1. Alice and Bob went to the Algebra Arcade to play math games. Together, they had $50 to spend. Alice spent 40% of her money and Bob spent 70% of his money. Together, they had $25.20 left. How many dollars did Alice have to start with?

2. Put the volumes of the following four figures in order of increasing size (smallest first). Your answer should be 4 letters in the correct order. (A) a cube of edge length 2 inches; (B) a cone of radius 1 inch and height 2 inches; (C) a cylinder of radius 1 inch and height 2 inches; (D) a sphere of radius 1 inch

3. Ruthie makes a list of all the prime numbers less than 100, in order of increasing size. How many different square numbers less than 200 could result from adding three consecutive numbers from Ruthie's list?

4. Stacey buys a CD costing $19.48, and pays with a twenty-dollar bill. The cashier gives her change in dimes, nickels and/or pennies. How many different ways can the change be made?

5. What is the difference in degrees between the larger and the smaller angles formed by the hands of an analog wall clock at 7:42 AM?

6. Give the letter or letters of all of the following statements that are true about the set of numbers {3,12, 0, −21,6}. If no statement is true, answer "none". (A) Exactly 4 of the 5 numbers are even. (B) Exactly 4 of the 5 numbers are positive. (C) Exactly 4 of the 5 numbers are greater than the mean of all 5 numbers. (D) Exactly 4 of the 5 numbers can be divided by 3 with no remainder. (E) Exactly 4 of the 5 numbers can be arranged to form an arithmetic sequence.

7. For the first 100 counting numbers, Joel calculates the square of each number, then subtracts the number itself from this square. When he writes out the final answers to these calculations, how many of these 100 answers will have 0 as the units (ones-place) digit?

8. My Reversing Calculator reverses the digits of every counting number I enter. It then calculates correctly using the reversed digits, but reverses the answer before it displays it. I entered three 2-digit counting numbers, with a plus sign between the first two numbers and a minus sign between the second and third (that is, _ _+ _ _− _ _ = ? , where each blank indicates a digit). The displayed answer was 49. What is the largest the correct answer could have been?

9. Malia puts together six 4-by-4-by-1 inch square layers with 1-inch cubes, then stacks them up to form a rectangular prism. This prism rests on a wooden table, on its square base. All the 1-inch cubes Malia used are white except one, which is red. As a reduced fraction, what is the probability that the red cube is visible if it is located at random?

10. Ron and Hermione are on a road trip. They decide to split the driving: for every three miles Ron drives, Hermione drives 5. Ron averages 30 miles per hour (mph) and Hermione averages 80 mph. What is the overall average speed for the trip, in mph? If your answer is not a whole number, round to the nearest whole number.

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