Practice Set 3

Problem #1: In the following diagram, what is the length of segment AB?
Problem #2: At Popo's Peppy Pizza Place, which serves circular pizzas, a large pizza has a diameter of 18 in. and costs $15. A medium pizza has a diameter of 16 in. and costs $10. A small pizza has a diameter of 12 in. and costs $7. Which size pizza (large, medium, or small) is the best deal?
Problem #3: The arithmetic mean of 25 numbers is 8% of a non-zero mystery number N. What is the ratio of N to the sum of those 25 numbers? Express your answer as a common fraction.
Problem #4: When I looked at the calendar today, I noticed that if I divided the numerical date by 9, I would get a remainder of 4. If I had multiplied the number by 4 first and then divided by 9, what would the remainder be?
Problem #5: A palindrome word is a series of letters that read the same forward and backward, such as NOON and RACECAR. How many 6-letter palindromes can be created using exactly 2 As, 2 Hs, and 2 Ns?
Problem #6: I entered middle school in the year 2002 and graduated in the year 2005. Let f(n) = the number of diagonals in a convex n-sided polygon. What is f(2005) - f(2002)?
Problem #7: On Farmer Foozy's farm, there are chickens, cows, and airplanes. Each chicken has 2 eyes, 2 wings, and 2 legs. Each cow has 2 eyes, 0 wings, and 4 legs. Each airplane has 0 eyes, 2 wings, and 0 legs. Farmer Foozy counts a total of 44 eyes, 30 wings, and 64 legs. How many airplanes are there?
Problem #8: For a certain sphere, the number of cubic yards in its volume is equal to the number of square feet in its surface area. What is the diameter of the sphere, in yards?
Problem #9: In Mathland, there are two nationalities of Shapes: Circles and Squares. Circles always tell the truth, while Squares always lie. You travel to Mathland and meet three Shapes: Gonzo, Fanny, and Anna-Marie-Juniper. They talk to you, but you don't know whether their statements are true or false.
Gonzo says, "Fanny and Anna-Marie-Juniper are of the same nationality."
Fanny says, "Gonzo is a Square."
Anna-Marie-Juniper says, "Fanny is a Circle."
How many Circles are there?
Problem #10: How many factors does 10! have?

Solutions