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MANHATTAN PREP > Quant > Flashcards

Quant Flashcards

1
Q
A
  1. Know that you can make the reciprocal of c/d (d/c) = the reciprocal of x/y (y/x) (i.e. y/x = d/c)
  2. y/x = b/a then ay = bx my multiplication
  3. If you have an algebraic expression where A is multiplied by Y then you cannot have A divisible by Y.

Answer is C: I and II only

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2
Q
A
  1. Know the unknown multiplier strategy
  2. 30x / 1x = 25/1
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3
Q

Powers of 2

  • 21
  • 22
  • 23
  • 24
  • 25
  • 26
A

Powers of 2

  • 21 = 2
  • 22 = 4
  • 23 = 8
  • 24 = 16
  • 25 = 32
  • 26 = 64
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4
Q

Powers of 3:

  • 31
  • 32
  • 33
  • 34
A

Powers of 3:

  • 31 = 3
  • 32 = 9
  • 33 = 27
  • 34 = 81
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5
Q

Powers of 4:

  • 41
  • 42
  • 43
A

Powers of 4:

  • 41 = 22 = 4
  • 42 = 24 = 16
  • 43 = 26 = 64
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6
Q

Powers of 10:

  • 101
  • 102
  • 103
A

Powers of 10:

  • 101 = 10
  • 102 = 100
  • 103 = 1,000
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7
Q

Extended Squares:

  • 102
  • 112
  • 122
  • 152
  • 202
  • 302
A

Extended Squares:

  • 102 = 100
  • 112 = 121
  • 122 = 144
  • 152 = 225
  • 202 = 400
  • 302 = 900
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8
Q

Cubes:

  • 13
  • 23
  • 33
  • 43
  • 53
  • 63
  • 103
A

Cubes:

  • 13 = 1
  • 23 = 8
  • 33 = 27
  • 43 = 64
  • 53 = 125
  • 63 = 216
  • 103 = 1,000
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9
Q
  1. What happens if you multiply same base numbers with exponents?
  2. What happens if you raise a power to a power?
A
  1. Add the exponents (a2 x a4) = a2 + 4 = a6
  2. Multiply the exponents (a2)4 = a(2)(4) = a8
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10
Q
  1. What is the square root of 2?
  2. What is the square roote of 3?
A
  1. Remember Valentines day (2/14). The square root of 2 is ~1.4
  2. Remember St. Patricks day (3/17). The square root of 3 is ~1.7
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11
Q

Is it possible to derive the multiplcation combo xy from the value for division of x/y?

A

It is not possible.

  • When given x/y = 2, the X could be 2 and the Y could be 1, in which case xy would = 2.
  • Alternatively X could be 4 and Y could be 2, in which case xy would be 8.
  • An infinite number of values could work
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12
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A
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13
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A
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14
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15
Q
A
  1. Remember to consider decimal spaces required
  • Each decimal spaces requires a multiple of 10 to move closer to becoming an integer
  • .025 needs three multiples of 10 to become integer
  • .0025 needs four multiples of 10 to become integer
  • .00025 needs five multiples of 10 to become integer

3 + 4 + 5 = 12 multiples of 10 to become an integer. 10 to the 12th power (E) is the answer

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16
Q

What are the common “Open” Paralellism Markers?

A
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17
Q

What are the common closed parallelism markers?

A
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18
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A
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19
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20
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A
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21
Q

Identify the Six strategies to Problem Solving

A
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22
Q

What is the Median?

A

The “middle” of a sorted list of number

  • e.g. {13, 23, 11, 16, 15, 10, 26}*
    • Reorder in ascending order*
  • {10, 11, 13, 15, 16, 23, 26}*
  • The middle number in this range of 7 integers is 15*
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23
Q

What is the formula for calculating the # of integers in a data set Inclusive?

A

(Last - First + 1)

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24
Q

What is the formula for counting consecutive multiples in a data set Inclusive?

A

( (Last - First) / Increment) + 1

  • If the increment is not a multiple of eacher terms in the range, find the closest multiple to either end and utilize those.
  • e.g. How many multiples of 7 are there between 10 and 80?*
  • Lowest = 14, Highest = 77*
  • ((77 - 14)/7)+1*
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25
Q

What is the formula to solve for the Sum of Consecutive Integers?

