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GMAT Quant > GMAT Quant > Flashcards

GMAT Quant Flashcards

1
Q

Rule for length of triangle sides (all triangle)

A

The length of a third side will always be between the sum and difference of the other two sides

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2
Q

Pythagorean theorem

A

For right triangles - a^2 + b^2 = c^2

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3
Q

Common right triangles

A

3-4-5
6-12-13
8-15-17

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4
Q

Icosoles right triangle

A

Degree angles: 45-45-90

Side length: 1 - 1 - SR2

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5
Q

30 -60 - 90 triangle

A

1/2 of an equilateral triangle

Side length: 1 - SR3 - 2 (short, long, hypot)

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6
Q

Diagonal of a square

A

D=side length x SR2

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7
Q

Main diagonal of a cube

A

D = side length x SR3

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8
Q

Similar triangles

A

Have same angles, therefore have same side ratios

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9
Q

Area of an equilateral triangle

A

(side length^2 x SR3)/4

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10
Q

Circumference

A

C=Dπ or C=2rπ

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11
Q

Diameter

A

D=2π

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12
Q

Area of a circle

A

A=πr^2

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13
Q

Area of a cylinder

A

A=2πr^2+ 2πrh

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14
Q

Volume of a cylinder

A

V=πr^2h

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15
Q

Divisibility properties (1-9)

A 
2 = ends in 2 or 0
3= sum of digits is divisible by 3 (ex. 72)
4 = divisible by 2 twice OR last 2 digits divisible by 4
6 = divisible 2 and three
8 = divisible by 2 three times OR the last three digits divisible by 8
9 = sum of digits divisible by 9
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16
Q

Prime numbers under 50

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

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17
Q

Remainders

A

Dividend = quotient x divisor + remainder

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18
Q

Find GCF

A

Multiply common primes (use prime columns if numbers are large)

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19
Q

Find LCM

A

Multiply non-common primes (use prime columns if numbers are large)

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20
Q

odd ± even

A

odd

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21
Q

odd ± odd

A

even

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22
Q

even ± even

A

even

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23
Q

odd x odd

A

odd

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24
Q

even x even

A

even

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25
Q

odd x even

A

even

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26
Q

even / even

A

even, odd, or non-int

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27
Q

even / odd

A

even or non-int

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28
Q

odd / even

A

non- int

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29
Q

odd / odd

A

odd or non-int

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30
Q

Sum of two primes

A

Always even unless one of the primes is 2

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31
Q

3!`

A

6

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32
Q

4!

A

24

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33
Q

5!

A

120

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34
Q

6!

A

720

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35
Q

7!

A

5040

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36
Q

8!

A

40320

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37
Q

Perfect squares

A

Have an odd number of total factors

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38
Q

Adding, multiplying, and subtracting remainders

A

Can be done, just correct for excess at the end

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39
Q

Factoring large numbers (finding number of factors)

A

Count total occurrences of each prime factor, including 0, add 1 to each of them, and then multiply together

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40
Q

Glue method

A

For combinatorics, when things can’t happen (e.g., people won’t sit next to each other)

1) calculate normal probability w/o constraints
2) imagine constrainers are glued (i.e., 1 person not 2), then calculate new number of total possibilities
3) double number in #2 because they could be “glued” either way
4) subtract step #1 from #1

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41
Q

Multiplying decimals

A

Ignore decimals at first, and multiply normally. Then add decimals back in OR move decimals same number of spaces in opposite directions (if multiplying very large and very small number)

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42
Q

Dividing decimals

A

If decimal is only in the dividend, bring it straight up to the answer and divide normally BUT if the decimal is in divisor, shift the decimal in both dividend and divisor until divisor is a whole number, then bring the decimal up

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43
Q

Decimal raised to a power or the root of a decimal

A

Rewrite as an integer times 10 to a power, and then distribute the exponent to the integer and the power of 10

Number of decimal points on a squared decimal is 2x the number of decimals in the original

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44
Q

Reciprocals

A

If 2 numbers are reciprocals, when multiplied by each other they equal 1

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45
Q

Percent change

A

Change in value / original value

46
Q

New percent

A

New value / original value

47
Q

Compound interest formula

A

CI = P (1+ (r/n))^nt

r= rate in decimalr form
n= number of times per year
t = number of years

But more useful to think of these as successive percents problems instead of applying formulas

48
Q

Solving ratios with 2+ parts

A

Use unknown multiplier OR create a common term

49
Q

FDP 1/8

A

.125, 12.5%

50
Q

FDP 1/6

A

.166666 , 16.7%

51
Q

FDP 3/8

A

.375, 37.5%

52
Q

FDP 5/8

A

.625, 62.5%

53
Q

FDP 5/6

A

.833333, 83.3%

54
Q

FDP 7/8

A

.875, 85.7%

55
Q

FDP 7/4

A

1.75, 175%

56
Q

Fraction form preferred for…

A

Multiplication

57
Q

Decimal or percent form preferred for…

A

Addition
Subtraction
Estimating numbers
Comparing numbers

58
Q

DS question asks for relative value of 2 pieces of any ratio, then you need…

A

Any statement that give the relative value of either of the pieces of the ratio

59
Q

DS question asks for concrete vale of one element of a ratio, then you need…

A

Both concrete and relative value of at least 1 element

60
Q

Repeating decimals

A

Solve through long division OR if the denominator can be multiplied to be only “9s” then the numerator is the repeating decimal

