1968 AMC 12 Problem 10
Attempt Problem 10 of the 1968 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 1968 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
10.
Assume that, for a certain school, it is true that
Some students are not honest.
All fraternity members are honest.
A necessary conclusion is:
Some students are fraternity members
Some fraternity members are not students
Some students are not fraternity members
No fraternity member is a student
No student is a fraternity member
Answer: C
Small hint:
Choose a student whose existence is guaranteed by statement
Big hint:
Could that dishonest student be a fraternity member under statement
Solution:
Statement guarantees a dishonest student. Statement says every fraternity member is honest, so that dishonest student cannot be a fraternity member. Hence some student is not a fraternity member.
Therefore, the correct answer is C.
Problem 10 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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