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1
Q

Mean

A

Mean = Average(sum of terms)/(no. of terms)

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2
Q

Median

A

Median = Middle value

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3
Q

Mode

A

Mode = most frequently occurring value

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4
Q

Range

A

Range = difference between largest and smallest values

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5
Q

Standard Deviation

A

S.D. = the measure of dispersion around the mean

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6
Q

Finding Median

A
  • place all the numbers in a set in an ascend/descend order to locate the middle value
  • if odd number of terms -> median is the middle number
  • if even number of terms -> median is the two middle terms divided by 2 (average of two middle terms)
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7
Q

Which of the following could be the range of the following set: {-21, 23, x, y, z}
I. -54
II. 40
III. 63

A
  • range cannot be negative –> eliminate I
  • based on the present two values, the range would be 23 - (-21) = 44 range could be larger than 44 but can’t be less –> eliminate II
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8
Q

Can the range be negative?

A

No; range can only be positive

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9
Q

If the range is = 0, all the numbers in the set are _____

A

If the range is = 0, all the numbers in the set are identical

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10
Q

How does changing any values other than the smallest and largest affect the range?

A

Changing any values other than the smallest and largest does not affect the range

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11
Q

For the set {1, 2, 3, 4, 5}

1) what is the mean
2) what is the median
3) what is the range

A

For the set {1, 2, 3, 4, 5}

1) mean = (1+2+3+4+5)/5 = 3
2) median = 3
3) range = 5-1 = 4

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12
Q

In evenly spaced sets, what’s the relationship between mean and median? How do we find them?

A

In evenly spaced sets, the mean and median are equal

to find both quickly, average the first and the last terms

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13
Q

Finding mean in an evenly spaced set {1, 2, 3, 4, 5}

A

1) mean = (1+2+3+4+5)/5 = 3

alternative: (1+5)/2 = 3

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14
Q

For the set {3, 1, 2, 3, 4, 5}

1) what is the mean
2) what is the median
3) what is the mode
4) what is the range
5) is the SD higher or lower than in the {1, 2, 3, 4, 5} set?

A

For the set {3, 1, 2, 3, 4, 5}

0) rearrange: {1, 2, 3, 3, 4, 5}
1) mean = 3
2) median = 3
3) mode = 3
4) range = 4
5) is the SD higher or lower than in the {1, 2, 3, 4, 5} set?new term = mean -> no added variation; BUT the AVERAGE variation is lower

this set has a smaller SD

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15
Q

Which of the following sets has the greatest SD?

I. {2, 4, 6, 8, 10}
II. {3, 6, 9, 12, 15}
III. {52, 54, 56, 58, 60}

A

I. mean = 6
II. mean = 9
III. mean = 56

set II has the highest dispersion around the mean (spacing is 3) sets

I and III have the same SD (in both sets, highest value is 4 > mean)

size of the terms is not important, just the difference from the mean

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16
Q

Set J consists of the first (smallest) seven prime numbers. Find:- mean- median- range

A

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

mean = 2+3+5+7+11+13+17 = 30+10+18= 58/7= 8 2/7

median = 7

range = 15

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17
Q

How to reduce the mean?

A

add a values that’s less than the current mean

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18
Q

How to reduce the median?

A

add a value that’s less than the current median

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19
Q

If the highest and lowest values of the set are unchanged, can the range change?

A

No, the range will only change if there’s a change to the highest or the lowest values

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20
Q

What’s the relationship between median and mean?

A

Generally, no relationship

in evenly spaced sets -> mean = median

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21
Q

If set A {2, x, y, z, 24} is evenly spaced and in ascending order, what is the value of y?

A

y = median = mean (24+2)/2 = 13y= 13

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22
Q

If the number of terms does not change, what’s the relationships between % change in average and % change in sum

A

% change in average = % change in sum

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23
Q

Rasheed scored 22, 16, 12, 14, 21 points in 5 games. His actual average was what percent less than his goal of averaging 20 points per game?

