Key GMAT Arithmetic
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| Define: Prime Numbers | A integer that is only divisible by itself and 1.
Neither 0 nor 1 is prime numbers.
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| Define: Divisor/Factor | A POSITIVE integer that can divide into another integer.
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| Define: Multiple | ANY integer (negative or positive) can divide into another integer with no remainder.
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| Define: Integer | ANY (positive or negative) “whole” number i.e. not a fraction or decimal.
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| 2x2= | 4
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| 2x3= | 6
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| 2x4= | 8
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| 2x5= | 10
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| 2x6= | 12
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| 2x7= | 14
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| 2x8= | 16
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| 2x9= | 18
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| 2x10= | 20
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| 2x11= | 22
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| 2x12= | 24
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| 2x13= | 26
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| 2x14= | 28
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| 2x15= | 30
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| 3x2= | 6
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| 3x3= | 9
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| 3x4= | 12
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| 3x5= | 15
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| 3x6= | 18
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| 3x7= | 21
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| 3x8= | 24
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| 3x9= | 27
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| 3x10= | 30
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| 3x11= | 33
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| 3x12= | 36
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| 3x13= | 39
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| 3x14= | 42
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| 3x15= | 45
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| 4x2= | 8
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| 4x3= | 12
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| 4x4= | 16
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| 4x5= | 20
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| 4x6= | 24
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| 4x7= | 28
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| 4x8= | 32
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| 4x9= | 36
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| 4x10= | 40
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| 4x11= | 44
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| 4x12= | 48
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| 4x13= | 52
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| 4x14= | 56
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| 4x15= | 60
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| 5x2= | 10
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| 5x3= | 15
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| 5x4= | 20
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| 5x5= | 25
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| 5x6= | 30
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| 5x7= | 35
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| 5x8= | 40
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| 5x9= | 45
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| 5x10= | 50
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| 5x11= | 55
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| 5x12= | 60
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| 5x13= | 65
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| 5x14= | 70
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| 5x15= | 75
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| 6x2= | 12
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| 6x3= | 18
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| 6x4= | 24
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| 6x5= | 30
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| 6x6= | 36
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| 6x7= | 42
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| 6x8= | 48
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| 6x9= | 54
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| 6x10= | 60
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| 6x11= | 66
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| 6x12= | 72
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| 6x13= | 78
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| 6x14= | 84
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| 6x15= | 90
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| 7x2= | 14
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| 7x3= | 21
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| 7x4= | 28
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| 7x5= | 35
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| 7x6= | 42
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| 7x7= | 49
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| 7x8= | 56
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| 7x9= | 63
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| 7x10= | 70
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| 7x11= | 77
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| 7x12= | 84
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| 7x13= | 91
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| 7x14= | 98
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| 7x15= | 105
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| 8x3= | 24
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| 8x4= | 32
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| 8x5= | 40
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| 8x6= | 48
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| 8x7= | 56
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| 8x8= | 64
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| 8x9= | 72
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| 8x10= | 80
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| 8x11= | 88
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| 8x12= | 96
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| 8x13= | 104
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| 8x14= | 112
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| 8x15= | 120
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| 9x3= | 27
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| 9x4= | 36
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| 9x5= | 45
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| 9x6= | 54
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| 9x7= | 63
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| 9x8= | 72
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| 9x9= | 81
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| 9x10= | 90
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| 9x11= | 99
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| 9x12= | 108
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| 9x13= | 117
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| 9x14= | 126
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| 9x15= | 135
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| 11x11= | 121
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| 11x12= | 132
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| 11x13= | 143
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| 11x14= | 154
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| 11x15= | 165
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| 12x2= | 24
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| 12x3= | 36
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| 12x4= | 48
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| 12x5= | 60
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| 12x6= | 72
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| 12x7= | 84
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| 12x8= | 96
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| 12x9= | 108
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| 12x10= | 120
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| 12x11= | 132
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| 12x12= | 144
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| 12x13= | 156
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| 12x14= | 168
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| 12x15= | 180
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| 13x2= | 26
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| 13x3= | 39
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| 13x4= | 52
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| 13x5= | 65
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| 13x6= | 78
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| 13x7= | 91
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| 13x8= | 104
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| 13x9= | 117
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| 13x10= | 130
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| 13x11= | 143
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| 13x12= | 156
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| 13x13= | 169
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| 13x14= | 182
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| 13x15= | 195
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| 14x2= | 28
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| 14x3= | 42
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| 14x4= | 56
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| 14x5= | 70
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| 14x6= | 84
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| 14x7= | 98
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| 14x8= | 112
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| 14x9= | 126
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| 14x10= | 140
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| 14x11= | 154
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| 14x12= | 168
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| 14x13= | 182
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| 14x14= | 196
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| 14x15= | 210
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| 15x2= | 30
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| 15x3= | 45
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| 15x4= | 60
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| 15x5= | 75
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| 15x6= | 90
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| 15x7= | 105
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| 15x8= | 120
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| 15x9= | 135
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| 15x10= | 150
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| 15x11= | 165
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| 15x12= | 180
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| 15x13= | 195
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| 15x14= | 210
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| 15x15= | 225
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| Divisibility rule of 2 | If the number's last digit is even.
