Math Competition - Phase 3

The sum of three consecutive odd numbers is 111. What is the largest of the three?

• 35

• 37

• 39

• 38

• 43

A cube has all faces painted. It is then cut into 64 smaller cubes. How many of the smaller cubes have exactly one face painted?

• 8

• 24

• 36

• 48

• 54

What is the 100th term of the sequence: 2, 6, 12, 20, 30, ...?

• 5050

• 10,100

• 5025

• 5150

• 5000

• 2

• 4

• None of the previuos

You have 3 red, 4 blue, and 5 green balls. How many ways can you choose 2 balls of different colors?

• 26

• 34

• 35

• 38

• 40

A fair die is rolled three times. What is the probability that the total is exactly 10?

You multiply four consecutive integers. Which of the following must always be true?

• The product is even

• Divisible by 4

• Divisible by 24

• Divisible by 8

• A square number

• 3

• 7

• 9

• 1

What comes next in the sequence? 1, 1, 2, 3, 5, 8, 13, ___

• 18

• 20

• 21

• 22

In how many ways can 5 books be arranged on a shelf if 2 particular books must always be together?

• 60

• 120

• 48

• 72

• 96