2004 AMC 8 Problems

1. On a map, a 12-centimeter length represents 72 kilometers. How many kilome- ters does a 17-centimeter length represent? (A) 6 (B) 102 (C) 204 (D) 864 (E) 1224

2. How many di®erent four-digit numbers can be formed by rearranging the four digits in 2004? (A) 4 (B) 6 (C) 16 (D) 24 (E) 81

3. Twelve friends met for dinner at Oscar's Overstu®ed Oyster House, and each ordered one meal. The portions were so large, there was enough food for 18 people. If they share, how many meals should they have ordered to have just enough food for the 12 of them? (A) 8 (B) 9 (C) 10 (D) 15 (E) 18

The following information is needed to solve problems 4, 5 and 6. Ms. Hamilton's eighth-grade class wants to participate in the an- nual three-person-team basketball tournament.

4. Lance, Sally, Joy and Fred are chosen for the team. In how many ways can the three starters be chosen? (A) 2 (B) 4 (C) 6 (D) 8 (E) 10

5. The losing team of each game is eliminated from the tournament. If sixteen teams compete, how many games will be played to determine the winner? (A) 4 (B) 7 (C) 8 (D) 15 (E) 16

6. After Sally takes 20 shots, she has made 55% of her shots. After she takes 5 more shots, she raises her percentage to 56%. How many of the last 5 shots did she make? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

7. An athlete's target heart rate, in beats per minute, is 80% of the theoretical maximum heart rate. The maximum heart rate is found by subtracting the athlete's age, in years, from 220. To the nearest whole number, what is the target heart rate of an athlete who is 26 years old? (A) 134 (B) 155 (C) 176 (D) 194 (E) 243

8. Find the number of two-digit positive integers whose digits total 7. (A) 6 (B) 7 (C) 8 (D) 9 (E) 10

9. The average of the ¯ve numbers in a list is 54. The average of the ¯rst two numbers is 48. What is the average of the last three numbers? (A) 55 (B) 56 (C) 57 (D) 58 (E) 59