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GMAT > Quant > Flashcards

Quant Flashcards

1
Q

(x + y)2 =

A

x2 + y2 + 2xy

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2
Q

(x - y)2 =

A

x2 + y2 - 2xy

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3
Q

(x + y)(x - y) =

A

x2 - y2

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4
Q

(x - y)

/

(y - x) = ?

and x =/ y

A

-1

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5
Q

List the prime numbers under 100:

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

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6
Q

LCM (x,y) * GCF (x,y) =

LCM = Least Common Multiple

GCF = Greatest Common Factor

A

LCM (x,y) * GCF (x,y) = xy

LCM (x,y) = xy / GCF (x,y)

GCF (x,y) = xy / LCM (x,y)

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7
Q

How to tell if a number is divisible by 4:

A

If the last 2 digits are divisible by 4

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8
Q

How to tell if a number is divisible by 6:

A

If the number’s digits add up to 3, AND it’s an even number

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9
Q

How to tell if a number is divisible by 8:

A

If the last 3 digits are divisible by 8 (has to be even)

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10
Q

How to tell if a number is divisible by 9:

A

If the sum of the number’s digits is divisible by 9

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11
Q

How to tell if a number is divisible by 11:

A

If the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is divisible by 11

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12
Q

How to tell if a number is divisible by 12:

A

If it’s divisible by both 3 and 4

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13
Q

Formula for division

x/y =

A

x/y = Quotient + remainder/y

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14
Q

Prime numbers from 10 to 19:

A

11, 13, 17, 19

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15
Q

0! =

A

0! = 1

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16
Q

3! =

A

6

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17
Q

4! =

A

24

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18
Q

5! =

A

120

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19
Q

6! =

A

720

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20
Q

7! =

A

5,040

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21
Q

8! =

A

40,320

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22
Q

9! =

A

362,880

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23
Q

10! =

A

3,628,800

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24
Q

In decimals, 1/6 =

A

0.166666

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25
Q

In decimals, 1/7 =

A

0.142857 142857 etc.

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26
Q

In decimals, 1/8 =

A

0.125

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27
Q

In decimals, 1/9 =

A

0.11111111 etc.

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28
Q

In decimals, 1/11 =

A

0.0909090909 etc.

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29
Q

Prime numbers from 0 to 10:

A

2, 3, 5, 7

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30
Q

Prime numbers from 20 to 29:

A

23, 29

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31
Q

Prime numbers from 30 to 39:

A

31, 37

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32
Q

Prime numbers from 40 to 49:

A

41, 43, 47

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33
Q

Prime numbers from 50 to 59:

A

53, 59

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34
Q

Prime numbers from 60 to 69:

A

61, 67

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35
Q

Prime numbers from 70 to 79:

A

71, 73, 79

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36
Q

Prime numbers from 80 to 89:

A

83, 89

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37
Q

Prime numbers from 90 to 99:

A

97

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38
Q

Square root of 2?

A

1.41

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39
Q

Square root of 3?

A

1.73

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40
Q

Square root of 5?

A

2.24

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41
Q

Square root of 6?

A

2.45

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42
Q

Square root of 7?

A

2.65

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43
Q

Square root of 8?

A

2.83

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44
Q

Square root of 10?

A

3.16

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45
Q

14 times 14 =

A

196

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46
Q

15 times 15 =

A

225

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47
Q

16 times 16 =

A

256

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48
Q

17 times 17 =

A

289

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49
Q

18 times 18 =

A

324

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50
Q

19 times 19 =

A

361

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51
Q

3^4 =

A

81

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52
Q

3^5 =

A

243

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53
Q

3^6 =

A

729

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54
Q

5^4 =

A

625

55
Q

6^3 =

A

216

56
Q

6^4 =

A

1296

57
Q

7^3 =

A

343

58
Q

7^4 =

A

2401

59
Q

8^3 =

A

512

60
Q

9^3 =

A

729

61
Q

If |x + y| = |x| + |y| then…

A

x and y must have the same sign (positive or negative)

62
Q

Why do you have to be careful about multiplying both sides of an inequality by an unknown variable?