A

Average * Number of Terms

e.g. Sum of integers from 20 to 50?

  • (20 + 50) / 2 = 35
  • (50-20) + 1 = 31
  • 35 * 31 = 1,085
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26
Q

What are the first 10 prime #’s?

A

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

  • For a number to be called as a prime number, it must have only two positive factors. Now, for 1, the number of positive divisors or factors is only one i.e. 1 itself. So, number one is not a prime number
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27
Q

What are the 3 rules of multiplying odds and evens?

A
  1. Two odds multiplied together will always have an odd solution
  2. Two evens multiplied together will always have an even solution
  3. One even and one odd multipled together will always have an even solution
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28
Q

What are the 3 rules of addition?

A
  1. Two evens added together will always be even
  2. An even and an odd added together will always odd
  3. Two odds added together will always be even
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29
Q

What is the formula for the Circumference of a circle?

A

Circumeference of a circle = π * D or (pi * Diameter)

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30
Q

What is the formula for the area of a circle?

A

Area of a circle = π * R2 or (pi * Radius squared)

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31
Q

What is the formula for the diameter of a circle?

A

Diameter of a circle = 2R or ( 2 times radius)

32
Q

What is slot method?

A

Use to slots (opportunities) to identify the potential combinatins / outcomes

(e.g. there are 10 students racing, 1st place receives gold, 2nd place receive silver, 3rd place receives bronze. How many different ways can the medals be awarded?)

    • 10 opportunities for 1st place*
    • 9 opportunities left for 2nd*
    • 8 opportunities left for 3rd*
  • 10 * 9 * 8 = 720 potential combinations for medal awarding*
33
Q

What is the permutation (Combination) formula?

A

A Permutation is an ordered combination

The formula for Permutation = N! / (N-R)!

n = Objects, R = Objects removed

(e.g. there are 10 students racing, 1st place receives gold, 2nd place receive silver, 3rd place receives bronze. How many different ways can the medals be awarded?)

N = 10 (students), R = 3 (medal winners)

N! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

(N-R)! = (10 - 3) or 7

(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (7 * 6 * 5 * 4 * 3 * 2 * 1) = 720

34
Q

What is the formula for the area of a trapezoid?

A

Height * Average of the 2 bases (top / bottom)

35
Q

How to get rid of a fraction within a fraction?

A

Multiple the entire fractions by the variable your trying to remove.

  • e.g. (1/m) / (M +3)*
  • Multiply ((1/m) / (M +3)) * (M/M)*
  • This results in 1 / m(M+3) as the M in the numerator cancels out*
36
Q

What do you do if you have a complex fractions problem?

A

Simplify step by step starting with the numerator, then moving to the denominator.

37
Q

What is the formula for the area of a triangle?

A

A = 1/2(bh)

Area of a triangle = 1/2 ()

38
Q

What purpose does the pythagorean Theorum serve, and what is the formula?

A

The Pythagorean Theorum can be used to find the missing values of a one of the measures of a triangle:

The forumulas = a2 + b2 = c2

Whereas a and b are legs of the triangle and c = the hypotenuse

39
Q

What are the 3 Triangle rules?

A
  1. The sum of the lenghts of any 2 sides of a triangle, must be greater than the length of the 3rd side
  2. The third side must be greater than the difference between the 2 other sides (And cannot be the lower limit)
  3. The perimiter of a triangle is the sum of the three sides
40
Q

What is the equation of a straight line?

A

y = mx + b

m = slope or gradient

b = y intercept

In leighmans terms:

  • y = how far up
  • x = how far along
  • m = slope / gradient (how steep the line is)
  • b = value of y when x = 0
41
Q

What does it mean in one of the sides of a triangle, inscribed in a circle, is a diameter of the circle?

A

Then the triangle must be a right triangle

42
Q

What is the formula for the area a Rectangle?

A

Length X Width

43
Q

What is the formula for the area of a square?

A

A = a2

A = Area

a = side

  • The area of a square is the product of a side * a side. Because the sides of squares are the same it = a2
44
Q

What are the common right triangle values?

