Difference between revisions of "2003 AMC 8 Problems"
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Revision as of 15:52, 29 July 2011
Contents
 1 Problem 1
 2 Problem 2
 3 Problem 3
 4 Problem 4
 5 Problem 5
 6 Problem 6
 7 Problem 7
 8 Bake Sale
 9 Problem 11
 10 Problem 12
 11 Problem 13
 12 Problem 14
 13 Problem 15
 14 Problem 16
 15 Problem 17
 16 Problem 18
 17 Problem 19
 18 Problem 20
 19 Problem 21
 20 Problem 22
 21 Problem 23
 22 Problem 24
 23 Problem 25
Problem 1
Jamie counted the number of edges of a cube, Jimmy counted the numbers of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?
Problem 2
Which of the following numbers has the smallest prime factor?
Problem 3
A burger at Ricky C's weighs grams, of which grams are filler. What percent of the burger is not filler?
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?
Problem 5
If of a number is , what is of the same number?
Problem 6
Given the areas of the three squares in the figure, what is the area of the interior triangle?
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?
Bake Sale
Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures
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:
Problem 8
Who gets the fewest cookies from one batch of cookie dough?
Problem 9
Each friend uses the same amount of dough, and Art makes exactly cookies. Art's cookies sell for cents each. To earn the same amount from a single batch, how much should one of Roger's cookies cost in cents?
Problem 10
How many cookies will be in one batch of Trisha's cookies?
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 $10%$ (Error compiling LaTeX. ! Missing $ inserted.). 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 dollars on Thursday?
Problem 12
When a fair sixsided 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 6?
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?
Problem 14
In this addition problem, each letter stands for a different digit.
$\setlength{\tabcolsep}{0.5mm}\begin{array}{cccc}&T & W & O\\ \plus{} &T & W & O\\ \hline F& O & U & R\end{array}$ (Error compiling LaTeX. ! Undefined control sequence.)
If T = 7 and the letter O represents an even number, what is the only possible value for W?
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?
Problem 16
Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has seats: Driver seat, front passenger seat, and back passenger seat. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there?
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?
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?
Problem 19
How many integers between and have all three of the numbers , , and as factors?
Problem 20
What is the measure of the acute angle formed by the hands of the clock at PM?
Problem 21
The area of trapezoid is . The altitude is , is , and is . What is , in centimeters?
Problem 22
The following figures are composed of squares and circles. Which figure has a shaded region with largest area?
Problem 23
In the pattern below, the cat (denoted as a large circle in the figures below) moves clockwise through the four squares and the mouse (denoted as a dot in the figures below) moves counterclockwise through the eight exterior segments of the four squares.
If the pattern is continued, where would the cat and mouse be after the 247th move?
Problem 24
A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight path from B to C. Which of these graphs best shows the ship's distance from Island X as it moves along its course?
Problem 25
In the figure, the area of square WXYZ is . The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In , , and when is folded over side BC, point A coincides with O, the center of square WXYZ. What is the area of , in square centimeters?