1987 AMC 8 Problem 18
Attempt Problem 18 of the 1987 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 1987 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
Half the people in a room left. One third of those remaining started to dance. There were then people who were not dancing. What was the original number of people in the room?
Answer: C
Small hint:
After half leave, the number remaining is what the dancing fraction applies to
Big hint:
The non-dancers are of those remaining
Solution:
Of those remaining, danced, so did not. Thus of the remaining people equals giving remaining.
Those are half the original group, so the room started with people.
Thus, the correct answer is C .
Problem 18 in other years
- 1985 AMC 8
- 1986 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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