1965 AMC 12 Problem 17
Attempt Problem 17 of the 1965 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 1965 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
Given the true statement: The picnic on Sunday will not be held only if the weather is not fair. We can then conclude that:
If the picnic is held, Sunday’s weather is undoubtedly
fair.
If the picnic is not held, Sunday’s weather is possibly
unfair.
If it is not fair Sunday, the picnic will not be held.
If it is fair Sunday, the picnic may be held.
If it is fair Sunday, the picnic will be
held.
Answer: E
Small hint:
Translate “ only if ” as
Big hint:
Take the contrapositive of “not held implies not fair”
Solution:
The statement says: if the picnic is not held, then the weather is not fair. Its contrapositive is: if the weather is fair, then the picnic will be held.
Therefore, the correct answer is E.
Problem 17 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
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