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GMAT Math > Properties of Numbers > Flashcards

Properties of Numbers Flashcards

1
Q

.167

A

1/6

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2
Q

.143

A

1/7

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3
Q

.125

A

1/8

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4
Q

.111

A

1/9

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5
Q

.083

A

1/12

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5
Q

.0909

A

1/11

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6
Q

.286

A

2/7

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7
Q

.429

A

3/7

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8
Q

.571

A

4/7

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9
Q

.714

A

5/7

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10
Q

.857

A

6/7

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11
Q

.875

A

7/8

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11
Q

.375

A

3/8

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12
Q

.222

A

2/9

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13
Q

2n= odd or even?

A

even

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14
Q

odd - even

A

odd

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15
Q

even + odd

A

odd

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16
Q

even - odd

A

odd

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17
Q

odd + odd

A

even

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18
Q

even + even

A

even

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19
Q

odd-odd

A

even

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20
Q

Product of even and any integer

A

Even

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21
Q

Product of two odd numbers

A

Odd

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22
Q

Even divided by even

A

Even or odd

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23
Q

Even divided by odd

A

Even

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24
Q

Odd divided by odd

A

Odd

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25
Q

sqrt(2)

A

1.4

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26
Q

sqrt(3)

A

1.7

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27
Q

sqrt(5)

A

2.2

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28
Q

sqrt(6)

A

2.4

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29
Q

sqrt(7)

A

2.6

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30
Q

sqrt(8)

A

2.9

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31
Q

2^6

A

64

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32
Q

13^2

A

169

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33
Q

16^2

A

256

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34
Q

14^2

A

196

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35
Q

15^2

A

225

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36
Q

18^2

A

324

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37
Q

17^2

A

289

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38
Q

3^5

A

243

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39
Q

6^3

A

216

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40
Q

ax^2+bx+c=0 has 2 solutions. What is the sum of the solutions

A

-b/a

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41
Q

ax^2+bx+c=0 has 2 solutions. What is the product of the solutions?

A

c/a

42
Q

divisibility of 4

A

If last 2 digits are divisible by 4; can be 00 too ex: 100, 244

43
Q

divisibility of 6

A

divisible by 3 and 2

44
Q

divisibility by 8

A

If # is even, last 3 digits must be divisible by 8; can be 1000, 160, etc

45
Q

divisibility by 9

A

If sum of all digits is divisible by 9

46
Q

divisibility by 12

A

if divisible by 3 and 4

47
Q

divisibility by 11

A

If the sum of the odd numbered digits minus the sum of even numbered digits is divisble by 11; ex: 2915 because (9+5)-(2+1)=11

48
Q

Equation to find Sum of the first n terms of an arithmetic sequence

A

Sn = n/2 ( a1 + an)

49
Q

Arithmetic Sequence Equation

A

an = a1 + (n-1) * d

50
Q

Geometric Sequence

A

an = a1 * r^(n-1)

51
Q

Reflection over x-axis

A

(x, y) -> (x, -y)

52
Q

Reflection over y-axis

A

(x, y) -> (-x, y)

53
Q

Reflection over origin

A

(x, y) -> (-x, -y)

54
Q

Reflection over y = x

A

(x, y) -> (y, x)

55
Q

Reflection over y = - x

A

(x, y) -> (-y, -x)

56
Q

Reflection over y = b

A

(x, y) -> (x, 2b-y)

57
Q

Reflection over x = a

A

(x, y) -> (2a-x, y)

58
Q

Absolute value of the sum of two numbers will ALWAYS be (less than or equal to/greater than or equal to) the sum of the absolute values of the 2 numbers

A

Absolute value of the sum of two numbers will ALWAYS be LESS THAN OR EQUAL TO the sum of the absolute values of the 2 numbers

59
Q

What can we say when |a + b| = |a| + |b|

A

Either
1. One or both quantities are zero
2. Both quantities are of the same sign

(If question says a and b are non-zero then that implies both quantities have same sign)

60
Q

What can we say when |a| = |b|

A

Either
1. The expressions within the absolute values are equal
2. The expressions within the absolute values are opposite

61
Q

Absolute value of the subtraction of two numbers will ALWAYS be (less than or equal to/greater than or equal to) the subtraction of the absolute values of the 2 numbers

A

Absolute value of the subtraction of two numbers will ALWAYS be GREATER THAN OR EQUAL TO the subtraction of the absolute values of the 2 numbers

62
Q

What can we say when |a - b| = |a| - |b|

A

Either
1. One or both quantities are zero
2. Both quantities are of same sign

63
Q

Minimum value of a quadratic function

A

If a>0 then minimum occurs at x = -b/2a

64
Q

Maximum value of a quadratic function

A

If a<0, then maximum occurs at x=-b/2a

65
Q

b^2-4ac < 0

A

Zero roots

66
Q

b^2-4ac = 0

A

One Root

67
Q

b^2-4ac > 0

A

Two Roots

68
Q

If a quadratic equation has exactly 2 solutions then:

A

The sum of the two solutions = ( - b) / a

The product of the two solutions = (c) / a

69
Q

How many solutions does a system of linear equations have if the equations are identical

A

Infinitely many; you can cancel them and say 0=0

70
Q

How many solutions does a system of linear equations have if system is equivalent to equation 0 = k where k is nonzero

A

Zero solutions.

71
Q

How many solutions does a system of linear equations have if we can solve the system

A

Exactly one solution

72
Q

3^3

A

27

73
Q

3^4

A

81

74
Q

3^5

A

243

75
Q

2^7

A

128

76
Q

4^3

A

64

77
Q

4^4

A

256

78
Q

5^3

A

125

79
Q

5^4

A

625

80
Q

6^3

A

216

81
Q

6^4

A

1296

82
Q

7^3

A

343

83
Q

7^4

A

2401

84
Q

8^3

A

512

85
Q

8^4

A

4096

86
Q

9^3

A

729

87
Q

Surface area of a box

A

2(l * w) + 2(l * h) + 2(w * h)

88
Q

Surface area of a cube

A

6 * (edge)^2

89
Q

1 meter = x cm

A

1 m = 100 cm

90
Q

Volume of a box

A

l * w * h

91
Q

Prime Numbers to 100

A

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

92
Q

If T distinct people are arranged such that g are next to each other, what is the total possible arrangements?

A

Total Possible Arrangements = (T - g + 1)! * g!

93
Q

X is what % less than y?

A

( x - y ) / y * 100%

94
Q

Distance between 2 points

A

sqrt[ delta(x)^2 + delta(y)^2 ]

95
Q

(x+y)^3

A

x^3 + y^3 +3x^2y + 3xy^2

96
Q

(x-y)^3

A

x^3 - y^3 - 3x^2y + 3xy^2

97
Q

|x-a|<b

A

a is the center of the segment, b is half of the length of the segment

98
Q

Adding the same positive constant to the numerator and denominator of a proper fraction (increases/decreases) the number?

A

Adding the same positive constant to the numerator and denominator of a proper fraction INCREASES the number

99
Q

Subtracting the same positive constant to the numerator and denominator of a proper fraction (increases/decreases) the number?

A

Subtracting the same positive constant to the numerator and denominator of a proper fraction DECREASES the number?

100
Q

Adding the same positive constant to the numerator and denominator of an improper fraction (increases/decreases) the number?

A

Adding the same positive constant to the numerator and denominator of an improper fraction DECREASES the number

101
Q

Subtracting the same positive constant to the numerator and denominator of an improper fraction (increases/decreases) the number?

A

Subtracting the same positive constant to the numerator and denominator of an improper fraction INCREASES the number as new numerator and denominator are still positive.

102
Q

If the product of two integers is 1

A

Then the two integers are -1, -1 OR 1, 1

103
Q

|px-a| = b

A

Divide everything by p –> |x - a/p | = b/p . Remember a = midpoint b = distance

104
Q

Assuming equal distances (in a rate/time/distance problem), if we have 1 leg (e.g. a->b) avg speed of 10 miles/hr then the average speed for the entire trip cannot be 20 miles/hr or greater.

A

GMAT Math (2 decks)

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