTIRE other side.

x + 4 = x/2

2(x+4) = (x/2)2

2x + 8 = x

140
Q

When you take the square root of an equation…

x2 = 49

sqr[x2] = sqr[49]

A

the equation usually splits into two separate equations.

x = 7 OR x = -7

141
Q

What is x in terms of y?

7x + 4 = y

A

Means create and equation where x = something containing only y’s.

7x + 4 = y

-4 to both sides

divide by 7 both sides

x = (y-4) / 7

142
Q

To isoloate a variable deep inside an expression…

2y3 - 3 = 51

A

follow PEMDAS in reverse to undo the expression.

2y3 - 3 = 51

+3 to both sides

divide by 2 both sides

take the cubed root to both sides

143
Q

What is the first thing you should in an equation like this?

(5x - 3) / 2x = 10

A

Get rid of the denominator. Always get vartiables out of the denominators.

(5x - 3) / 2x = 10

mulitply by 2x both sides first!

144
Q

When you have variables in the exponents…

3x = 274

A

Rewrite the terms so that they have the same base, usually by breaking the bases into primes.

3x = 274

3x = (33)4

3x = 312

x = 12

145
Q

When you have variables in the exponents, there are three bases you cannot set the exponents the same for to solve.

A

1, 0, -1

146
Q

What are the two strategies to solve a system of equations?

A

Isolate, then Subsitute OR

Combine Equations

147
Q

How to do you Isolate, then Substitute to solve a system of equations. (aka subsitution)

2x - 3y = 16

y - x = -7

A

First isolate the variable you don’t ultimately want. If the problem asks for x, isolate y. Isolate the variable in the equaition that’s easier to deal with.

y - x = -7, add x to both sides y = x -7

No replace y in the second equation with (x-7).

2x - 3(x-7) = 16 and solve for x.

If you need to solve for y two, use the new value of x in the equation you created to isolate y.

148
Q

How do you kill an equation and an unknown (aka combination)?

A

If adding or subtracting the equations together will kill off a variable, it may be faster than subsitution.

You may also multiply or divide the ONE ENTIRE equation to setup an expression that can be combined to eliminate a variable.

149
Q

If the system of equations have three or more unknowns…

a + b - c = 12 and c - b = 8

What is the value of c in terms of a & b?

A

Isolate whatever the question asks for, and use subsitution to eliminate unwanted variables.

150
Q

What is a quadratic expression?

A

A quadratic express contains a squared variable and no higher power, such as…

z2

y2 + y - 6

x2 + 8x +16

151
Q

When dealing with quadratic equations, what is the factored form and what is the distributed form?

A

The factored form is

(x+2)(x+3) =

The distrubted form is

x2 + 5x + 6 =

152
Q

When factoring a quadratic expression, the two factors must _____ to the x coefficient and they must ____ to the constant.

A

Factors must ADD to the x coefficient and they must MULTIPLY to the constant.

153
Q

in a quadratic expression, if the constant is positive, the two numbers in the factored form must be…

z2 + 7z + 12 =

x2 - 9x +18 =

A

both positive or both negative, depending on the sign of the x term.

z2 + 7z + 12 = (z+3)(z+4)

x2 - 9x +18 = (x-3)(x-6)

154
Q

In a quadratic expression if the constant is negative, the factored numbers must be..

w2 + 3w - 10 =

A

One number is positive and the other one is negative.

155
Q

In a quadratic expression if the constant is negative, how do you find the factor pair?

w2 + 3w - 10 =

A

First find the factor pairs of your constant that differ by the coefficent. (5 & 2).

Then make one of the factors negative so they add to the correct coefficent. (5 + -2, NOT -5 + 2)

Now keep the signs when you place the pair.

w2 + 3w - 10 = (w + 5)(w - 2)

156
Q

How do you factor this?

3x2 + 21x + 36 =

A

The express is multiplied through by a common numerical factor. Pull out the common factor FIRST and then calculate normally.

3x2 + 21x + 36 = 3(x2 + 7x + 12) = 3(x+3)(x+4)

157
Q

How do you deal with a negative x2 term?

-x2 + 9x + 18 =

A

Pull out the -1, which becomes a minus side outside the parentheses.

  • x2 + 9x + 18 =
  • (x2 - 9x + 18) =
  • (x-3)(x-6)
158
Q

How do you solve a quadratic expression?

