1991 AMC 8 Problem 19
Attempt Problem 19 of the 1991 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1991 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
The average (arithmetic mean) of different positive whole numbers is The largest possible value of any of these numbers is
Answer: C
Small hint:
The ten numbers must sum to
Big hint:
To make one number as large as possible, make the other nine as small as possible:
Solution:
The ten numbers sum to To maximize one of them, the other nine (all different positive whole numbers) should be as small as possible:
The largest number is then
Thus, the correct answer is C .
Problem 19 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1992 AMC 8
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