1986 AMC 8 Problem 18
Attempt Problem 18 of the 1986 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 1986 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
A rectangular grazing area is to be fenced off on three sides using part of a meter rock wall as the fourth side. Fence posts are to be placed every meters along the fence, including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area m by m?
Answer: B
Small hint:
To use the fewest posts, let the meter side lie along the wall, so the fenced length is as short as possible
Big hint:
The fenced path is meters; place a post every meters, counting both ends
Solution:
The fewest posts are used when the wall serves as the longer meter side, so the fence covers two meter sides and one meter side, a path of meters.
Placing a post every meters, including both ends, uses posts.
Thus, the correct answer is B .
Problem 18 in other years
- 1985 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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- 1999 AMC 8
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