A

Rearrange the equpation to make one side euqal to 0.

x2 + x = 6 —-> x2 + x + 6 = 0

Factor the quadratic expression.

(x+3)(x-2) = 0

Set each factor equal to 0.

x + 3 = 0 -> x = -3

x - 2 = 0 -> x = 2

Th esolution is called its roots. Only one is true at the same time.

159
Q

How do you solve a quadratic equation with squared parentheses?

(y + 1)2 = 16

A

Either treat (y+1) as a new variable like z. OR

Take the postiive and negative square roots of 16 right away. OR

FOIL (y+1)(y+1) to create a normal quadratic equation.

160
Q

How to solve a higher power quadratic formula.

x3 = x

A

Solve like a normal quadratic: set the equation to zero, factor, and set factors equal to zero. Never divide by x unless you know x does not equal 0. X to the third power usually means three solutions.

x3 = x

x3 - x = 0

x(x2-1) = 0

x(x+1)(x-1) = 0

x = 0, -1, or 1

161
Q

If you see a quadratic expression in the numerator or denominator, try…

(x2 - 2x - 3) / x +1 =

A

Try factoring the quadratic expression to see if one of the factor pairs can be canceled out.

(x2 - 2x - 3) = (x + 1)(x -3)

cancels out with x+1 on the bottom.

162
Q

If x does not equal y, then (y-x) / (x-y) =

A

The two expressions are identical except for the sign change.

(y-x) = -(x-y)

Expressions that only differ by a sign change are only different by a factor of -1.

If you cancel -(x-y) / (x-y) you are left with -1.

163
Q

What does the factored version of squar of a sum look like?

(x+y)2 =

A

x2 + 2xy + y2

Only one solution will be valid.

164
Q

What is the factored form of square of a difference?

(x - y)2

A

x2 - 2xy + y2

There is only one valid soution.

165
Q

What is the factored form of difference of squares?

(x + y )(x - y) =

A

x2 - y2

The inner and outer temes cancel the coefficent term.

Square each term and subtract the difference.

166
Q

Unlike equations, inequalities have how many solutions?

A

A whole range.

167
Q

The only thing you can do to one side of an inequality and not the other is…

A

simplify. Do NOT change the value.

168
Q

What operations can you perform on a system of inequalities? What should you avoid?

A

Add or subtract from both sides.

Multiply or divide both sides. If you multiply or divide by a negaive number flip the sign.

You shouldn’t divide by a variable unless you know the variables sign.

169
Q

Treat absolute numbers in inequalities as ________.

|4-7| =

A

as parentheses. Solve the equation inside first and then find the absolute value of the result.

170
Q

How do you solve an equation with a variable inside the absolute value signs?

6 x |2x + 4| = 30

A

First isolate the absolute value on one side of the inequality or equation.

6 x |2x + 4| = 30 –> |2x + 4| = 5

Set-up two equations, one negative and the other positive.

2x + 4 = 5 & -(2x + 4) = 5 –> -2x - 4 = 5

Solve both.

Get two possible values.

171
Q

How do you solve an absolute value in an inequality?

|y + 3| < 5

A

Isolate the absolute value on one side.

Setup two inequalities (positive & negative).

|y + 3| < 5 –> -y - 3 < 5 &

+ y + 3 < 5

Isolate the variable and solve both. Remember to flip the sign if you mult/divide by a negative number.

172
Q

If you know the radius of a circle, you can also find…

A

Diameter (2r)

Circumference (πd)

Area (π r2)

You can find the radius from any of these pieces of imformation too.

173
Q

What is the formula for circumference of a circle?

A

πd

~3.14 * diameter

174
Q

What is the forumal for the area of circle?

A

π(r)2

~3.14 * radius2

175
Q

What is a fractional portion of a circle know as?

What is its portion of circumference called?

A

A sector (like a slice of pizza).

Arc length.

176
Q

How do you calculate the sector area?

Central angle = 45

Radius = 5

A

Figure out the faction of the circle that the sector represents.

45/360 = 1/8

1/8π52 = (25/8)π

177
Q

What are the four steps to solve a word problem?

A
  1. What do they want? (write down variable = ?) 2. What do they give me? (note any relationships or specific numbers.) 3. How do I turn this information into equations? (write down the information as an equation). 4. How do I solve the quations for the desired value (use algebra).
178
Q

If you multiply two quantities that each have units…

Area = 6 feet x 9 feet

A

multiply the units too.

