2018 AMC 8 Problem 10
Attempt Problem 10 of the 2018 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 2018 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
10.
The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of and
Answer: C
Small hint:
Average the reciprocals of and .
Big hint:
The harmonic mean is the reciprocal of that average.
Video solution:
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Written solution:
The reciprocals of , , and are , , and , respectively. The average of these reciprocals is
As the harmonic mean is the reciprocal of the average of the reciprocals of the numbers (which we just calculated to be ), we conclude that the harmonic mean is
Thus, the correct answer is C.
Problem 10 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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