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| Divisibility rule of 3 | If the sum of the digits is divisible by 3.
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| Divisibility rule of 4 | If the last two digits are divisible by 4.
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| Divisibility rule of 5 | If the number ends in 0 or 5.
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| Divisibility rule of 6 | If the number is even and the sum of the digits is divisible by 3.
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| Divisibility rule of 8 | If the number is even when divided by 2 twice.
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| Divisibility rule of 9 | If the sum of the digits is divisible by 9.
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| Divisibility rule of 10 | If the number ends in 0.
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| Divisibility rule of 25 | If the last two digits are divisible by 25 or are 00.
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| Divisibility rule of 11 | If (sum of the odd digits) minus (sum of even digits) is divisible by 11
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| Divisibility rule of 12 | If divisibility rule 3 and 4 are true:
-If the sum of the digits is divisible by 3.
and
-If the last two digits are divisible by 4.
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| ______?_______ ? | ___numerator___
denominator
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| 1/2 = | 0.5
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| 1/3 = | 0.333....
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| 1/4 = | 0.25
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| 1/5 = | 0.20
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| 1/6 = | .1667
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| 1/7 = | 0.143
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| 1/8 = | .125
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| 1/9 = | .1111
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| Define: Least Common Multiple | The smallest non-zero number that two or more numbers are a multiple of.
Procedure: Factor each number and multiple the highest exponent example of each factor against one another.
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| Define: Greatest Common Factor | The largest number that divides into each of a given set of numbers.
Procedure: Factor each number and multiple the factors they have in common against one another.
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| Odd +/- Odd = | Even
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| Odd +/- Even = | Odd
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| Even +/- Even = | Even
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| Odd x Odd = | Odd
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| Odd x Even = | Even
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| Even x Even = | Even
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| Positive + Positive = | Positive
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| Positive + Negative = | Positive or Negative
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| Negative - Negative = | Negative
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| Positive x Positive = | Positive
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| Positive x Negative = | Negative
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| Negative x Negative = | Positive
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| -1^2= | 1
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| 0^2= | 0
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| 1^2= | 1
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| 2^2= | 4
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| 2^3= | 8
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| 2^4= | 16
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| 2^5= | 32
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| 2^6= | 64
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| 3^2= | 9
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| 3^3= | 27
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| 3^4= | 81
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| 4^2= | 16
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| 4^3= | 64
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| 4^4= | 256
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| 5^2= | 25
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| 5^3= | 125
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| 5^4= | 625
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| 6^2= | 36
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| 7^2= | 49
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| 8^2= | 64
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| 9^2= | 91
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| 10^2= | 100
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| 11^2= | 121
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| 12^2= | 144
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| 13^2= | 169
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| 14^2= | 196
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| 15^2= | 225
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| 20^2= | 400
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| 25^2= | 625
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| Define: Units Digit | The last digit in a number.
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| Is zero even or odd? | Even
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| How many decimal places will this problem result in? .00678 x 3.42 = | 7 decimal places
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| How many decimal places will this problem result in? .0022 / .003 = | 1 decimal places
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| What is the only even prime number? | 2
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| Are 0 and 1 prime numbers? | No
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