A

goal: 20 points per game = 20*5 = 100 points

actual sum = 85 points

percentage difference: (85-100)/100 * 100 = -15%

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24
Q

Area of circle

A

A = pi * r^2

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25
Circumference of circle
C = 2*pi*r
26
simple interest formula
A = P(1 + rt)
27
Area of a TRIANGLE
(Base x Height) / 2
28
Area of a RECTANGLE
Length x Width
29
Area of a TRAPEZOID
((Base1 + Base 2) x Height) / 2
30
Area of a PARALLELOGRAM
Base x Height
31
Area of a RHOMBUS
(Diagonal 1 x Diagonal 2) / 2
32
Surface Area
the SUM of the areas of all of the faces
33
Surface Area of a Rectangular Solid
2(Base x Height) + 2 (Width x Height) + 2 (Base x Width)
34
surface area of a cube
6 x (Side)²
35
Volume =
Length x Width x Height
36
Volume of a Cube
Side³
37
How many Books, each with a volume of 100 in³, can be packed into a crate with a volume of 5,000 in³?
if you are fitting 3 dimensional objects into other 3-dimensional objects, knowing the respective volumes is not enough You cannot answer to this question without knowing the exact dimensions of each book.
38
The sum of the three angles of a triangle equals
180
39
The sum of any two sides of a triangle MUST BE _______ the third side. So, if you are given two sides of a triangle, the length of the third side must lie _________ of the two given sides
GREATER than the third side between the difference and the sum
40
Common Right Triangles
3-4-5 and its key multiples: 6-8-10, 9-12-15, 12-16-20 5-12-13 and its key multiples: 10-24-26 8-15-17
41
isosceles triangle
isosceles triangle is a triangle that has two sides of equal length
42
45-45-90 triangle
2 equal sides and a relation between each side If you are given one dimension on a 45-45-90 triangle, you can find the others
43
Relationship between sides of a 45-45-90 triangle
1: 1: √2
44
if you are given the diagonal of a square, how can you find the sides?
from properties of 45-45-90 triangle: 1: 1: √2 if you know the diagonal, you can find the sides by using this ratio
45
Equilateral Triangles
equilateral triangle is a triangle in which all three sides have the same length
46
30-60-90 ratio
The basic 30-60-90 triangle ratio is: Side opposite the 30° angle: x Side opposite the 60° angle: x*√3 Side opposite the 90° angle: 2x
47
diagonal of a square
d = side * √2
48
Main Diagonal of a Cube
d = side * √3
49
To find the diagonal of a rectangle, you must know
either both sides or the length of one side and the proportion from this to the other side
50
To find the diagonal of a rectangular solid, if you know the 3 dimensions
you can use pythagorean theorem twice 1) use pythagorean theorem with the length and the width to find the diagonal of the bottom face. 2) use pythagorean theorem again to find the main diagonal. The sides for this second pythagorean will be: the height, the bottom face diagonal and the main diagonal
51
inscribed angle
equal to half of the degree measure of the arc that it intercepts
52
What is the percent formula?
Part = Percent x Whole
53
How much is 15 percent of 20?
15% of 20 is: 15/100 * 20 = 300/100 = 3
54
Percent Change Formula
(new - old) / old * 100 which is (amount of change) / original amount * 100
55
``` If the production of hybrid cars tripled last year, by how many percent did it increase? A 100% B 200% C 250% D 300% E 333% ```
The correct answer is B – increased by 200% For example, if production was 10 cars, and it tripled to 30 cars, the increase was 20 cars, which is 200% of 10
56
50% of 25 is 25% of which number?
1) Long solution: 50% of 25 is 12.5 12.5 *100 = x * 25 x = 50 2) Short solution but a harder to come up with: 50% * 25 = x * 25% 50 = x
57
Odd + Odd =
Odd + Odd = even
58
Odd – Even =
Odd – Even = odd
59
Even + Odd =
Even + Odd = odd
60
odd x odd =
odd x odd = odd
61
Odd ÷ Even =
not an integer
62
Odd x Even
even
63
Is 0 odd or even?
0 (zero) is Even
64
Is 0 positive or negative?
It is not positive or negative | – it is neutral
65
Is 0 an integer
Yes
66
Is 54780 divisible by 2?
Yes. Divisibility by 2 – last digit of a number is even
67
Is 1671 divisible by 3?
Yes. Divisibility by 3 – sum of all digits is a multiple | of 3
68
Is 5632 divisible by 4?
Yes. Divisibility by 4 – last 2 digits is a multiple of 4
69
Is 3830 divisible by 5?
Yes. Divisibility by 5 – the last digit is either 0 or 5
70
Is 2658 divisible by 6?
Yes. Divisibility by 6 – the sum of digits is a multiple | of 3 and the last digit is even
71
Is 396 divisible by 9?
Yes. Divisibility by 9 – the sum of digits is a multiple | of 9
72
``` Which of the following integers represents a sum of 3 consecutive even integers? - 200 - 303 - 400 - 554 - 570 ```
To answer the question, check which integer is both divisible by 3 (since there are 3 integers) and is even. The only number that falls into both of those 2 categories is 570. Correct answer is E
