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GMAT Math > Volume 1 > Flashcards

Volume 1 Flashcards

0
Q

Elevenths (1/11..2/11..3/11..) decimal equivalent pattern.

A 
2 digit number repeating
Numerator times 9 
1/11 = .090909
2/11 = .181818
3/11 = .272727
4/11 = .363636
5/11 = .454545
6/11 = .545454
7/11 = .636363
8/11 = .727272
9/11 = .818181
10/11 = .909090
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1
Q

Ninths (1/9..2/9..3/9..) decimal equivalent pattern.

A 
1/9 = .11111
2/9 = .22222
3/9 = .33333
4/9 = .44444 
5/9 = .55555
6/9 = .66666
7/9 = .77777
8/9 = .88888
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2
Q

Eighths (1/8..3/8..) decimal equivalent pattern.

A 
Nearest inferior quarter (.25, .5, .75)
Plus .125
1/8 = .125
3/8 = .375
5/8 = .625
7/8 = .875
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6
Q

Calculating circumference, diameter, and radius

A 
c = πd
c = 2πr
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7
Q

Surface area of a sphere

A

4πr^2

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8
Q

Remainder formula

A

Dividend/Divisor = decimal quotient = integer quotient + remainder/divisor

Dividend = (integer quotient)*(divisor) + remainder

*** DECIMAL PART OF DECIMAL QUOTIENT = REMAINDER/DIVISOR

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9
Q

Divide small number by large number. Eg, 3/47

A 
(100 * 3) / 47 {plus 2 positions}
= 300 / 47
= 6 + 42/47
= .06???
{420/47=8
= } ???
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10
Q

Cancel BEFORE you multiply

Eg, 56/x = 24/27

A 
56/x = 24/27
56 * 27 = 24x
x = 56*27/24
x = 56*9/8
x = 7*9
x = 63
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11
Q

Negative power

Eg (2)^-3

A

Base raised to a negative power is equal to the reciprocal of (ie 1 divided by) the base raised to the original power positive

= 1 / 2^3 = 1/8 = .125

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12
Q

Area of a circle

A

Pi*r^2

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13
Q

Exponential Equations

(X^n) * (X^m = ?

A

X^n+m

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14
Q

Exponential Equations

(X^n) / (X^m) = ?

A

X^n-m

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15
Q

Exponential Equations

(X/Y)^n = ?

A

(X^n) / (Y^n)

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16
Q

Exponential Equations

(X^n) * (Y^n) = ?

A

(XY)^n

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17
Q

Exponential Equations

(X^y)^z = ?

A

X^yz

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18
Q

Exponential Equations

X^-n = ?

A

1/(X^n)

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19
Q

Exponential Equations

1^n = ?

A

1

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20
Q

Exponential Equations

X^0 = ?

A

1

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21
Q

Exponential Equations

X^0 = ?

A

0, except 0^0 = 1 or undefined

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22
Q

Exponential Equations

F(v) = ?

A

C(v) * (1+g)^T

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23
Q

Distance formula

A

Rate*Time

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24
Q

Wage formula

A

Rate*Time

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25
Q

FOIL

A

First
Outside
Inside
Last

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26
Q

Difference of squares

A

A^2 - B^2 = (A+B)(A-B)

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27
Q

Squares 11-20

A 
11*11 = 121
12*12 = 144
13*13 = 169
14*14 = 196
15*15 = 225
16*16 = 256
17*17 = 289
18*18 = 324
19*19 = 361
20*20 = 400
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28
Q

Simple probability

A

(# of ways that fit the argument) / (# of total ways)

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29
Q

Common factors

What factors greater than 1 do 135 and 225 have in common?

A 
5...
135=5*27=5*3*3*3
225=5*45{45=5*9}=5*5*9=5*5*3*3
...5s and 3s...
Strand in common: 5*3*3
3*3=9
5*3=15
5*3*3=45
Answer: 3, 5, 9, 15, 45
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30
Q

Gross profit

A

Selling price - Cost

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31
Q

Fast fractions

1/x + 1/y

Eg, 1/7 + 1/20

A

x+y / xy

1/7 + 1/20
= 27/140

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32
Q

Multiplying fractions

A

1) Multiply numerators
2) Multiply denominators
3) Simplify the fraction if necessary

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33
Q

Pythagorean theorem

A

Relationship of right triangle sides
A^2 + B^2 = C^2
Where C is hypotenuse

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34
Q

Area of a triangle

A

A = 1/2 * bh

Half of a square/rectangle

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35
Q

Divide by 9 pattern

A

0.22222222… = 2/9
0.54545454… = 54/99
0.298298298… = 298/999
Division by 9’s causes the repeating pattern.
Number of numerator digits = number of denominator 9s

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36
Q

Divide by 9 pattern of 0

Eg, 2/90

A

Answer: .022
Note the pattern if zeros preceed the repeating decimal:
0.022222222… = 2/90
0.00054545454… = 54/99000
0.00298298298… = 298/99900
Adding zero’s to the denominator adds zero’s before the repeating decimal.

Number of numerator digits = number of denominator 9s

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37
Q

Sixths fraction-decimal equivalent

A 
1/6 = .166...
5/6 = .833...
38
Q

Sevenths fraction-decimal pattern

A 
Remember 14 28 42 57 71 85 with varying combinations. 
* These 6 integers are the first 2 decimal digits for ascending sevenths beginning 1/7. 
1/7 = .142857
2/7 = .285714
3/7 = .428571
4/7 = .571428
5/7 = .714285
6/7 = .857142
39
Q

Twelfths fraction-decimal pattern

A 
1/12 = .0833...
5/12 = .4166...
7/12 = .5833...
11/12 = .9166...
40
Q

TAKEAWAY

A

If you need a calculator, you’re probably going about the problem wrong.

41
Q

Prime numbers

Single digits

A

2, 3, 5, 7

42
Q

Prime numbers

1’s

A

11, 31, 41, 61, 71

43
Q

Prime numbers

3’s

A

13, 23, 43, 53, 73, 83

44
Q

Prime numbers

7’s

A

17, 37, 47, 67, 97

45
Q

Prime numbers

9s

A

19, 29, 59, 79, 89

46
Q

Common powers and roots

2

A 
2^1  = 2
2^2  = 4
2^3  = 8
2^4  = 16
2^5  = 32
2^6  = 64
2^7  = 128
2^8  = 256
2^9  = 512
2^10  = 1024
47
Q

Common powers and roots

3

A 
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
48
Q

Common powers and roots

4

A 
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^5 = 1024
49
Q

Common powers and roots

5

A 
5^1 = 5
5^2 = 25
5^3 = 125
5^4 = 625
5^5 = 3125
50
Q

Remainder formula

A

Dividend/Divisor = decimal quotient = integer quotient + remainder/divisor

Dividend = (integer quotient)*(divisor) + remainder

*** DECIMAL PART OF DECIMAL QUOTIENT = REMAINDER/DIVISOR

51
Q

Divide small number by large number. Eg, 3/47

A 
(100 * 3) / 47 {plus 2 positions}
= 300 / 47
= 6 + 42/47
= .06???
{420/47=8
= } ???
52
Q

Cancel BEFORE you multiply

Eg, 56/x = 24/27

A 
56/x = 24/27
56 * 27 = 24x
x = 56*27/24
x = 56*9/8
x = 7*9
x = 63
53
Q

Negative power

Eg (2)^-3

A

Base raised to a negative power is equal to the reciprocal of (ie 1 divided by) the base raised to the original power positive

= 1 / 2^3 = 1/8 = .125

54
Q

Area of a circle

A

Pi*r^2

55
Q

Exponential Equations

(X^n) * (X^m = ?

A

X^n+m

56
Q

Exponential Equations

(X^n) / (X^m) = ?

A

X^n-m

57
Q

Exponential Equations

(X/Y)^n = ?

A

(X^n) / (Y^n)

58
Q

Exponential Equations

(X^n) * (Y^n) = ?

A

(XY)^n

59
Q

Exponential Equations

(X^y)^z = ?

A

X^yz

60
Q

Exponential Equations

X^-n = ?

