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1. ### 2006 AMC8 Problem 13

Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike. He bikes at a uniform rate of 16 miles per hour. They both bike on the same 62-mile route between Escanaba...
2. ### 2006 AMC8 Problem 14

A Novel Assignment The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. If Bob and Chandra both read the...
3. ### 2006 AMC8 Problem 15

A Novel Assignment The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. Chandra and Bob, who each have a...
4. ### 2006 AMC8 Problem 16

A Novel Assignment The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. Before Chandra and Bob start...
5. ### 2006 AMC8 Problem 18

A cube with 3-inch edges is made using 27 cubes with 1-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? \textbf{(A)}\...
6. ### 2006 AMC8 Problem 20

A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica (the sixth player) win? \textbf{(A)}\ 0\qquad\textbf{(B)}\...
7. ### 2006 AMC8 Problem 21

An aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. The aquarium is filled with water to a depth of 37 cm. A rock with volume 1000 \text{ cm}^3 is then placed in the aquarium and completely submerged. By how many centimeters does the water level...
8. ### 2006 AMC8 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...
9. ### 2007 AMC8 Problem 1

Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 10 hours per week helping around the house for 6 weeks. For the first 5 weeks she helps around the house for 8, 11, 7, 12 and 10 hours. How many hours must she work for the final week to earn...

11. ### 2007 AMC8 Problem 4

A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a different window? \textbf{(A)}\ 12 \qquad\textbf{(B)}\ 15 \qquad\textbf{(C)}\ 18 \qquad\textbf{(D)}\ 30 \qquad\textbf{(E)}\ 36
12. ### 2007 AMC8 Problem 5

Chandler wants to buy a $500 mountain bike. For his birthday, his grandparents send him$50, his aunt sends him $35 and his cousin gives him$15. He earns \$16 per week for his paper route. He will use all of his birthday money and all of the money he earns from his paper route. In how many weeks...
13. ### 2007 AMC8 Problem 6

The average cost of a long-distance call in the USA in 1985 was 41 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 7 cents per minute. Find the approximate percent decrease in the cost per minute of a long-distance call. \textbf{(A)}\ 7 \qquad\textbf{(B)}\...
14. ### 2007 AMC8 Problem 7

The average age of 5 people in a room is 30 years. An 18-year-old person leaves the room. What is the average age of the four remaining people? \textbf{(A)}\ 25 \qquad\textbf{(B)}\ 26 \qquad\textbf{(C)}\ 29 \qquad\textbf{(D)}\ 33 \qquad\textbf{(E)}\ 36
15. ### 2007 AMC8 Problem 10

For any positive integer n, define \boxed{n} to be the sum of the positive factors of n. For example, \boxed{6} = 1 + 2 + 3 + 6 = 12. Find \boxed{\boxed{11}} . \textbf{(A)}\ 13 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 28 \qquad \textbf{(E)}\ 30
16. ### 2007 AMC8 Problem 14

The base of isosceles \triangle ABC is 24 and its area is 60. What is the length of one of the congruent sides? \textbf{(A)}\ 5 \qquad \textbf{(B)}\ 8 \qquad \textbf{(C)}\ 13 \qquad \textbf{(D)}\ 14 \qquad \textbf{(E)}\ 18
17. ### 2007 AMC8 Problem 15

Let a, b and c be numbers with 0 < a < b < c. Which of the following is impossible? \textbf{(A)} \ a + c < b \\\textbf{(B)} \ a \cdot b < c \\ \textbf{(C)} \ a + b < c \\ \textbf{(D)} \ a \cdot c < b \\\textbf{(E)}\dfrac{b}{c} = a
18. ### 2007 AMC8 Problem 17

A mixture of 30 liters of paint is 25\% red tint, 30\% yellow tint and 45\% water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? \textbf{(A)}\ 25 \qquad \textbf{(B)}\ 35 \qquad \textbf{(C)}\ 40 \qquad \textbf{(D)}\ 45 \qquad...
19. ### 2007 AMC8 Problem 18

The product of the two 99-digit numbers 303,\!030,\!303,\!...,\!030,\!303 and 505,\!050,\!505,\!...,\!050,\!505 has thousands digit A and units digit B. What is the sum of A and B? \textbf{(A)}\ 3 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 10
20. ### 2007 AMC8 Problem 19

Pick two consecutive positive integers whose sum is less than 100. Square both of those integers and then find the difference of the squares. Which of the following could be the difference? \textbf{(A)}\ 2 \qquad \textbf{(B)}\ 64 \qquad \textbf{(C)}\ 79 \qquad \textbf{(D)}\ 96 \qquad...