73
How many distinct integers are | there between 1 and 21 inclusive?
Most often GMAT questions will say “inclusive” but sometimes they don’t – need to remember to check The formula for calculating the number of integers between two numbers is: N-M+1 Therefore, the answer is: 21 – 1 + 1 = 21 You can also write out all of the numbers though it is not always possible but just in case: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
74
What is a multiple?
The multiple of a number is the product of the number and any other whole number. (For example, 2,4,6,8 are multiples of 2)
75
Is 5 a multiple of 55 or is 55 a | multiple of 5?
55 is a multiple of 5
76
Is 0 (zero) a multiple of 100?
Yes, 0 (zero) is a multiple of everything However, it is unlikely that GMAT will test this property but it helps to remember
77
How to find a Least Common Multiple (LCM)?
Option 1: Step 1: Find the prime factors of each of the numbers Step 2: Multiply the unique factors (exclude duplicates) Option 2: Step 1: Multiply the two numbers Step 2: Find any factors the two numbers share Step 3: Divide the product in Step 1 by the factors that the two numbers have in common
78
What is the Least Common Multiple of 18 and 24?
``` 18 = 2 x 3 x 3 24 = 2 x 3 x 2 x 2 ``` Multiply unique factors: 2 x 3 x 3 x 2 x 2 = 72
79
1/2 =
1/2 = 50%
80
1/4 =
1/4 = 25%
81
2/5 =
2/5 = 40%
82
1/20 =
1/20 = 5%
83
1/8 =
1/8 = 12.5%
84
1/6 =
1/6 = 16.67%
85
Are permutations ordered or unordered?
Ordered
86
Combination or Permutation? Seating arrangement
ordered, permutation
87
Combination or Permutation? Passwords
ordered, permutation
88
Combination or Permutation? finishing sequences in a competition
ordered, permutation
89
Combination or Permutation? hands of cards
unordered, combination
90
Combination or Permutation? teams
unordered, combination
91
Combination vs Permutation
permutation -> changing the order creates a new arrangement | combination -> changing the order does not create a new arrangement
92
Determining if a counting problem is a permutation or a combination
If i change the order, would the new arrangement be considered distinct?
93
How to find the number of possible arrangements in most counting problems?
multiply the number of choices for each available spot in the arrangement
94
formula for counting the number of consecutive integers in a set that includes the first and last numbers
highest number - lowest number +1 `
95
how many multiples of 2 are there between 51 and 99, inclusive?
((highest # divisible by the given number - lowest # divisible by the given number)/given number) + 1 ((98 - 52)/2) + 1 23 +1 = 24
96
how many multiples of 3 are there between 17 and 41, inclusive?
((39-18)/3) + 1 | 7+1 = 8
97
count the number of consecutive integers that includes only one of its endpoints, but not both
last number - first number
98
tom is 10th in line, sara is 50th in line; how many people are there from tom to sara, including tom but not sara
50 - 40 = 10
99
tom is 10th in line, sara is 50th in line; how many people are there between tom and sara
50 - 40 - 1 = 39
100
how to find the number of terms between two numbers in a consecutive set of integers?
subtract the first number from the last number, and then subtract 1 from the difference last number - first number - 1
101
what is the average of all three-digit numbers?
100 + 999 = 1099 1099/2=549.5
102
what is the sum of the integers from 101 to 202, inclusive?
sum = average * #of terms average = (101+202)/2 = 151.5 number of terms = 202-101 +1 = 102 sum = 151.5 * 103 = 15453
103
what is the sum of the odd integers from 5 to 55, inclusive
``` avg = sum/# sum = avg * #of terms ``` 5 to 55 - evenly spaced set (55+5)/2 = 30 (avg) number of numbers ((55-5)/2) +1 -> 26 numbers 26*30 = 780 (sum)
104
weighted average formula
(sum of weighted terms)/(total number of weighted terms)
105
volume of a cylinder
volume = pi * r^2 * h
106
two events are complementary if and only if
they are the only two possibilities that can occur
107
formula for complementary events
P(A) + P(not A) = 1
108
"and" in probability means
multiply
109
probability formula for two independent events A and B
P(A and B) = P(A) * P(B)
110
probability formula for two dependent events A and B
P(A and B) = P(A) * P(B|A) P(A and B) - probability that both event A and B will occur P(A) - probability that event A will occur P(B|A) - probability that B will occur given that A has already occurred
111
mutually exclusive events
cannot occur at the same time
112
formula for calculating probability of mutually exclusive events
P(A or B) = P(A) + P(B)
113
formula for calculating probability of event A or B occurring when A and B are not mutually exclusive
P(A or B) = P(A) + P(B) - P(A and B)

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