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GMAT > Arithemetic > Flashcards

Arithemetic Flashcards

(63 cards)

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0
Q

Common fraction - decimal conversions

1/3

A

0.333

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1
Q

Greatest common divisor Using Euclid’s algorithm

A

A much more efficient method is the Euclidean algorithm, which uses a division algorithm such as long division in combination with the observation that the gcd of two numbers also divides their difference. Ignore the quotient in each step except to notice when the remainder reaches 0, signalling that we have arrived at the answer.

gfc(a,b)

a -> remainder1 -> remainder2
__ __________ ___________
b a remainder1

GFC=quotient when remainder =0

To compute gcd(48,18), divide 48 by 18 to get a quotient of 2 and a remainder of 12. Then divide 18 by 12 to get a quotient of 1 and a remainder of 6. Then divide 12 by 6 to get a remainder of 0, which means that 6 is the gcd.

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2
Q

Common fraction - decimal conversions

1/5 =

A

0.2

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3
Q

Common fraction - decimal conversions

1/6 =

A

1/2 *1/3 = 0.333/2 = 0.167

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4
Q

Common fraction - decimal conversions

1/8 =

A

1/2 * 1/4 = 0.25/2 = 0.125

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5
Q

Common fraction - decimal conversions

1/9 =

A

1/3 * 1/3 = 0.333/3 = 0.111

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6
Q

Common fraction - decimal conversions

1/7 =

A

0.143

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7
Q

Manipulating fractions

4/9 =

A

4 * 1/9 = 4 * 0.111 = 0.444

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8
Q

Manipulating fractions

7/8 =

A

1 - 1/8 = 1 - 0.125 = 0.875

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9
Q

Multiplying large numbers - trick

Using answers

A

Check answers where units digit agrees

If there is more than 1, use approximation

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10
Q

Multiplication Table

6 x 12

A

72

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11
Q

Multiplication Table

6 x 13

A

78

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12
Q

Multiplication Table

6 x 14

A

84

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13
Q

Multiplication Table

6 x 15

A

90

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14
Q

Multiplication Table

7 x12

A

84

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15
Q

Multiplication Table

7 x13

A

91

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16
Q

Multiplication Table

7 x 14

A

98

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17
Q

Multiplication Table

7 x 15

A

105

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18
Q

Multiplication Table

8 x 12

A

96

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19
Q

Multiplication Table

8 x 13

A

104

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20
Q

Multiplication Table

8 x 14

A

112

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21
Q

Multiplication Table

8 x 15

A

120

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22
Q

Multiplication Table

9 x 12

A

108

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23
Q

Multiplication Table

9 x 13

A

117

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24
Multiplication Table 9 x 14
126
25
Multiplication Table 9 x 15
135
26
Multiplication Table 11 x 11
121
27
Multiplication Table 11 x 12
132
28
Multiplication Table 11 x 13
143
29
Multiplication Table 11 x 14
154
30
Multiplication Table 11 x 15
165
31
Multiplication Table 12 x 12
144
32
Multiplication Table 12 x 13
156
33
Multiplication Table 12 x14
168
34
Multiplication Table 12 x 15
180
35
Multiplication Table 13 x 13
169
36
Multiplication Table 13 x 14
182
37
Multiplication Table 13 x 15
195
38
Multiplication Table 14 x 14
196
39
Multiplication Table 14 x 15
210
40
Multiplication Table 15 x 15
225
41
Prime Numbers Between 0 and 10
2 3 5 7
42
Prime Numbers Between 10 and 20
11 13 17 19
43
Prime Numbers Between 20 and 30
23 | 29
44
Prime Numbers Between 30 and 40
31 | 37
45
Prime Numbers Between 40 and 50
41 43 47
46
How to check for prime
Check for divisibility big primes: ``` 2 & 5 3 7 11 13 ``` Remember that you can stop when you have checked the primes up to the sqroot of the number
47
Check for how many primes exist between two numbers
1) write down all odd #'s (eliminates all multiples of 2) 2) eliminate all multiples of 3 & 5 3) eliminate all multiples of 7 & 11 & 13
48
Finding how many unique primes for a number
Do prime factorization of the number and count the unique Ex. 20 = 2^2 x 5 So it has 2 unique primes
49
Finding the number of unique factors for a number
1) Do prime factorization of the number 2) Add 1 to the exponent of each prime 3) Multiply the result Ex 20 = 2^2 x 5 Number of unique factors = (2+1)(1+1) = 6
50
How to check if an integer is divisible by a #
Prime factorization of the number | See if the factors can be combined to equal the #
51
Divisibility Rules When is a number divisible by 4
If last 2 digits are divisible by 4
52
Divisibility Rules When is a number divisible by 6
If it is even and divisible by 3
53
Divisibility Rules When is a number divisible by 9
If the sum of the digits is a multiple of 9
54
Lowest Common Multiplier | How to find LCM of two numbers
1) Perform prime factorization on each number | 2) Take each prime at its highest power and multiply
55
What is the terminology for the terms in division?
Numerator --> Dividend _____________ = Quotient Denominator --> Divisor
56
What is a composite?
A Non-prime number
57
What are the properties of 0?
It is an even number It is neither + nor - It is a multiple of all numbers It is never a factor of any number
58
What are the common factors shared by x and (x+1)?
None, except 1
59
What is the LCM of x and (x+1)?
(X)(x+1)
60
Properties of even/odd numbers | Addition/Subtraction
odd +/- odd = even even +/- even = even odd +/- even = odd
61
Properties of even/odd numbers | Multiplication/Division
odd x odd = odd even x even = even odd x even = even
62
Inclusive Sets | Find the multiples of x in set a..b
b - a ____ + 1 x If set is not inclusive move range inward to next numbers that are multiples if x

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