1974 AMC 12 Problem 27
Attempt Problem 27 of the 1974 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 1974 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
If for all real then the statement:
“ whenever and and ”
is true when
The statement is never true.
Answer: A
Small hint:
Factor in terms of
Big hint:
The condition becomes whenever
Solution:
We have If and then as required. If one can choose strictly between and so the statement fails. Thus the exact condition is
Therefore, the correct answer is A.
Problem 27 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
- 1959 AMC 12
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- 1961 AMC 12
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- 1999 AMC 12