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Sample Problems for the Media
MATHCOUNTS has provided this set of sample problems for the media’s use. These are actual problems from the 2017 MATHCOUNTS Competition Series and are representative of the problems Mathletes® will be solving this year. Learn more about the MATHCOUNTS Competition Series.
 
This year’s problems may not be published or used in any manner by the media. We appreciate your efforts to recognize the students participating in MATHCOUNTS, and your assistance to ensure Competition Series problems are not compromised for students taking the competition at a later date.

Sprint Round

  • Students cannot use calculators
  • Students have 40 minutes to complete 30 problems
  • Students must work independently
Sample Problem #1 (Chapter Level): By switching two of the digits of the number 123,456, Rodrigo obtains a new number that is 1980 more than the original. What is the product of the two digits Rodrigo switched? (answer: 15)
 
Sample Problem #2 (State Level): Oliver rolls three fair standard six-sided dice. What is the probability that there is at least one pair of dice whose top faces sum to 6? Express your answer as a common fraction. (answer: 19/54)

 

Target Round

  • Students are permitted to use calculators
  • Students have 6 minutes for each of 4 pairs of problems
  • Students must work independently
Sample Problem #1 (Chapter Level): Aiden and Bryce are racing around a race track. They begin together at the starting line, and Aiden’s car completes a lap every 44 seconds, while Bryce’s car completes a lap every 40 seconds. How many seconds after they begin the race will Aiden and Bryce first reach the starting line at the same time? (answer: 440 seconds)
 
Sample Problem #2 (State Level): One evening, Varun finishes reading a novel that he has been reading for several days and finds the ending so exciting that he immediately begins reading the novel’s sequel. Each novel has pages numbered consecutively, starting with page 1. Each novel has fewer than 1000 pages. If Varun reads a total of 42 pages in one sitting and the sum of the page numbers he reads in that sitting is 2018, what is the number of the last page of the first novel? (answer: Page 265)

 

Team Round

  • Students are permitted to use calculators
  • Students have 20 minutes to answer 10 problems
  • Students work in teams of 4 members
Sample Problem #1 (Chapter Level): The degree measures of the angles of a hexagon are x + 10, 2x + 80, 3x − 60, 4x + 40, 5x − 10, and 6x − 33. What is the degree measure of the largest angle of the hexagon? (answer: 172 degrees)
 
Sample Problem #2 (State Level): Jackie sold two cars for $25,000 each. The first car sold for a profit of 22%, and the second sold at a loss of 7%. What was the total percent profit on the sale of the two cars? Express your answer to the nearest hundredth. (answer: 5.54 percent)

 

Countdown Round

  • Students cannot use calculators
  • Students have no more than 45 seconds to answer each problem
  • Each round is a head-to-head challenge between two students
Sample Problem #1 (Chapter Level): A prize of $900 is to be shared in the ratio of 2:1:1 among three awardees. How many dollars are in the smallest share? (answer: 225 dollars)
 
Sample Problem #2 (State Level): What is the perimeter, in units, of a regular hexagon whose longest diagonal has length 8 units? (answer: 24 units)

 

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