Think you’ve got what it takes?

Here are sample questions courtesy of MATHCOUNTS:

These are actual problems from the 2005 MATHCOUNTS competition season.

The answers are provided at the end.

Sprint Round (no calculator; 30 problems in 40 minutes; students work alone)

Problem 1: A rectangular tile measures 3 inches by 4 inches. What is the fewest number of these tiles that are needed to completely cover a rectangular region that is 2 feet by 5 feet?

Problem 2: How many combinations of pennies, nickels and/or dimes are there with a total value of 25 cents?

Target Round (calculator permitted; 6 minutes for each of 4 pairs of problems; students work alone)

Problem 3: What is the greatest whole number that must be a factor of the sum of any four consecutive positive odd numbers?

Team Round (calculator permitted; 10 problems in 20 minutes; students work with three other team members)

Problem 4: A four-digit perfect square integer is created by placing two positive two-digit perfect square integers next to each other. What is the four-digit square integer?

Countdown Round (no calculator; head-to-head challenge between two students; first-to-answer; no more than 45 seconds permitted)

Problem 5: When Bob exercises, he does jumping jacks for 5 minutes and then walks the track at 4 minutes per lap. If he exercised for 73 minutes on Monday, how many laps did he walk?

Problem 6: What number is 17 less than its negative? Express your answer as a decimal to the nearest tenth.


1) 120 tiles

2) 12 combinations

3) 8

4) 1681

5) 17 laps

6) −8.5

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