Question 1

Each of the six students Glenda, Helga, Ioana, Julia, Karl, and Liu had a different number on their uniform from the list

11, 12, 13, 14, 15, 16

. Helga's and Julia's numbers were even. Karl's and Liu's numbers were prime. Glenda's number was a perfect square. What was Ioana's number?

Accepted Answer

15

Answer

13

Answer

14

Answer

12

Question 2

At a potluck, the ratio of vegetarians to non-vegetarians is

11, 12, 13, 14, 15, 16

. If there are

21

vegetarians at the potluck, what is the total number of people at the potluck?

Accepted Answer

49

Answer

28

Answer

63

Answer

35

Question 3

The average (mean) of a list of

11, 12, 13, 14, 15, 16

numbers is

21

. When one number is removed from the list, the new average is

18

. What number was removed?

Accepted Answer

30

Answer

26

Answer

32

Answer

22

Question 4

How many of the integers from 1 to 100, inclusive, have at least one digit equal to 6?

Accepted Answer

19

Answer

18

Answer

10

Answer

20

Question 5

If

11, 12, 13, 14, 15, 16

is a positive integer, the notation

21

(factorial) represents the product of the integers from

18

to

n

. If

n! = 2^4 	imes 3^2 	imes 5 	imes 7

, what is the value of

n

?

Accepted Answer

7

Answer

8

Answer

5

Answer

6

Question 6

Suppose that

11, 12, 13, 14, 15, 16

and

21

are two different prime numbers and that

18

. If

n

, how many possible values of

n! = 2^4 	imes 3^2 	imes 5 	imes 7

are there?

Accepted Answer

14

Answer

13

Answer

12

Answer

15

Question 7

When the numbers

11, 12, 13, 14, 15, 16

,

21

,

18

,

n

, and

n! = 2^4 	imes 3^2 	imes 5 	imes 7

are arranged in increasing order, which number is in the middle?

Accepted Answer

Answer

Answer

Answer

Question 8

On February 1, it was

11, 12, 13, 14, 15, 16

outside Jacinta’s house at 3:00 p.m. On February 2, it was

21

outside at 2:00 a.m. If the temperature changed at a constant rate between these times, what was the rate at which the temperature decreased in

18

?

Accepted Answer

2.27

Answer

2.50

Answer

1.92

Answer

2.08

Question 9

Five balls, numbered

11, 12, 13, 14, 15, 16

to

21

, are placed in order on a table. In step 1, the rightmost ball is picked up and put in the middle of the four remaining balls:

18

. In step 2, the leftmost ball is picked up and put in the middle of the four remaining balls:

n

. If this pattern continues (alternating rightmost then leftmost), what is the order of the balls after step 4?

Accepted Answer

1, 2, 3, 4, 5

Answer

5, 4, 3, 2, 1

Answer

4, 3, 1, 2, 5

Answer

2, 1, 4, 3, 5

Question 10

Suppose that

11, 12, 13, 14, 15, 16

and

21

are different prime numbers such that

18

. What is the value of the product

n

?

Accepted Answer

58

Answer

210

Answer

150

Answer

84

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