61
Q

Deluxe pythagorean theorem

A

Used to find diagonal in a 3D shape: l^2 + w^2 + h^2 = d^2

62
Q

If given an inequality with more than two parts…

A

Break down into multiple inequalities, each with just one inequality sign, and solve for potential values, then plug potential answers back into original equation

63
Q

If given equation where one side is an absolute value…

A

Make two different equations, and set one positive and one negative. Then plug solutions into original equation to test it

64
Q

Exterior angles of a triangle

A

Sum of non-adjascent angles

65
Q

Slope of a line

A

y1-y2 / x1-x2

66
Q

Find distance between 2 points on a coordinate plane by…

A

Creating an invisible triangle and using the pythagorean theorem

67
Q

Prime factoring large numbers

A

Add all digits, and find the prime factors of the sum of the digits

68
Q

Applying exponents to negative numbers…

A

If negative is not in parentheses: apply exponent, then negative sign (number will always be negative)
If negative is in parens: then include it in the calculation

69
Q

When multiplying terms with exponents…

A

Add the exponents if the bases are the same

70
Q

When dividing terms with exponents…

A

Subtract the exponents if the bases are the same

71
Q

Negative exponents…

A

Are fractions (ex: a^-2 = 1/a^2)

72
Q

Raising an exponent to another power…

A

Multiply the exponents

73
Q

Difference of squares

A

x2 - y2

74
Q

Multiply or divide ineqaulity by a negative…

A

Flip the sign

75
Q

Standard deviation

A

1) Find difference between each measurement and the mean
2) Square differences
3) Add squared differences
4) Divide sum by the number of measurements - this quotient will equal the variance
5) Find the positive square root of the variance

76
Q

Sum of interior angles of a polygon

A

180 (n-2)

77
Q

Fractional exponents are the same as…

A

Roots equal to the value of the fraction (e.x. 1/2 exponent is same as taking square root)

78
Q

If an exponent is outside parentheses…

A

Apply it to everything inside the parens

79
Q

When finding the maximum area of a polygon…

A

Squares usually give max area

80
Q

When finding the minimum perimeter of a polygon..

A

Squares usually have minimum primeter

81
Q

Finding max. area when given two sides of a parallelogram or triangle…

A

Make the two sides be perpendicular to each other, and calculate area

82
Q

To find how many times a parabola touches the X axis…

A

Set y=0 and solve by factoring or solving the quadratic equation

83
Q

Steps to find information about perpendicular lines…

A

1) Find slope of line 1
2) Find slope of line 2 (negative recip)
3) Find midpoint on given line (use coordinates given, or find midpoint and then figure out missing)
4) Substitute midpoint coordinates into y=mx+b formula to find y-intercept

84
Q

Negative exponents

A

(1/n^x)

85
Q

Anything raised to a power of 0

A

1

86
Q

Negative rules for exponents

A

Unless - is in ( ), the exponent doesn’t distrubute to the - sign

87
Q

Fractional exponents

A

Numerator = power to raise base to
Denominator= which root to take
Ex: 25^3/2 = square root of 25^3

88
Q

If 2+ exponents with the same base are added or subtracted….

A

Can factor out a common term

89
Q

Even exponents _____ the sign of the base

A

Hide the sign, as they usually have 2 answers

90
Q

Odd exponents _____ the sign of the base

A

Keep the sign, and only have one solution

91
Q

If exponents are on both sides of an exponential equation….

A

Rewrite the equation so bases or exponents are the same, and then eliminate

92
Q

Fraction raised to a negative exponent

A

Take reciprocal of fraction and raise to a positive exponent

93
Q

Can only simplify roots via combination and separation using…

A

Multiplication and division NOT addition and subtraction

94
Q

First step in quadratic equations

A

Set to 0 before solving

95
Q

Components of quadratic equations

A

Variable raised to 2nd power, variable raised to first power, 2 solutions

96
Q

Square root of quadratic equations

A

Can be done if one side is a perfect square, but must consider both positive and negative solutions

97
Q

x^2-y^2

A

(x+y)(x-y)

98
Q

Sum of squares: x^2+2xy+y^2

A

(x+y)^2

99
Q

Difference of squared: x^2-2xy+y^2

A

(x-y)^2

100
Q

Making an equation not a fraction

A

Multiple whole side by LCD

101
Q

Can’t multiply or divide inequalities with variables unless…

A

know the sign of the # the variable stands for

102
Q

In compound inequalities, you must apply all actions to…

A

All parts of the inequality

103
Q

Can add inequalities as long as sign is facing the same way, but…

A

Must add 2nd inequality twice???

104
Q

Combination problems with variables

A

Combine equations to isolate the combination first, don’t try to solve for each variable

105
Q

If a variable combination problem results in quadratics…

A

Answer in DC problems is E because there could be two answers

106
Q

Raising any fraction to a power…

A

Brings it closer to 0 on the number line

107
Q

Any positive proper fraction raised to a power >1 wil…

A

Result in a number smaller than the original fraction

108
Q

Any positive proper fraction raised to a power between 0-1 will…

A

Result in a number larger than the original fraction

109
Q

VIC problems

A

1) Replace variables in question with numbers (small primes are good choices), 2) Calculate answer using chosen numbers, 3) Plug same numbers into answer choices to get matching answers

110
Q

2+ variable in 2+ absolute value expressions (usually lack constants)….

A

Use conceptual approach, not easy to solve with algebra

111
Q

One variable, at least one constant, and 1+ absolute value expressions…

A

Solve with algebra

GMAT Quant (2 decks)

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