2013 AMC 8 Problems - ThothTech

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2013 AMC 8 ProblemsProblem 1Amma wants to arrange her model cars in rows with exactly 6 cars in each row. She nowhas 23 model cars. What is the smallest number of additional cars she must buy in order tobe able to arrange all her cars this way?SolutionProblem 2A sign at the fish market says, "50% off, today only: half-pound packages for just 3 perpackage." What is the regular price for a full pound of fish, in dollars?SolutionProblem 3What is the value of?SolutionProblem 4Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgother money, each of her seven friends paid an extra 2.50 to cover her portion of the totalbill. What was the total bill?SolutionProblem 5Hammie is in thegrade and weighs 106 pounds. His quadruplet sisters are tiny babiesand weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these fivechildren or the median weight, and by how many pounds?

Problem 6The number in each box below is the product of the numbers in the two boxes that touch itin the row above. For example,. What is the missing number in the top row?Problem 7Trey and his mom stopped at a railroad crossing to let a train pass. As the train began topass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 secondsto clear the crossing at a constant speed. Which of the following was the most likely numberof cars in the train?SolutionProblem 8A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?SolutionProblem 9The Incredible Hulk can double the distance he jumps with each succeeding jump. If his firstjump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then onwhich jump will he first be able to jump more than 1 kilometer?

Problem 10What is the ratio of the least common multiple of 180 and 594 to the greatest commonfactor of 180 and 594?SolutionProblem 11Ted's grandfather used his treadmill on 3 days this week. He went 2 miles each day. OnMonday he jogged at a speed of 5 miles per hour. He walked at the rate of 3 miles per houron Wednesday and at 4 miles per hour on Friday. If Grandfather had always walked at 4miles per hour, he would have spent less time on the treadmill. How many minutes less?SolutionProblem 12At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If youbuy one pair of sandals at the regular price of 50, you get a second pair at a 40% discount,and a third pair at half the regular price. Javier took advantage of the "fair special" to buythree pairs of sandals. What percentage of the 150 regular price did he save?SolutionProblem 13When Clara totaled her scores, she inadvertently reversed the units digit and the tens digitof one score. By which of the following might her incorrect sum have differed from thecorrect one?Problem 14Abe holds 1 green and 1 red jelly bean in his hand. Bea holds 1 green, 1 yellow, and 2 redjelly beans in her hand. Each randomly picks a jelly bean to show the other. What is theprobability that the colors match?

Problem 15If,, and, what is the product of , , and ?SolutionProblem 16A number of students from Fibonacci Middle School are taking part in a community serviceproject. The ratio of-graders to-graders is, and the ratio of-graders tograders is. What is the smallest number of students that could be participating in theproject?SolutionProblem 17The sum of six consecutive positive integers is 2013. What is the largest of these sixintegers?Solution

Problem 18Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feetwide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocksdoes the fort contain?SolutionProblem 19Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannahshows Bridget and Cassie her test, but Bridget and Cassie don't show theirs to anyone.Cassie says, 'I didn't get the lowest score in our class,' and Bridget adds, 'I didn't get thehighest score.' What is the ranking of the three girls from highest to lowest?Problem 20Arectangle is inscribed in a semicircle with longer side on the diameter. What is thearea of the semicircle?

Problem 21Samantha lives 2 blocks west and 1 block south of the southwest corner of City Park. Herschool is 2 blocks east and 2 blocks north of the northeast corner of City Park. On schooldays she bikes on streets to the southwest corner of City Park, then takes a diagonal paththrough the park to the northeast corner, and then bikes on streets to school. If her route isas short as possible, how many different routes can she take?SolutionProblem 22Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. Howmany toothpicks are used altogether?Solution

Problem 23Angleofis a right angle. The sides ofare the diameters ofsemicircles as shown. The area of the semicircle onequals, and the arc of thesemicircle onhas length. What is the radius of the semicircle on?Problem 24Squares,, andare equal in area. Points andare themidpoints of sidesand, respectively. What is the ratio of the area of the shadedpentagonto the sum of the areas of the three squares?

Problem 25A ball with diameter 4 inches starts at point A to roll along the track shown. The track iscomprised of 3 semicircular arcs whose radii areinches,inches,andinches, respectively. The ball always remains in contact with the track anddoes not slip. What is the distance the center of the ball travels over the course from A toB?

2013 AMC 8 Answer Key1. A2. D3. E4. C5. E6. C7. C8. C9. C10. C11. D12. B13. A14. C15. B16. E17. B18. B19. D20. C21. E22. E23. B24. C25. A

2013 AMC 8 Problems Problem 1 Amma wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way? Solution Problem 2 A sign at the fish market says, "50% off, today only: half-pound packages for just 3 per package." What is the regular price .

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