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Question 1

How many permutations of n objects?

Answer 1

n! (“n factorial”)

Question 2

How many combinations of size r taken from a set of n objects?

Answer 2

n! / ( r! (n-r)! )

Question 3

How many permutations of size r taken from a set of n objects?

Answer 3

n! / ( (n-r)! )

Question 4

Is the sum / difference of two numbers odd or even?

Answer 4

Even if the numbers are both odd or both even, otherwise odd.

Question 5

45 - 45 - 90 triangles have lengths of sides in ratio …

Answer 5

45 - 45 - 90 triangle has lengths of side in ratio 1 : 1 : sqrt (2)

Question 6

30 - 60 - 90 triangles have lengths of sides in ratio …

Answer 6

30 - 60 - 90 triangles have lengths of sides in ratio 1 : sqrt(3) : 2

Question 7

x + y | …

Answer 7

x + y | <= | x | + | y |

Question 8

If a triangle is inscribed in a circle such that one of its sides is a diameter of the circle then …

Answer 8

If a triangle is inscribed in a circle such that one of its sides is a diameter of the circle then IT IS A RIGHT TRIANGLE

Question 9

Work formula:

Answer 9

1/r + 1/s = 1/h Where r is the time for r to complete the job alone, s is the time for s to complete the job alone, and h is the time for them to complete the job together.

Question 10

Compound interest formula

Answer 10

FutureValue = PresentValue (1 + InterestPerPeriod)^(NumberOfPeriods)

Question 11

Normal distribution. x% of values are within [1 / 2 / 3] standard distributions of the mean

Answer 11

About 68% of the values are within 1 standard deviation of the mean. About 95% of the values are within 2 standard deviations of the mean. About 99.7% of the values are within 3 standard deviations of the mean.

Question 12

How to find the lowest common multiple?

Answer 12

Union of the two sets of prime factors

Question 13

How to find the greatest common factor?

Answer 13

Take the intersection of the sets of prime factors

Question 14

To list all of the factors of a number…

Answer 14

List the factor pairs

Question 15

How many factors does a square number have?

Answer 15

3

Question 16

Area of an equilateral triangle

Answer 16

Question 17

Simple interest

Answer 17

Total = Principal * Rate * Number of periods

Question 18

Sum of consecutive integers up to and including n

Answer 18

Question 19

When numbers in a set are consecutive, the mean is equal to:

Answer 19

The median of the set

Question 20

Pythagorean triplets

Answer 20

3:4:5 and 5:12:13

Question 21

Unknown multiplier for ratio a:b

Answer 21

a * x + b * x = total amount

Question 22

Two parallelogram facts

Answer 22

1. Two adjacent angles of a parallelogram = 180 degrees
2. Two opposite angles of a parallelogram are equal

Question 23

For any evenly spaced set, the mean of the set is always equal to…

Answer 23

…the median

Question 24

An isoceles triangle has…

Answer 24

… at least 2 sides of equal length

Question 25

Probability formula

Answer 25

P(A or B) = P(A) + P(B) - P(A and B)

Question 26

When adding a to the numerator and b to the denominator of a fraction…

Answer 26

… the resultant fraction will be closer to a/b than the initial fraction

Question 27

In a triangle the largest angle is opposite…

Answer 27

… the longest side

Question 28

Remainder rule. x / y =

Answer 28

x / y = Q + R / y

Question 29

Rule for divisibility by 3

Answer 29

If the sum of all digits is divisible by 3, the number is divisible by 3

Question 30

Rule for divisibility by 4

Answer 30

Take the last 2 digits of the number. If they’re divisible by 4, then so is the whole number

Question 31

Rule for divisiblity by 6

Answer 31

Divisible by 6 if the number is divisible by 3 & 2, i.e.:

1. Is even
2. Sum of digits divisible by 3

Question 32

Rule for divisibility by 9

Answer 32

Divisible by 9 if sum of digits divisible by 9