A

If it is negative, the inequality sign will have to be reversed.

63
Q

Which sign does this phrase translate to:

“up to”

A

<= (less than or equal to)

64
Q

Which sign does this phrase translate to:

“at least”

A

>= (greater than or equal to)

65
Q

Which sign does this phrase translate to:

“no more”

A

<= (less than or equal to)

66
Q

Which sign does this phrase translate to:

“at most”

A

<= (less than or equal to)

67
Q

Which sign does this phrase translate to:

“as few as”

A

>= (greater than or equal to)

68
Q

Formula for calculating number of positive integers that will divide evenly into a number?

A

N = (e1 + 1)(e2 + 1)(e3 + 1)

e1 is the exponent of first prime number etc

69
Q

Any product of three consecutive integers is divisible by…

A

3! = 6

70
Q

If a 2 digit integer x has a tens digit of a and a units digit of b, then the formula for x in the terms of a and b is x = :

A

x = 10a + b

71
Q

Formula for the sum of consecutive numbers:

A

(n/2) * (first number + last number)

72
Q

Surface Area of a cube formula:

A

Surface Area = 2(Length * Width) + 2(Length * Height) + 2(Height * Width)

73
Q

13 * 3 =

A

39

74
Q

13 * 4 =

A

52

75
Q

13 * 5 =

A

65

76
Q

13 * 6 =

A

78

77
Q

13 * 7 =

A

91

78
Q

13 * 8 =

A

104

79
Q

13 * 9 =

A

117

80
Q

13 * 11 =

A

143

81
Q

13 * 12 =

A

156

82
Q

13 * 14 =

A

182

83
Q

13 * 15 =

A

195

84
Q

14 * 6 =

A

84

85
Q

14 * 7 =

A

98

86
Q

14 * 8 =

A

112

87
Q

14 * 9 =

A

126

88
Q

14 * 11 =

A

154

89
Q

14 * 12 =

A

168

90
Q

16 * 7 =

A

112

91
Q

Units digit pattern for exponents of numbers ending in 2:

A

2, 4, 8, 6 repeated

  1. 2
  2. 4
  3. 8
  4. 6
  5. 2
  6. 4

etc

92
Q

Units digit pattern for exponents of numbers ending in 3:

A

3, 9, 7, 1 repeated

93
Q

List the perfect squares up to 225:

A

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.

94
Q

List the perfect cubes up to 1000:

A

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

95
Q

Permutation formula?

A

nPk = n! / (n−k)!

or

Box and fill method (just multiply the boxes)

96
Q

Formula for the area of an equilateral triangle:

A

area = (a² * √3)/ 4

97
Q

Area of a trapezoid?

A

Area = ((base1 + base 2) * height) / 2

98
Q

The sum of the interior angles of a polygon =

A

(n - 2) * 180

where n = the number of sides of a polygon

So triangle = 180

rectangle = 360

pentagon = 540

etc.

99
Q

The measure of any one interior angle in a regular polygon =

A

180 * (n - 2)

/

n

where n is the number of sides of the polygon

100
Q

The interior angles of a hexagon sum to:

A

720 degrees

101
Q

One interior angle of a regular hexagon measures:

A

120 degrees

102
Q

The area of a regular hexagon =

A

(3√3 * s2)

/

2

or 2.6s2

103
Q

The exterior angles of any polygon sum to:

A

360 degrees

104
Q

Three-part circle ratio:

A

central angle / 360

=

arc length / circumfrence

=

area of sector / area of circle

105
Q

Extended Pythagoras Theorem:

(for finding diagonals in 3D shapes, e.g. a room)

A

a2 = b2 + c2 + d2

106
Q

A central angle (of a circle) is always ____ the inscribed angle

A

A central angle (of a circle) is always twice the inscribed angle

107
Q

The slopes of two perpendicular lines are negative reciprocals and therefore multiply to:

A

The slopes of two perpendicular lines are negative reciprocals and therefore multiply to -1.

