2016 AMC 8 Problem 18
Attempt Problem 18 of the 2016 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
In an All-Area track meet, sprinters enter a -meter dash competition. The track has lanes, so only sprinters can compete at a time. At the end of each race, the five non-winners are eliminated, and the winner will compete again in a later race.
How many races are needed to determine the champion sprinter?
Answer: C
Small hint:
Think about how many sprinters are eliminated in each race.
Big hint:
To leave one champion from sprinters, all but one sprinter must be eliminated.
Video solution:
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Written solution:
Note that each race eliminates people. For there to be a winner, must be eliminated. Therefore, races are required to eliminate this number of people.
Thus, C is the correct answer.
Problem 18 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
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- 1998 AMC 8
- 1999 AMC 8
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