Quant Flashcards

1
Q

Sum of 3 numbers = 3 times one of numbers

A

Median = average of 3 numbers

The number that is x3 is the average/median.

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2
Q

Prime to an exponent

A

Factor the product into a prime box

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3
Q

Find average equation

A

Sum of terms/number of terms

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4
Q

Given right triangle hypotenuse and area

A

Sufficient to find perimeter. Substitute pythag theorem with area.

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5
Q

Vertex located on midpoint of larger triangle

A

Smaller triangle area is 1/4 that of the larger. 1/2 base size and 1/2 height size

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6
Q

30-60-90 Triangle angle to side relationships

A

Opposite of:
30 - x
60 - x(sqrt(3))
90 - 2x

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7
Q

Probability of x AND y

A

Multiply probability

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8
Q

Probability of x OR y

A

Add probability

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9
Q

First (11) prime numbers

A

2,3,5,7,11,13,17,19,23,29,31

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10
Q

Terms need to be in alphabetical order

A

Can be AB, AC, AD, not just AB, BC, CD, etc.

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11
Q

Rate - time - distance (approach)

A

Set up a RxT = D chart

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12
Q

Sum of consecutive integers formula

A

S = (1st + last)/2 * (Last - first + 1)

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13
Q

Arranging digits in a required pattern (approach)

A

Draw examples of each pattern/possible choice

ie: DS209

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14
Q

Finding min answer

A

use extremes for smart numbers or test cases

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15
Q

(x+y)^2

A

x^2 + 2xy + y^2

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16
Q

(x-y)^2

A

x^2 - 2xy + y^2

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17
Q

(x-y)(x+y)

A

x^2 - y^2

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18
Q

A system of inequalities (approach)

A

Stack them and add

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19
Q

(2) inequality signs in a statement

A

Split them and solve separately

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20
Q

First step in inequ equation

A

Try algebra

Then test numbers

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21
Q

If x is doubled, then y is tripled (or similar statement) (Approach)

A

Test cases

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22
Q

One variable in the question stem (ie: s^3 + 12 =?)

A

Isolate the q stem to one variable (ie: what is s?)

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23
Q

What is volume? (Approach)

A

Draw the picture and get the equations on paper

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24
Q

A trianglein a semi circle (hyp is the diameter)

A

Triangle is a right triangle

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25
Q

Looking for whether a combination of variables are odd/even

A

List out each variable and determine if it is odd even or either

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26
Q

Small % and smart numbers (ie: 4.5%)

A

use 1000 to account for 0.5% in avoiding decimals in answers

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27
Q

% of two different variables in comparison to a % of the sum

A

Weighted averages

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28
Q

Partial list in question

A

Draw list on page and fill out as you go

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29
Q

Working backwards to find the min value

A

Start with the smallest answer choice

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30
Q

Main number properties to try in testing cases

A

Pos/Neg; Odd/Even; Fraction/Int; Zer0

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31
Q

Comparing fractions (esp in intervals)

A

Put into common denominator on paper

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32
Q

% Increase/decrease (algebra)

A

(1+ x/100) or (1- x/100)

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33
Q

Finding greatest value in overlapping set

A

Put > or < in matrix

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34
Q

Relationship between 3 sides of a triangle

A

Third side must lie between the difference and the sum of the other 2

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35
Q

3 most common triangles

A

30-60-90
45-45-90
3-4-5

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36
Q

Diagonal of a rectangle (approach)

A

Use pythagorean theorem with sides

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37
Q

Diagonal of a cube

A

x√3

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38
Q

(2) rules for similar triangles

A
  1. ) Sides are directly proportional

2. ) Angles are the same

39
Q

Compare the areas of similar triangles

A
  • Given sides a:b

- Area is a^2 : b^2

40
Q

Maximize the area when given 2 sides of a triangle

A

Make 2 sides perpendicular to each other / right triangle

41
Q

Sum of angles of any polygon (n sides)

A

(n-2)(180)

42
Q

Area of trapezoid

A

( (B1 + B2) (h) ) / 2

43
Q

Area of parallelogram

A

(b)(h)

44
Q

Area of rhombus

A

(Diagonal 1 x Diagonal 2) / 2

45
Q

Relationship between a central angle and the arc it intercepts

A

Proportion of central angle to 360 : proportion of arc length to center of circle

46
Q

Relationship between central angle and inscribed angle

A

Inscribed is 1/2 of central angle

47
Q

Surface area of a cylinder

A

2πrh + 2(πr^2)

