2012 AMC 8 Problem 11
Attempt Problem 11 of the 2012 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 2012 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
11.
The mean, median, and unique mode of the positive integers and are all equal. What is the value of
Answer: D
Small hint:
The unique mode must be the repeated listed number.
Big hint:
If the mean is that number, the total sum is fixed.
Video solution:
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Written solution:
Every listed value except appears once while appears twice. If equals any of the other listed values, then we have two modes, which means we do not have a unique mode. Otherwise, the only value that shows up more than once is making that the unique mode. This also means is the mean. Since there are elements, the sum of the elements is The sum is also so
Thus, the answer is D .
Problem 11 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
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