2015 AMC 8 Problem 13
Attempt Problem 13 of the 2015 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 2015 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
How many subsets of two elements can be removed from the set so that the mean (average) of the nine remaining numbers is
Answer: D
Small hint:
Find the sum the remaining nine numbers must have.
Big hint:
So the two removed numbers must have a fixed sum.
Video solution:
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Written solution:
The original set has sum After removing two numbers, numbers remain and must have mean so their sum must be
Therefore the two removed numbers must have sum The possible two-element subsets are so there are choices.
Thus, D is the correct answer.
Problem 13 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
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- 1998 AMC 8
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