1. A rectangular prism with edges that are natural numbers has a total volume of 100 cubic centimeters. The longest side of the prism is twice as long as the next longest side, and the area of the base is 10 square centimeters. What are the dimensions of the prism?

7. A pile of nickels and quarters is on a table. The total amount of money in the pile is more that 0 and less than 1 dollar. If all the coins (both nickels and quarters) were turned into dimes, the amount of money in the pile would be unchanged. How many coins could there be in the pile?

8. Nine players line up single file to shoot free throws. Exactly 4 of the players are seniors. In how many ways can the line be formed if the first 2 and the last 2 people in the line are seniors?

2. Jacob and Patty are starting a lawn mowing business for the summer. On average, Jacob can mow 4 lawns in 6 hours, and Patty can mow 5 lawns in 8 hours. Assuming that they both spend the same amount of time working, how long will it take Jacob and Patty to mow 62 lawns?

3. Suppose that, when divided by 4, the number a has a remainder of 2 and the number b has a remainder of 3. What will be the remainder of the product ab when divided by 4?

4. Your sock drawer contains 6 socks, all of which are either blue or red. Without looking, you take 2 socks out of the drawer. If your probability of drawing a pair of blue socks is 2/3, how many blue socks are in the drawer?

5. If a can be chosen from the set (2, 3, 6, 9), b can be chosen from the set (4, 5, 6, 7), and c can be chosen from the set (1, 2, 4, 5), what values of a, b, and c will produce the largest solution for the equation ax + b = c? What values of a, b, and c will produce the smallest solution?

6. An imaginary island is called the Island of Knights and Knaves. On this island, there are people called knights, who always tell the truth, and people called knaves, who always lie. The two types are indistinguishable by sight, On a vacation to this island, you meet two inhabitants: Bill and Bob. Bob says, "We are both the same kind," but Bill says, "We are both different kinds." Who is the knight, and who is the knave?

9. A 1/2 mile long train is going at 60 miles per hour and is just entering a tunnel that is 1 mile in length. How many minutes will it take the entire train to go completely through the tunnel?