ΒΆ 2006 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 2006 AMC8 problems here.
Discussion Forum
Engage in discussion about the 2006 AMC8 math contest by visiting Random Math 2006 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2006 AMC8 problems, please refer below:
Problem 1: Mindy made three purchases for and . What was her total, to the nearest dollar?
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Problem 2: On the contest Billy answers questions correctly, answers questions incorrectly and doesn't answer the last . What is his score?
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Problem 3: Elisa swims laps in the pool. When she first started, she completed laps in minutes. Now she can finish laps in minutes. By how many minutes has she improved her lap time?
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Problem 4: Initially, a spinner points west. Chenille moves it clockwise revolutions and then counterclockwise revolutions. In what direction does the spinner point after the two moves?
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Problem 5: Points and are midpoints of the sides of the larger square. If the larger square has area , what is the area of the smaller square?
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Problem 6: The letter is formed by placing two inch inch rectangles next to each other, as shown. What is the perimeter of the , in inches?
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Problem 7: Circle has a radius of . Circle has a circumference of . Circle has an area of . List the circles in order from smallest to largest radius.
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Problem 8: The table shows some of the results of a survey by radio station KAMC. What percentage of the males surveyed listen to the station?
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Problem 9: What is the product of
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Problem 10: Jorge's teacher asks him to plot all the ordered pairs of positive integers for which is the width and is the length of a rectangle with area . What should his graph look like?
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Problem 11: How many two-digit numbers have digits whose sum is a perfect square?
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Problem 12: Antonette gets on a -problem test, on a -problem test and on a -problem test. If the three tests are combined into one -problem test, which percent is closest to her overall score?
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Problem 13: Cassie leaves Escanaba at AM heading for Marquette on her bike. She bikes at a uniform rate of miles per hour. Brian leaves Marquette at AM heading for Escanaba on his bike. He bikes at a uniform rate of miles per hour. They both bike on the same -mile route between Escanaba and Marquette. At what time in the morning do they meet?
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Problem 14: The students in Mrs. Reed's English class are reading the same -page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in seconds, Bob reads a page in seconds and Chandra reads a page in seconds.
If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?
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Problem 15: The students in Mrs. Reed's English class are reading the same -page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in seconds, Bob reads a page in seconds and Chandra reads a page in seconds.
Chandra and Bob, who each have a copy of the book, decide that they can save time by "team reading" the novel. In this scheme, Chandra will read from page to a certain page and Bob will read from the next page through page , finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?
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Problem 16: The students in Mrs. Reed's English class are reading the same -page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in seconds, Bob reads a page in seconds and Chandra reads a page in seconds.
Before Chandra and Bob start reading, Alice says she would like to team read with them. If they divide the book into three sections so that each reads for the same length of time, how many seconds will each have to read?
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Problem 17: Jeff rotates spinners and and adds the resulting numbers. What is the probability that his sum is an odd number?
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Problem 18: A cube with -inch edges is made using cubes with -inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white?
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Problem 19: Triangle is an isosceles triangle with . Point is the midpoint of both and , and is units long. Triangle is congruent to triangle . What is the length of
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Problem 20: A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won games, Ines won games, Janet won games, Kendra won games and Lara won games, how many games did Monica win?
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Problem 21: An aquarium has a rectangular base that measures by and has a height of . The aquarium is filled with water to a depth of . A rock with volume is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?
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Problem 22: Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cell?
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Problem 23: A box contains gold coins. If the coins are equally divided among six people, four coins are left over. If the coins are equally divided among five people, three coins are left over. If the box holds the smallest number of coins that meets these two conditions, how many coins are left when equally divided among seven people?
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Problem 24: In the multiplication problem below, and are different digits. What is
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Problem 25: Barry wrote different numbers, one on each side of cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. What is the average of the hidden prime numbers?
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The problems on this page are the property of the MAA's American Mathematics Competitions