A

1/(X^n)

61
Q

Exponential Equations

1^n = ?

A

1

62
Q

Exponential Equations

X^0 = ?

A

1

63
Q

Exponential Equations

X^0 = ?

A

0, except 0^0 = 1 or undefined

64
Q

Exponential Equations

F(v) = ?

A

C(v) * (1+g)^T

65
Q

Distance formula

A

Rate*Time

66
Q

Wage formula

A

Rate*Time

67
Q

FOIL

A

First
Outside
Inside
Last

68
Q

Difference of squares

A

A^2 - B^2 = (A+B)(A-B)

69
Q

Squares 11-20

A 
11*11 = 121
12*12 = 144
13*13 = 169
14*14 = 196
15*15 = 225
16*16 = 256
17*17 = 289
18*18 = 324
19*19 = 361
20*20 = 400
70
Q

Simple probability

A

(# of ways that fit the argument) / (# of total ways)

71
Q

Common factors

What factors greater than 1 do 135 and 225 have in common?

A 
5...
135=5*27=5*3*3*3
225=5*45{45=5*9}=5*5*9=5*5*3*3
...5s and 3s...
Strand in common: 5*3*3
3*3=9
5*3=15
5*3*3=45
Answer: 3, 5, 9, 15, 45
72
Q

Gross profit

A

Selling price - Cost

73
Q

Fast fractions

1/x + 1/y

Eg, 1/7 + 1/20

A

x+y / xy

1/7 + 1/20
= 27/140

74
Q

Multiplying fractions

A

1) Multiply numerators
2) Multiply denominators
3) Simplify the fraction if necessary

75
Q

Pythagorean theorem

A

Relationship of right triangle sides
A^2 + B^2 = C^2
Where C is hypotenuse

76
Q

Area of a triangle

A

A = 1/2 * bh

Half of a square/rectangle

77
Q

Divide by 9 pattern

A

0.22222222… = 2/9
0.54545454… = 54/99
0.298298298… = 298/999
Division by 9’s causes the repeating pattern.
Number of numerator digits = number of denominator 9s

78
Q

Divide by 9 pattern of 0

Eg, 2/90

A

Answer: .022
Note the pattern if zeros preceed the repeating decimal:
0.022222222… = 2/90
0.00054545454… = 54/99000
0.00298298298… = 298/99900
Adding zero’s to the denominator adds zero’s before the repeating decimal.

Number of numerator digits = number of denominator 9s

79
Q

Sixths fraction-decimal equivalent

A 
1/6 = .166...
5/6 = .833...
80
Q

Secenths fraction-decimal pattern

A 
1/7 = .142857
2/7 = .285714
3/7 = .428571
4/7 = .571428
5/7 = .714285
6/7 = .857142
81
Q

Twelfths fraction-decimal pattern

A 
1/12 = .0833...
5/12 = .4166...
7/12 = .5833...
11/12 = .9166...
82
Q

Addition ‘wording’

A 
Increased by
More than
Combined
Together
Total of
Sum
Added to
And
Plus
83
Q

Subtraction ‘wording’

A 
Decreased by
Minus
Less
Difference between/of
Less than
Fewer than
Minus
Subtracted from
84
Q

Multiplication ‘wording’

A 
Of
Times
Multiplied by
Product of
Increased/Decreased by a factor of
85
Q

Division ‘wording’

A 
Per
Out of
Ratio of
Quotient of
Percent (divide by 100)
Divided by
Each
86
Q

Equals ‘wording’

A 
Is
Are
Was
Were
Will be
Gives
Yields
Sold for
Costs
Adds up to
The same as
As much as
87
Q

Variable or Value ‘wording’

A

A number
How much
How many
What

88
Q

Dividing fractions

EG, (2/3) / (1/4)

A

Multiple numerator by reciprocal of denominator.

EG, (2/3) / (1/4) = (2/3) * (4/1) = 8/3

89
Q

Reciprocals

A

2 numbers are reciprocals if and only if their product is equal to 1.

Tricks: square root of x = (square root if x) / x

GMAT Math (2 decks)

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