A

8-15-17 right triangle

3-4-5

45
Q

What does a line measure to in degrees?

A

A line measures 180 degrees

46
Q

What are verticle angles?

A

When two lines intersect, angles found opposite each other are equal (verticle angles)

47
Q

What is an acute angle?

A

An acute angle is an angle less than 90 degrees

48
Q

What is an obtuse angle?

A

An obtuse angle is greater than 90 but less than 180 degrees

49
Q

What do an acute and obtuse angle add to?

A

Any acute angle plus any obtuse angle equals 180 degrees

50
Q

What do the interior angles of intersecting lines equal?

A

Interior angles formed by intersecting lines form a circle 360 degreess

51
Q

What is the formula for the area of a Parallelogram?

A

Base * Height

52
Q

What is the formula for the area a Trapezoid?

A

Area of a Trapezoid = ((Base 1 + Base 2)/2) * (Height)

53
Q

What is the formula for Surface Area?

A

Surface Area = The Sum of the areas of ALL of the faces

54
Q

What is the formula for the volume of an object?

A

Volume = Length * Width * Height

55
Q

What are the commong right triangles (“Pyathagorean Triples”)

A
56
Q

What are the common ratios of an isosceles triangle?

A
57
Q

What are the ratios of a 30-60-90 Triangle?

A
58
Q

What are the ratios of a 45-45-90 Triangle?

A

x : x : x√x

59
Q

What makes up an exterior angle?

A

Exterior Angle = The sum of the two non adjacent (opposite) interior angles of the triangle

60
Q

What are the common right trianlges?

A
61
Q

What is the value of Pi

A

Approximately 3.14

62
Q

What is the formula for the volume of a cylinder?

A

V = πr2h

63
Q

What is the formula for slope?

A

Slope = Rise / Run

  • Slope of a line can be determined by taking any two points on the line and:
  1. Determining the rise, or difference between their y coordinates, and
  2. Determining the run, or the difference between their x-coordinates
64
Q

What are linear equations?

A

Linear equations represent lines in the coordinate plane

65
Q

What is the Slope Intercept form of a linear equation?

A

y = mx +b

  • m = Slope
  • b = y intercept (y coordinate where x = 0)
66
Q

What is the Combination Formula?

A

C(n,r) = n! / (r!(n-r)!)

n = Number of things your choosing from (pool)

r = Number of things chose (

Unlike Permutations, combinations not not have a required order. Permutations would be used for something like a race, whereas Combinations would be used to determining fruit or flower combinations

67
Q

What is the Work Formula?

A

Rate * Time = Work

68
Q

What is the formulat for the perimeter of a rectangle

A

P = 2(L+W)

69
Q

What is the diagonal of a cube?

A

The diagonal of a cube is √3

  • This can be found by applying the pythagorean theorem twice
    1. To find the diagonal of the face of a cube
    2. To find the diagonal through the center
70
Q

What is the volume of a cube?

A

Edge length to the 3rd power:

V = s3

71
Q

What is the Mode?

A

The mode is the observation that shows up the most often

  • (i.e. If you have 10 pieces of fruit, 4 apples, 3 pears, and 3 Bananas, Apples are the most as they appear most often)
72
Q

What is the the range of a data set?

A

The largest value - the smallest value

73
Q

What is the standard deviation

A

How far, on average, each data point is from the mean.

74
Q

What is a Units Digit?

A

Units digit of a number is the digit in the one’s place of the number. i.e It is the rightmost digit of the number. For example, the units digit of 243 is 3

75
Q

What should I immediately now when I see k3-k?

A

This represents 3 consecutive integers: (k – 1), k, and (k + 1)

  • If you factor k3-k out you get k(k2-1) then k(k + 1)(k – 1)
76
Q

What is the Simplified Combinatrics formula?

A

If n = 5 and r = 3,

  • rather than setting is up (5!) / (3! (5-3)!), which is (5*4*3*2*1) (3!(5-3)!)
  • you set it up as the first 3 factors of 5 / the factors of 3
    • 5*4*3 / (3*2*1)
    • We get the same result

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MANHATTAN PREP (9 decks)

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