MathMania 2010

  1. If an item in a store is marked up 20%, exactly what percentage must it then be marked down to result in the original price?

  2. At a bake sale, brownies cost 50 cents each and cookies cost 35 cents each. If 70 items were sold for a total of $29, how many cookies were sold?

  3. Each interior angle of a regular polygon has a measure of 168 degrees. How many sides does the polygon have?

  4. What’s the first time after 12 noon that the angle between the minute hand and hour hand of a clock is 110 degrees?

  5. Find the most likely next term in the sequence: 1, 2, 4, 7, 13, 24, 44, 81,…

  6. Find all solutions to the equation x2 + x − 3 = |x|.

  7. What are the coordinates of the centroid of the triangle whose vertices are (0, 0), (1, 7), and (2,5)?

TIEBREAKER: There are five ways to divide a set with three elements into nonempty disjoint subsets: If there is only one subset in our partition we must have {{A, B, C}}. If there are two subsets we could have {{A, B}, {C}}, {{A, C}, {B}}, or {{B, C}, {A}}. If there are three subsets we must have {{A}, {B}, {C}}. What is the number of ways to divide a set with 10 elements into nonempty disjoint subsets? The team getting closest to the correct answer wins.

Here are the answers.