¶ 2003 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 2003 AMC8 problems here.
Discussion Forum
Engage in discussion about the 2003 AMC8 math contest by visiting Random Math 2003 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2003 AMC8 problems, please refer below:
Problem 1: Jamie counted the number of edges of a cube, Jimmy counted the number of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 2: Which of the following numbers has the smallest prime factor?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 3: A burger at Ricky C's weighs grams, of which grams are filler. What percent of the burger is not filler?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 4: A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted children and wheels. How many tricycles were there?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 5: If of a number is , what is of the same number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 6: Given the areas of the three squares in the figure, what is the area of the interior triangle?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
22
View Solution
Problem 7: Blake and Jenny each took four -point tests. Blake averaged on the four tests. Jenny scored points higher than Blake on the first test, points lower than him on the second test, and points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 8: Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
- Art's cookies are trapezoids:
.jpg)
- Roger's cookies are rectangles:
.jpg)
- Paul's cookies are parallelograms:
- Trisha's cookies are triangles:
.jpg)
Each friend uses the same amount of dough, and Art makes exactly cookies.
Who gets the fewest cookies from one batch of cookie dough?
Answer Choices:
A. Art
B. Paul
C. Roger
D. Trisha
E. There is a tie for fewest.
Solution:
Problem 9: Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
- Art's cookies are trapezoids:
- Roger's cookies are rectangles:
- Paul's cookies are parallelograms:
- Trisha's cookies are triangles:
Each friend uses the same amount of dough, and Art makes exactly cookies.
Art's cookies sell for each. To earn the same amount from a single batch, how much should one of Roger's cookies cost?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 10: Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
- Art's cookies are trapezoids:
- Roger's cookies are rectangles:
- Paul's cookies are parallelograms:
- Trisha's cookies are triangles:
Each friend uses the same amount of dough, and Art makes exactly cookies.
How many cookies will be in one batch of Trisha's cookies?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 11: Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by . Over the weekend, Lou advertises the sale: "Ten percent off the listed price. Sale starts Monday." How much does a pair of shoes cost on Monday that cost on Thursday?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 12: When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 13: Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 14: In this addition problem, each letter stands for a different digit.
If and the letter represents an even number, what is the only possible value for
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 15: A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 16: Ali, Bonnie, Carlo and Dianna are going to drive together to a nearby theme park. The car they are using has four seats: one driver's seat, one front passenger seat and two back seats. Bonnie and Carlo are the only two who can drive the car. How many possible seating arrangements are there?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 17: The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?
Answer Choices:
A. Nadeen and Austin
B. Benjamin and Sue
C. Benjamin and Austin
D. Nadeen and Tevyn
E. Austin and Sue
Solution:
Problem 18: Each of the twenty dots on the graph below represents one of Sarah's classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah's party?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 19: How many integers between and have all three of the numbers and as factors?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 20: What is the measure of the acute angle formed by the hands of a clock at a.m.?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 21: The area of trapezoid is . The altitude is is , and is . What is , in centimeters?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 22: The following figures are composed of squares and circles. Which figure has a shaded region with largest area?
.jpg)
Answer Choices:
A. only
B. only
C. only
D. both and
E. all are equal
Solution:
Problem 23: In the pattern below, the cat moves clockwise through the four squares and the mouse moves counterclockwise through the eight exterior segments of the four squares.
.jpg)
If the pattern is continued, where would the cat and mouse be after the th move?
Answer Choices:
A.
.jpg)
.jpg)
.jpg)
.jpg)
Solution:
Problem 24: A ship travels from point to point along a semicircular path, centered at Island . Then it travels along a straight path from to . Which of these graphs best shows the ship's distance from Island as it moves along its course?
Answer Choices:
A.
Solution:
Problem 25: In the figure, the area of square is . The four smaller squares have sides long, either parallel to or coinciding with the sides of the large square. In , and when is folded over side , point coincides with , the center of square . What is the area of , in square centimeters?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions