Number Properties

Question 0

An integer is divisible by 4 if

Answer 0

The last two digits are divisible by 4

Question 1

An integer is divisible by 3 if

Answer 1

The sum of its digits is divisible by 3

Question 2

An integer is divisible by 6 if

Answer 2

It is divisible by both 2 and 3

Question 3

An integer is divisible by 8 if

Answer 3

The last 3 digits are divisible by 8

Question 4

An integer is divisible by 9 if

Answer 4

The sum of the integers digits is divisible by 9

Question 5

Given that integer n is divisible by 3,7 and 11, what other factors must be divisors of n?

Answer 5

N must also be divisible by all possible products of 3, 7 and 11:

21, 33, 77, and 231

Question 6

What is the least common multiple of 18 and 24?

Answer 6

72

Question 7

If the sum or product of two primes is even…

Answer 7

One of the numbers must be 2

Question 8

Algebraic form of even number

Answer 8

2n

n = any integer

Question 9

Algebraic form of odd number

Answer 9

2n + 1 or 2n - 1

Question 10

Is zero a digit?
Is zero even?
Is zero an integer?
0! = ?

Answer 10

Zero is a digit
Zero is an even integer
0! = 1

Question 11

Remainder formula

Answer 11

(5/2) = 2 + (1/2)

Dividend/Divisor = Quotient + (Remainder/ Divisor)

Question 12

First 10 prime numbers

Answer 12

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

Question 13

Standard set of numbers for testing

Answer 13

Every integer and half integer btw -2 and 2:

{-2,-3/2,-1,0,1/2,1,3/2,2}

Question 14

(Even) + (even) =

Answer 14

Even

Question 15

(Odd) + (odd) =

Answer 15

Even

Question 16

(Even) + (odd) =

Answer 16

Odd

Question 17

(Even) x (even) =

Answer 17

Even

Question 18

(Odd) x (odd) =

Answer 18

Odd

Question 19

(Even) x (odd) =

Answer 19

Even

Question 20

If two numbers have no primes in common (greatest common factor and least common multiple)

Answer 20

then their GCF is 1 and their LCM is simply their product

Question 21

First multiple of any number

Answer 21

Is zero.

Question 22

If a + b is even, what is ab?

Answer 22

Cannot be determined.

A and b are both even or both odd

Question 23

If c,d,e are consecutive integers, what is cde?

Answer 23

Even (group must have at least one even)

Question 24

Molly is rolling a number cube cube with faces 1 to 6. She will stop when she receives a 1. What is probability that Molly will roll the die less than 4 times before stopping?

Answer 24

91/216

Question 25

Six people are going to the movies together and will sit in 6 adjacent seats. If two of them will not sit next to each other, in how many arrangements can the six ppl sit?

Answer 25

Use glue method.

First, ignore constraint: 6! = 720

Imagine 2 ppl are stuck together, now effectively 5 ppl. 5! = 120
Multiply by 2 to account for order =240

720 - 240 = 480

Question 26

What is the greatest integer k for which 3^k is a factor of p? Translation:

Answer 26

…how many 3’s are there in p?

Question 27

Order least to greatest:

.345

Sq rt (.346)

(.345)^2

Answer 27

Smallest: (.345)^2

2nd: .345

Largest: sq rt (.345)