1975 AMC 12 Problem 25
Attempt Problem 25 of the 1975 AMC 12 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 1975 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
A woman, her brother, her son and her daughter are chess players (all relations by birth). The worst player’s twin (who is one of the four players) and the best player are of opposite sex. The worst player and the best player are the same age. Who is the worst player?
the woman
her son
her brother
her daughter
No solution is consistent with the given information.
Answer: B
Small Hint:
List the only possible same-generation twin pairs among the four people
Big Hint:
If the son is worst, his twin is the daughter and the best can be the brother
Solution:
If the son is worst, the daughter can be his twin and the brother can be best; the son and brother may have the same age, so all conditions can hold. If the woman is worst, the brother is her twin and the daughter must be best, but mother and daughter cannot be the same age. If the brother is worst, the woman is his twin and the son must be best, again impossible in age. If the daughter is worst, her twin is the son and the woman must be best, also impossible in age. Thus only the son works.
Therefore, the correct answer is B.
Problem 25 in Other Years
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