2014 AMC 8 Problems - ThothTech

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2014 AMC 8 ProblemsProblem 1Harry and Terry are each told to calculate. Harry gets the correct answer. Terry ignores theparentheses and calculates. If Harry's answer isand Terry's answer is , what is?SolutionProblem 2Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that hecan use to pay her. What is the difference between the largest and the smallest number of coins he canuse to pay her?SolutionProblem 3Isabella had a week to read a book for a school assignment. She read an average of 36 pages per day forthe first three days and an average of 44 pages per day for the next three days. She then finished thebook by reading 10 pages on the last day. How many pages were in the book?SolutionProblem 4The sum of two prime numbers is 85. What is the product of these two prime numbers?SolutionProblem 5Margie's car can go 32 miles on a gallon of gas, and gas currently costs 4 per gallon. How many milescan Margie drive on 20 worth of gas?SolutionProblem 6Six rectangles each with a common base width of 2 have lengths of 1, 4, 9, 16, 25, and 36. What is thesum of the areas of the six rectangles?Solution

Problem 7There are four more girls than boys in Ms. Raub's class of 28 students. What is the ratio of number of girlsto the number of boys in her class?SolutionProblem 8Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talkabout problem solving at their math club meeting. They paid their guest speaker. What is themissing digit A of this 3-digit number?SolutionProblem 9In,is a point on sidedegree measure of?such thatandmeasures. What is theSolutionProblem 10The first AMC 8 was given in 1985 and it has been given annually since that time. Samantha turned 12years old the year that she took the seventh AMC 8. In what year was Samantha born?SolutionProblem 11Jack wants to bike from his house to Jill's house, which is located three blocks east and two blocks northof Jack's house. After biking each block, Jack can continue either east or north, but he needs to avoid adangerous intersection one block east and one block north of his house. In how many ways can he reachJill's house by biking a total of five blocks?Solution

Problem 12A magazine printed photos of three celebrities along with three photos of the celebrities as babies. Thebaby pictures did not identify the celebrities. Readers were asked to match each celebrity with the correctbaby pictures. What is the probability that a reader guessing at random will match all three correctly?SolutionProblem 13Ifandandoddare integers andis even, which of the following is impossible?are evenandare oddnone of these are impossibleis evenisSolutionProblem 14Rectangle ABCD and right triangle DCE have the same area. They are joined to form a trapezoid, asshown. What is DE?Solution

Problem 15The circumference of the circle with center is divided into 12 equal arcs, marked theletters through as seen below. What is the number of degrees in the sum of the anglesand ?SolutionProblem 16The "Middle School Eight" basketball conference has 8 teams. Every season, each team plays everyother conference team twice (home and away), and each team also plays 4 games against nonconference opponents. What is the total number of games in a season involving the "Middle School Eight"teams?SolutionProblem 17George walks mile to school. He leaves home at the same time each day, walks at a steady speedof miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weatherand walked the firstrun the lastSolutionmile at a speed of onlymiles per hour. At how many miles per hour must Georgemile in order to arrive just as school begins today?

Problem 18Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or agirl. Which of the following outcomes is most likely?all 4 are boysthe other genderall 4 are girls2 are girls and 2 are boysall of these outcomes are equally likely3 are of one gender and 1 is ofSolutionProblem 19A cube with 3-inch edges is to be constructed from 27 smaller cubes with 1-inch edges. Twenty-one of thecubes are colored red and 6 are colored white. If the 3-inch cube is constructed to have the smallestpossible white surface area showing, what fraction of the surface area is white?SolutionProblem 20Rectangle ABCD has sides CD 3 and DA 5. A circle of radius 1 is centered at A, a circle of radius 2 iscentered at B, and a circle of radius 3 is centered at C. Which of the following is closest to the area of theregion inside the rectangle but outside all three circles?SolutionProblem 21The 7-digit numbersthe value of ?Solutionandare each multiples of 3. Which of the following could be

Problem 22A 2-digit number is such that the product of the digits plus the sum of the digits is equal to the number.What is the units digit of the number?SolutionProblem 23Three members of the Euclid Middle School girls' softball team had the following conversation.Ashley: I just realized that our uniform numbers are all 2-digit primes.Bethany: And the sum of your two uniform numbers is the date of my birthday earlier this month.Caitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month.Ashley: And the sum of your two uniform numbers is today's date.What number does Caitlin wear?SolutionProblem 24One day the Beverage Barn sold 252 cans of soda to 100 customers, and every customer bought at leastone can of soda. What is the maximum possible median number of cans of soda bought per customer onthat day?SolutionProblem 25A straight one-mile stretch of highway, 40 feet wide, is closed. Robert rides his bike on a path composedof semicircles as shown. If he rides at 5 miles per hour, how many hours will it take to cover the one-milestretch?Note: 1 mile 5280 feetSolution

2014 AMC 8 Answer Key1. A2. E3. B4. E5. C6. D7. B8. D9. D10. A11. A12. B13. D14. B15. C16. B17. B18. D19. A20. B21. A22. E23. A24. C25. B

2014 AMC 8 Problems Problem 1 Harry and Terry are each told to calculate . Harry gets the correct answer. Terry ignores the parentheses and calculates . If Harry's answer is and Terry's answer is , what is ? Solution Problem 2 Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay her. What is the difference between the largest .

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