1987 AMC 8 Problem 24
Attempt Problem 24 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).
24.
A multiple choice examination consists of questions. The scoring is for each correct answer, for each incorrect answer, and for each unanswered question. John’s score on the examination is What is the maximum number of questions he could have answered correctly?
Answer: D
Small hint:
If answers are correct and are wrong, then
Big hint:
Try the largest possible : must be a nonnegative even number with
Solution:
Let be the number correct and the number wrong, so Then which requires to be even.
Trying gives but too many; every larger even would require still more answered questions. Trying gives and which works. So the maximum is
Thus, the correct answer is D .
Problem 24 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
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