48
Q

Quadrants

A

I - IV, counterclockwise from top right

49
Q

DS Process

A
  1. Deep breath
  2. Identify givens
  3. Yes/no v. val
  4. Answer grid
  5. Rephrase question
  6. Prove statement to be S or NS
50
Q

PS Process

A
  1. Deep breath
  2. Glance at answers
  3. Read question
  4. Jot givens
  5. Reflect on strategy
  6. Organize/work
51
Q

Working backwards when given that x is greater than y

A

Eliminate answers when working backwards where y is greater than x

52
Q

Working backwards when given that x is greater than y

A

Eliminate answers when working backwards where y is greater than x

53
Q

Variables in answer choice

A

Smart numbers if algebra doesn’t look easy

54
Q

Finding % complete of a combined rate

A

Make a new RxT=D chart

55
Q

Find slope greater or less than 1

A

Wrtie rise/run for slope

56
Q

Discount or markup between 1-100

A

Test max/min cases within parameter

57
Q

Unknown multiplier with modifications including real numbers (building block ex)

A

Adjust fractions with modifiers and solve for x (or multiplier)

58
Q

Dollars and cents for smart numbers. how to choose smart nubers (taxi rate example)

A

Double or dingle digit number for dollars

Triple digit for cents

59
Q

Dollars and cents in the question stem to be used in an equation (approach) (taxi rate example)

A

Assign smart numbers but convert to dollars before solving

60
Q

Consecutive set with odd number of terms

A

sum of integers is a multiple of the number of terms

61
Q

Consecutive set with even number of terms

A

Sum of integers is not a multiple of the number of terms

62
Q

“X is the sum of Y consecutive terms” What does Y represent?

A

The number of consecutive terms in the set

63
Q

% for quantity of something before and after a modification (gold/silver example)

A

Write as a fraction with total in denominator

64
Q

Probability of something happening, often in a series of events (technique?)

A

Use the (1-x) technique. Where you find the opposite event and subtract it from 1.

65
Q

Probability of a sequence of events (how to capture on paper)

A

Use a table to show each step

66
Q

x^2 - y^2 = a given int

A

Can solve for x and y by listing the squares of integers and comparing differences

67
Q

Rhombus definition

A

Parallelogram with (4) even sides

68
Q

Find minimum of a set of numbers

A

Maximize every other number in the set

69
Q

A decimal raised to an exponent (simplify)

A

change the decimal to a fraction if possible

70
Q

Any 3 numbers in a set = a given int

A

All numbers in the set are the same

71
Q

Sum of angles of polygon

A

(n-2)(180)

72
Q

Intersecting lines with angles

A

Opposite angles are equal
Adjacent angles sum to 180
Write it on the paper

73
Q

Multiply a number by 10

A

Each digit moves “up” one place

74
Q

Multiple equations that share a point (r,s)

A

Plug the point in and solve for the system of equations

75
Q

A number raised to a larger exponent (eg (33)^43 and (43)^33)

A

Find patter in 3^2, 3^3, 3^4, etc.

76
Q

Sum of consecutive set

A

Find the average (1st + last)/2 times the # of terms

77
Q

Find a % of a big complex number (approach)

A

First find 10% of the number then add and subtract increments of 5% or 1% to hone in on the desired percent

78
Q

14^2

A

196

79
Q

15^2

A

225

80
Q

16^2

A

256

81
Q

17^2

A

289

82
Q

Approximate (approach)

A

Estimate/round number whenever possible

83
Q

Find number of options when order is not important

A

Multiply the number of options in each position of the sequence together for the total number possible

84
Q

(3) equations that share a point on a coordinate graph

A

Plug the point into the system of equations and solve

85
Q

Expression divided by 2 with solution that must be integer

A

Look for even terms

86
Q

Arc length (approach)

A

Start with circumference as proportion of central angle

87
Q

Probability of favorable outcome (approach)

A

Use anagram method for favorable outcomes over total number of outcomes for probability

88
Q

Int^x (ex: 12^x) simplify

A

Split out factors and raise to x (ex: 2^x * 3^x)

89
Q

Volume ratio with no real # (approach)

A
  1. ) ID smart # for volume
  2. ) ID target value
  3. ) Work backwards from answers
90
Q

Small group size for probability

A

Write out every option

91
Q

Factor a large number into a prime tree when looking for multiples (what to watch out for)

A

Can combine primes to make different factors of the larger value

92
Q

Average of consecutive set

A

Last term + 1st term divided by 2

93
Q

Time interval question (approach)

A

Run through the problem, increasing the interval each step to get different values