Question 1
Ike and Mike go into a sandwich shop with a total of 
to spend. Sandwiches cost 
each and soft drinks cost 
each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?
Solution
Question 2
Three identical rectangles are put together to form rectangle 
, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 
feet, what is the area in square feet of rectangle ?
Solution
Question 3
Which of the following is the correct order of the fractions 
, 
, and 
, from least to greatest?
Solution
Question 4
Quadrilateral is a rhombus with perimeter 
meters. The length of diagonal 
is 
meters. What is the area in square meters of rhombus ?
Solution
Question 5
A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance 
traveled by the two animals over time 
from start to finish?
Solution
Question 6
There are 
grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point 
is in the center of the square. Given that point 
is randomly chosen among the other 
points, what is the probability that the line 
is a line of symmetry for the square?
Solution
Question 7
Shauna takes five tests, each worth a maximum of 
points. Her scores on the first three tests are 
, 
, and 
. In order to average for all five tests, what is the lowest score she could earn on one of the other two tests?
Solution
Question 8
Gilda has a bag of marbles. She gives 
of them to her friend Pedro. Then Gilda gives 
of what is left to another friend, Ebony. Finally, Gilda gives 
of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
Solution
Question 9
Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 
cm in diameter and 
cm high. Felicia buys cat food in cylindrical cans that are cm in diameter and cm high. What is the ratio of the volume one of Alex's cans to the volume one of Felicia's cans?
Solution
Question 10
The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and median values, Coach discovers that there were actually 
participants on Wednesday. Which of the following statements describes the change in the mean and median after the correction is made? 
The mean increases by 
and the median does not change.
The mean increases by and the median increases by .
The mean increases by and the median increases by .
The mean increases by and the median increases by .
The mean increases by and the median increases by .
Solution
Question 11
The eighth grade class at Lincoln Middle School has 
students. Each student takes a math class or a foreign language class or both. There are 
eighth graders taking a math class, and there are 
eight graders taking a foreign language class. How many eight graders take only a math class and not a foreign language class?
Solution
Question 12
The faces of a cube are painted in six different colors: red 
, white 
, green 
, brown 
, aqua 
, and purple 
. Three views of the cube are shown below. What is the color of the face opposite the aqua face?
Solution
Question 13
A palindrome is a number that has the same value when read from left to right or from right to left. (For example 12321 is a palindrome.) Let 
be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of ?
Solution
Question 14
Isabella has coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every 
days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?
Solution
Question 15
On a beach 
people are wearing sunglasses and 
people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is is also wearing sunglasses is 
. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
Solution
Question 16
Qiang drives 
miles at an average speed of 
miles per hour. How many additional miles will he have to drive at 
miles per hour to average miles per hour for the entire trip?
Solution
Question 17
What is the value of the product 
Solution
Question 18
The faces of each of two fair dice are numbered , 
, 
, , 
, and 
. When the two dice are tossed, what is the probability that their sum will be an even number?
Solution
Question 19
In a tournament there are six teams that play each other twice. A team earns points for a win, point for a draw, and 
points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?
Solution
Question 20
How many different real numbers 
satisfy the equation 
Solution
Question 21
What is the area of the triangle formed by the lines 
, 
, and 
?
Solution
Question 22
A store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. Given that the resulting price was 
of the original price, by what percent was the price increased and decreased?
Solution
Question 23
After Euclid High School's last basketball game, it was determined that 
of the team's points were scored by Alexa and 
were scored by Brittany. Chelsea scored points. None of the other team members scored more than points What was the total number of points scored by the other team members?
Solution
Question 24
In triangle 
, point 
divides side so that 
. Let 
be the midpoint of 
and let 
be the point of intersection of line 
and line 
. Given that the area of 
is 
, what is the area of 
?
Solution
Question 25
Alice has apples. In how many ways can she share them with Becky and Chris so that each of the people has at least apples?
Solution
Answer Keys
Question 1: D
Question 2: E
Question 3: E
Question 4: D
Question 5: B
Question 6: C
Question 7: A
Question 8: E
Question 9: B
Question 10: B
Question 11: D
Question 12: A
Question 13: A
Question 14: C
Question 15: B
Question 16: D
Question 17: B
Question 18: C
Question 19: C
Question 20: D
Question 21: E
Question 22: E
Question 23: B
Question 24: B
Question 25: C