1964 AMC 12 Problem 27
Attempt Problem 27 of the 1964 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 1964 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 is a real number and where then:
Answer: E
Small hint:
Interpret the sum as the distances from to and
Big hint:
Find its minimum for , remembering the inequality is strict
Solution:
By the triangle inequality, Equality holds for every between and Therefore the strict inequality has a real solution exactly when
Thus, the correct answer is E.
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
- 1960 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
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