= 54 feet2

179
Q

When a problem has multiple units in it…

How many hours are in two days?

A

you can cancel units in the same way numbers and variables do.

2 days * 24/hours / 1 day = 48 hours

the day units cancel each other

180
Q

How do you convert from one unit to another?

How many seconds in 20 minutes?

A

Mulitiply by a conversion factor (fancy form of 1/1 with units on top and whole on the bottom) and cancel.

20 min * (60 sec / 1 min) = 1,200 sec

the minutes cancel each other

181
Q

When express rates as time and distance…

It took Joe 4 hours to go 60 miles.

A

always put the time in the denominator.

60 miles / 4 hours = 15 miles per hour

182
Q

The sum of any two sides of a tringle ______ than the third side.

Any side is _______ than the difference of the other two side lengths.

A

The sum of any two sides is greater than the third side.

Any side is greater than the difference of the other two side lengths.

183
Q

The sum of all three interior angles of a triangle is _______.

A

180 degrees

184
Q

On a triangle, the largest angle will be across from the ________ side.

A

largest angle will be across from the longest side.

like an alligator opening its mouth

185
Q

What is an isoceles triangle?

A

A triangle that has 2 equal angles and 2 equal sides.

186
Q

What is an equilateral triangle?

A

A triangle with 3 equal angles (60) and 3 equal sides.

187
Q

What is the forumula for the area of a triangle?

A

1/2 base * height

any side of the triangle can act as the base, as long as the height is perpendicular to it.

188
Q

What is a right triangle?

A

Any triangle in which one of the angles is a right angle (90 degrees).

189
Q

What is the Pythagorean Theorem?

A

a2 + b2 = c2

For any right triangle where a & b are the legs and c is they hypotenuse.

190
Q

What are the three most common right triangles on the GMAT?

A

3-4-5 (and 6-8-10)

5-12-13 (and 10-24-26)

8-15-17

191
Q

What is a parallelogram?

A

Any 4 sided fiture in which the oppostie sides are parallel and equal. Opposite angles are also equal and the adjacent angles add up to 180 degrees. They can be divided into 2 equal triangles on the diagonal.

192
Q

How do you calculate the perimeter of a parallelogram?

A

Add the lengths of all sides. Since the opposite sides are equal you just need one of the top and side lengths to calculate this.

193
Q

How do you calculate the area of a parallelogram?

A

Base x Height

194
Q

What makes a rectangle?

A

All 4 internal angles are right angles. (It’s a parallelogram with right angles.)

Rectangles may be cut into two right triangles with a diagonal.

195
Q

What are the four steps to solving geometry problem?

A
  1. Redraw the figures, fill in all the given information, indentify the target (make note of any equal sides/angles).
  2. Identify relationships and create equations (the GMAT rarely provides extraneous info).
  3. Solve the equations for the missing value.
  4. Make inferences from the figures.
196
Q

What is the formula for a line in a coordinate plane?

A

y = mx + b

b is the y-intercept (where the line crosses the y-axis)

m = slope of the line

197
Q

How do you calculate the slope of a line?

A

rise / run = change in y / change in x

198
Q

What is the formulate for weighted average?

A

WA = (weight * data point) + (weight * data point) + (weight * data point) …. / Sum of Weights

199
Q

How many arithmetic operations will the right answer require on the GMAT?

A

at least two

200
Q

When answers are spread out (and/or use the word “approximately) you can…

A

Round one number and the other one down to estimate an anwer.

201
Q

How do you figure out the ratio of a weighted average problem?

Solution X at 40% strength and Y at 25% strength are mixed to create a 30% mixture. What is the ratio of the X & Y used?

A

Place 30% in the middle.

X is 10 away from the middle and Y is 5 away from the middle.

Swap the two.

5 X : 10 Y = 1: 2 Ratio

202
Q

How do you find the first number in a string of 5 consecutive integers with a sum of 560?

A

x + (x+1) + (x+2) + (x+3) + (x+4) = 560

5x + 10 = 560

5x = 550

x = 110

203
Q

Is 5! divisible by 5?

A

Yes!

5 * 4 * 3 * 2 *1

204
Q

What is the forumla for the sum of interior angles for any polygon?