108
Q

When point (3, 2) is reflected over line y = x, it becomes:

A

(2, 3)

(x, y) becomes (y, x)

109
Q

When point (x, y) is reflected over line y = -x, it becomes:

A

(-y, -x)

110
Q

When point (x, y) is reflected over line y = b, it becomes:

A

(x, 2b - y)

E.g. (5, -2) becomes (5, 4) when it’s reflected over the line y = 1

111
Q

When point (x, y) is reflected over line x = a, it becomes:

A

(2a - x, y)

E.g. when reflected over line x = 2, (5, -2) becomes (-1,-2)

112
Q

When (x, y) is reflected over some point (a, b), it becomes:

A

(2a - x, 2b - y)

E.g. when reflected over point (2, 1), (5, -2) becomes (-1, 4).

113
Q

Distance between two points =

A

Distance between two points =

[(x2 - x1)2 + (y2 - y1)2 ] 0.5

114
Q

Midpoint of a line segment =

A

( (x1 + x2) / 2 , (y1 + y2) / 2 )

115
Q

The 2 major concerns fo the domain of a function are:

A

1) we can’t take the square root of a negative number
2) we aren’t allowed to divide by zero

116
Q

What is the vertical line test?

A

If a graph is the graph of a function, then any vertical line drawn can only intersect the graph at exactly one point or at no points.

117
Q

Arithmetic sequence formula:

A

an = a1 + (n - 1)d

d = is the common difference

118
Q

The sum of the first n terms of an arithmetic sequence is:

A

Sn = (n/2) * (a1 + an)

119
Q

Geometric sequence formula:

A

an = a1 * rn-1

r = the common ratio

120
Q

Addition rule for Mutually Exclusive Events:

P(A or B) =

A

P(A or B) = P(A) + P(B)

121
Q

Addition Rule for Events That Are Not Mutually Exclusive

P(A or B) =

A

P(A or B) = P(A) + P(B) - P(A and B)

122
Q

2n + 2n =

A

2n + 2n = 2n+1

123
Q

3n + 3n + 3n =

A

3n + 3n + 3n = 3n+1

124
Q

4n + 4n + 4n + 4n =

A

4n + 4n + 4n + 4n = 4n+1

125
Q

When |a + b| = |a| + |b|, this means:

A

One or both quantities are 0; or

Both quantities (a and b) have the same sign

126
Q

When |a - b| = |a| - |b|, this means:

A

b is zero; or

Both quantities have the same sign and the absolute value of |a - b| is greater than or equal to the absolute value of |a| - |b|

127
Q

Profit Equation:

Profit =

A

Profit = Total Revenue - (Total Fixed Costs + Total Variable Costs)

128
Q

a is what percent of b?

Formula:

A

(a/b) * 100

129
Q

“x is n percent less than y”

Formula:

A

x = [(100 - n) / 100] * y

130
Q

(A or B) =

Overlapping Sets:

Number of Members in Either Set

A

(A or B) = #(A) + #(B) - #(A and B)

131
Q

Overlapping Sets

When the number of unique items is known

Total # of unique members =

A

[A only + B only + C only] +

Total # of unique members =

+ #[Neither A nor B nor C]

132
Q

Overlapping Sets

When the number of unique items is Unknown

Total # of unique members =

A

Total # of unique elements =

in (Group A) + # in (Group B) + # in (Group C) -

in (Groups of exactly two) -

2[# in (group of exactly three)] +

in (Neither)

133
Q

Number of ways to arrange a set of items in a circle:

A

(k - 1)!

k = number of objects to be arranged in circle

GMAT (2 decks)

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