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GMAT > Math > Flashcards

Math Flashcards

1
Q

Leona bought a 1 year, $10,000 certificate of deposit that paid interest at an annual rate of 8% compounded semiannually.

A

2 payments in one year, each half of the annual rate. Two payments of 4% interest rate

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2
Q

5/4

A

1.25

125%

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3
Q

7/4

A

1.75

175%

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4
Q

1/8

A
  1. 125

12. 5%

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5
Q

3/8

A
  1. 375

37. 5%

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6
Q

5/8

A
  1. 625

62. 5%

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7
Q

7/8

A
  1. 875

87. 5%

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8
Q

2/3

A
  1. 6666

66. 6%

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9
Q

1/6

A
  1. 16666

16. 7%

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10
Q

5/6

A
  1. 833

83. 3%

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11
Q

1/9

A
  1. 111

11. 1%

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12
Q

Convert a decimal to a fraction

A

Put the digits to the right of the decimal point. Over the appropriate power of 10. Simplify.

0.036 = 36/1000

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13
Q

Convert a percent to a fraction

A

Write over 100

OR

Convert to a decimal first then convert decimal to fraction
3.6% = 0.036 = 36/1000 = 9/250

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14
Q

Percent change of an original percent

A

% change = change in value/original value

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15
Q

New percent of an original percent

A

New % = new value /original value

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16
Q

Percent INCREASE of 10%

A

110%

Or 1.1

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17
Q

Percent increase of 20%
Percent increase of 25%
Percent increase of 50%

A

120% or 1.2 or 6/5
125% or 1.25 or 5/4
150% or 1.5 or 3/2

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18
Q

Percent DECREASE of 10%

A

90% or 0.9

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19
Q

Percent decrease of 20%
Percent decrease of 25%
Percent decrease of 50%
Percent decrease of 75%

A

80% or 0.8 or 4/5
75% or 0.75 or 3/4
50% or 1/2
25% or 1/4

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20
Q

If you have a variable in an exponent or exponents…

Example: 3^x = 27^4

A

Make the bases equals usually by breaking the given bases down to primes.

3^x = 27^4
3^x = (3^3)^4
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21
Q

“Each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew.”

A

As many = of

Can multiply
3/4x

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22
Q

Fractions/decimals (0-1) decrease and exponents increase

A

Because denominator increases.

(1/2)^2= 1/4

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23
Q

Pay attention to the parentheses with exponents (PEMDAS)

A

-2^4=-16

(-2)^4=16

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24
Q

When multiplying exponents with same base = ADD

When dividing exponents with the same base = SUBTRACT

A

x^15/x^8 = x^7

2^2 x 2^3 = 2^5

*when simplifying or solving try to get to the same base!

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25
Q

Nested exponents = when you raise an exponential term to an exponent, multiply the exponents

A

(a^5)^4 = a^20

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26
Q

Raise a fraction to a negative power = raise reciprocal to the equivalent positive power

A

(3/7)^-2 = (7/3)^2

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27
Q

1.4^2

A

2

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28
Q

1.7^2

A

3

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29
Q

2.25^2

A

5

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30
Q

12^2

A

144

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31
Q

13^2

A

169

32
Q

14^2

A

196

33
Q

15^2

A

225

34
Q

16^2

A

256

35
Q

25^2

A

625

36
Q

2^3

A

8

37
Q

3^3

A

27

38
Q

4^3

A

64

39
Q

5^3

A

125

40
Q

2^4

4^2

A

16

41
Q

2^5

A

32

42
Q

2^6

4^3

A

64

43
Q

2^7

A

128

44
Q

2^8

4^4

A

256

45
Q

2^9

A

512

46
Q

2^10

4^5

A

1024

47
Q

3^4

A

81

48
Q

0=0 (combo algebra problem)

A

True statement, same line = infinite many solutions

49
Q

0=5 (combo algebra)

A

False statement (i.e. Parallel lines, No solutions)

50
Q

Square of a sum

A

(X+y) ^2 = x^2 + 2xy + y^2

51
Q

Square of a difference

A

(X-y)^2 = x^2 - 2xy + y^2

52
Q

Differences of squares

A

(X+y) (x-y) = x^2 - y^2

53
Q

Average rate

A

Because the object spends more time traveling at the slower rate, the average rate will ALWAYS be closer to the SLOWER of the two rates.

54
Q

Average speed

A

Average speed = total distance/total time

55
Q

Relative Rates

A
  1. Bodies move toward each other (r1 + r2)
  2. Bodies move away from each other
    (r1+ r2)
  3. Bodies move in the same direction on the same path.
    (r1-r2)
56
Q

Counting integers (if both extremes need to be added)

A

(Last - First) + 1

57
Q

Counting consecutive multiples, if extremes are included

A

(Last - First) / increment + 1

The bigger the increment the smaller the result

58
Q

Properties of evenly spaced sets (ALL evenly spaced sets)

A
  1. Mean and median are equal to each other
    Ex: mean if 4, 8, 12, 16, 20? Mean = 12 and median = 12
  2. Mean and median of the set are equal to the average of the FIRST and LAST terms.
    (First + last)/ 2
59
Q

Sum of consecutive integers

A

Sum = average x number of terms

Average of an odd number of consecutive integers will always be an integer.

Average of an even number of consecutive integers will never be an integer.

60
Q

Triangle properties

A

Sum of 2 side lengths will always be greater than the third side length.

Any side is greater than the difference of the other 2 side lengths.

All angles = 180

Sides correspond with angles: the largest angle is opposite the longest side.

61
Q

Right triangles (and triples)

A

A^2 + B^2 = C^2

3: 4:5
5: 12:13
8: 15:17

62
Q

Sum of interior angles of a polygon

A

(n-2) x 180

63
Q

Area of a Trapezoid

A

(Base 1 + Base 2) x Height/2

64
Q

45: 45:90 triangle
30: 60:90 triangle

A

45: 45:90
x: x : x root2

30:60:90
x : x root 3 : 2x

65
Q

Similar triangles

A

If all corresponding angles are equal AND corresponding sides are in proportion, triangle is similar.

66
Q

Inscribed Angle

A

Inscribed angle: has its vertex on the circle itself

Inscribed angle is equal to half of the angle of the arc it intercepts.

67
Q

Inscribed triangle

A

Inscribed triangle: if all of the vertices of the triangle are points on the circle

** RULE: if one of the sides of an inscribed triangle is the diameter of the circle, triangle must be a right triangle.

68
Q

Divisibility Rules: 3 and 9

A

If the sum of the integer’s digits is a multiple of 3 - divisible by 3

If the sum of the integer’s is a multiple of 9 - divisible by 9

69
Q

Prime numbers

A

2, 3, 5, 7, 11, 13, 17, 19

1 is NOT a prime number (only divisible by itself)

2 is the only even prime number

70
Q

Divisibility rules: 4

Divisibility rules: 8

A

If the last two numbers are divisible 4.

Example:
23,456 because 56 is divisible by 4

25,678 not because 78 not divisible by 4.

If the last three numbers are divisible by 8.

71
Q

Divisibility rules: 6

A

If the integer is divisible by both 2 and 3.

48/2 AND. 48/3

72
Q

Addition/Subtraction Odd Even Rules

A

Even +/- Even = Even

Odd +/- Odd = Even

Even +/- Odd = Odd

73
Q

Multiplication Odd/Even Rules

A

Even x Even = Even

Even x Odd = Even

Odd x Odd = Odd

74
Q

Average of consecutive integers

A

(First + last)/2

Average of first and last term

75
Q

Integer m has an odd number of positive factors

A

Odd number of factors = perfect square

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