A

(n-2) * 180

Pentagon = 540

Hexagon = 720

205
Q

What is the formula for the area of a trapezoid?

A

[(Base1 + Base2) * Height] / 2

206
Q

What is the formula for the area of a Rhombus?

A

(Diagonal 1 + Diagonal 2) / 2

207
Q

What is the formula for the length of the legs on an isoceles triangle?

A

45 - 45 - 90 Triangle

45 = x leg

45 = x leg

90 = x * sqr[2]

208
Q

What is the formula for the lengths of legs on an equilateral triangle?

A

30 - 60 - 90 Triangle

30 (short) = x

60 (long) = x*sqr[3]

90 (hyponteneuse) = 2x

209
Q

What is the formula for the diagonal of a square?

A

d = s*sqr[2]

s = side of square

210
Q

What is the formula for the diagonal of a cube?

A

d = s * sqr[3]

s = side of cube

211
Q

What is the formula for the diagonal of a rectangle?

A

h2 + w2 + l2 = d2

212
Q

How do you calculate a central angle from the inscribed angle?

inscribed angle = 45 degrees

A

Double it.

45 x 2 = 90 degree central angle

213
Q

What is the formula for surface area of a cylinder?

A

SA = 2(π * r2) + 2π*rh

214
Q

What is the formula for the volume of a cylinder?

A

V = π*r2h

215
Q

On a coordinate plane, how do you find the distance between two points?

A

Draw a right triangle with the points on the hyponteneuse.

Find the length of the legs by calculating rise over run.

Use the pythagorean theorem.

216
Q

When a triangle is inscribed in a circle and one side of the triangle is the diameter it must be…

A

a right triangle.

217
Q

How do you know if a number is divisible by 4?

A

If it’s divisible by 2 twice OR the last two digits are divisible by 4.

218
Q

How do you know if a number is divisible by 6?

A

If it is divisible by 2 and 3.

219
Q

How do you know if a number is divisible by 8?

A

If it is divisible by 2 three times or the last 3 digits are divisible by 8.

220
Q

How do you know if a number is divisible by 9?

A

If the sume of the integer’s digits are divisible by 9.

221
Q

What is GCF?

A

The greatest common factor. The largest divsor of 2+ integers.

If no primes in common, the GCF = 1.

222
Q

Even +/- Odd =

A

Odd

223
Q

Odd +/- Odd =

A

Even

224
Q

In multiplication, how do you know if the result will be even or odd?

A

If any integer is even = even.

If all integers are odd = odd.

225
Q

If you multiply 3 even integers, the product is divisible by ?

A

2, 4, 8

226
Q

Even / Even will be …

A

Even (12/6)

Odd (12/4)

Non-integer (12/8)

227
Q

Odd / Even will be…

A

Even (12/3)

Non Integer (12/5)

228
Q

Odd / Even will be…

A

Non integer (9/6)

229
Q

Odd / Odd will be..

A

Odd (15/5)

Non Integer (15/25)

230
Q

The algebraic representation for odds and evens is…

A

Evens = 2n

Odds = 2n + 1 or 2n - 1

231
Q

An exterior angle of a triange is equal to:

A

the sum of the two non-adjacent (opposite) interior angles of the triangle.

232
Q

To divide 12.42 by 0.3

A

Move the decimal in the same direction until the divsor is a whole number.

124.2 / 3

233
Q

To raise a decimal to a power of 4 or higher:

(0.5)4 =

A

Rewrite the decimal as the product of an integer and a power of 10: 0.5 = 5 x 10-1

Apply the exponent to each part: (5 x 10-1)4 = 54 x 10-4

Compute the first part and combine: 54 = 252 = 625

625 x 10-4 = 0.0625

Use the same method for roots of decimals (raise them a fractional power).

234
Q

How many decimal points?

(0.04)3 =

A

Multiply the existing number of declimal points by the exponent.

2 places x 3 = 6 places

0.000064

235
Q

How many decimal points?

cube root (0.000000008)

A

DIVIDE the number of existing decimals points by root.

9 places / 3 = 3 places

0.002

236
Q

When dealing with a ration equation. How do you simplify and solve?

4 girls / 7 boys = x girls / 35 boys

A

You can simplify vertically or horizontall but never diagonally across the equal sign.

4 girls / 1 boy = x girls / 5 boys

cross multiply

4 girls * 5 boys = x

20 girls = x

GMAT (2 decks)

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