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GMAT > Arithemetic > Flashcards

Arithemetic Flashcards

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
Q

Multiplication Table

9 x 14

A

126

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25
Q

Multiplication Table

9 x 15

A

135

26
Q

Multiplication Table

11 x 11

A

121

27
Q

Multiplication Table

11 x 12

A

132

28
Q

Multiplication Table

11 x 13

A

143

29
Q

Multiplication Table

11 x 14

A

154

30
Q

Multiplication Table

11 x 15

A

165

31
Q

Multiplication Table

12 x 12

A

144

32
Q

Multiplication Table

12 x 13

A

156

33
Q

Multiplication Table

12 x14

A

168

34
Q

Multiplication Table

12 x 15

A

180

35
Q

Multiplication Table

13 x 13

A

169

36
Q

Multiplication Table

13 x 14

A

182

37
Q

Multiplication Table

13 x 15

A

195

38
Q

Multiplication Table

14 x 14

A

196

39
Q

Multiplication Table

14 x 15

A

210

40
Q

Multiplication Table

15 x 15

A

225

41
Q

Prime Numbers

Between 0 and 10

A

2
3
5
7

42
Q

Prime Numbers

Between 10 and 20

A

11
13
17
19

43
Q

Prime Numbers

Between 20 and 30

A

23

29

44
Q

Prime Numbers

Between 30 and 40

A

31

37

45
Q

Prime Numbers

Between 40 and 50

A

41
43
47

46
Q

How to check for prime

A

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
Q

Check for how many primes exist between two numbers

A

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
Q

Finding how many unique primes for a number

A

Do prime factorization of the number and count the unique

Ex.
20 = 2^2 x 5
So it has 2 unique primes

49
Q

Finding the number of unique factors for a number

A

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
Q

How to check if an integer is divisible by a #

A

Prime factorization of the number

See if the factors can be combined to equal the #

51
Q

Divisibility Rules

When is a number divisible by 4

A

If last 2 digits are divisible by 4

52
Q

Divisibility Rules

When is a number divisible by 6

A

If it is even and divisible by 3

53
Q

Divisibility Rules

When is a number divisible by 9

A

If the sum of the digits is a multiple of 9

54
Q

Lowest Common Multiplier

How to find LCM of two numbers

A

1) Perform prime factorization on each number

2) Take each prime at its highest power and multiply

55
Q

What is the terminology for the terms in division?

A

Numerator –> Dividend
_____________ = Quotient
Denominator –> Divisor

56
Q

What is a composite?

A

A Non-prime number

57
Q

What are the properties of 0?

A

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
Q

What are the common factors shared by x and (x+1)?

A

None, except 1

59
Q

What is the LCM of x and (x+1)?

A

(X)(x+1)

60
Q

Properties of even/odd numbers

Addition/Subtraction

A

odd +/- odd = even
even +/- even = even
odd +/- even = odd

61
Q

Properties of even/odd numbers

Multiplication/Division

A

odd x odd = odd
even x even = even
odd x even = even

62
Q

Inclusive Sets

Find the multiples of x in set a..b

A

b - a
____ + 1
x

If set is not inclusive move range inward to next numbers that are multiples if x

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