Question 1
How many square yards of carpet are required to cover a rectangular floor that is 
feet long and 
feet wide? (There are 
feet in a yard.)
Solution
Question 2
Point 
is the center of the regular octagon 
, and 
is the midpoint of the side 
What fraction of the area of the octagon is shaded?
Solution
Question 3
Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of 
miles per hour. Jack walks to the pool at a constant speed of 
miles per hour. How many minutes before Jack does Jill arrive?
Solution
Question 4
The Dragonvale Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible?
Solution
Question 5
Billy's basketball team scored the following points over the course of the first 
games of the season: 
If his team scores 40 in the 12th game, which of the following statistics will show an increase?
Solution
Question 6
In 
, 
, and 
. What is the area of ?
Solution
Question 7
Each of two boxes contains three chips numbered 
, 
, . A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?
Solution
Question 8
What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19?
Solution
Question 9
On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working 
days?
Solution
Question 10
How many integers between 
and 
have four distinct digits?
Solution
Question 11
In the small country of Icosahedrontopia, all automobile license plates have four symbols. The first must be a vowel (
or 
), the second and third must be two different letters among the 
non-vowels, and the fourth must be a digit (
through ). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read "
"?
Solution
Question 12
How many pairs of parallel edges, such as 
and 
or 
and 
, does a cube have?
Solution
Question 13
How many subsets of two elements can be removed from the set 
so that the mean (average) of the remaining numbers is 
?
Solution
Question 14
Which of the following integers cannot be written as the sum of four consecutive odd integers?
Solution
Question 15
At Euler Middle School, 
students voted on two issues in a school referendum with the following results: 
voted in favor of the first issue and 
voted in favor of the second issue. If there were exactly 
students who voted against both issues, how many students voted in favor of both issues?
Solution
Question 16
In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If 
of all the ninth graders are paired with 
of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?
Solution
Question 17
Jeremy's father drives him to school in rush hour traffic in minutes. One day there is no traffic, so his father can drive him 
miles per hour faster and gets him to school in minutes. How far in miles is it to school?
Solution
Question 18
An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, 
is an arithmetic sequence with five terms, in which the first term is and the constant added is . Each row and each column in this 
array is an arithmetic sequence with five terms. What is the value of ?
Solution
Question 19
A triangle with vertices as 
, 
, and 
is plotted on a 
grid. What fraction of the grid is covered by the triangle?
Solution
Question 20
Ralph went to the store and bought pairs of socks for a total of 
. Some of the socks he bought cost 
a pair, some of the socks he bought cost 
a pair, and some of the socks he bought cost 
a pair. If he bought at least one pair of each type, how many pairs of socks did Ralph buy?
Solution
Question 21
In the given figure hexagon 
is equiangular, 
and 
are squares with areas and 
respectively, 
is equilateral and 
. What is the area of 
?
Solution
Question 22
On June , a group of students are standing in rows, with 
students in each row. On June , the same group is standing with all of the students in one long row. On June , the same group is standing with just one student in each row. On June , the same group is standing with students in each row. This process continues through June with a different number of students per row each day. However, on June 
, they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?
Solution
Question 23
Tom has twelve slips of paper which he wants to put into five cups labeled 
, 
, 
, 
, 
. He wants the sum of the numbers on the slips in each cup to be an integer. Furthermore, he wants the five integers to be consecutive and increasing from to . The numbers on the papers are 
and 
. If a slip with goes into cup and a slip with goes into cup , then the slip with 
must go into what cup?
Solution
Question 24
A baseball league consists of two four-team divisions. Each team plays every other team in its division 
games. Each team plays every team in the other division 
games with 
and 
. Each team plays a 
-game schedule. How many games does a team play within its own division?
Solution
Question 25
One-inch squares are cut from the corners of this 
inch square. What is the area in square inches of the largest square that can fit into the remaining space?
Solution
Answer Keys
Question 1: A
Question 2: D
Question 3: D
Question 4: E
Question 5: A
Question 6: B
Question 7: E
Question 8: D
Question 9: D
Question 10: B
Question 11: B
Question 12: C
Question 13: D
Question 14: D
Question 15: D
Question 16: B
Question 17: D
Question 18: B
Question 19: A
Question 20: D
Question 21: C
Question 22: C
Question 23: D
Question 24: B
Question 25: C