1968 AMC 12 Problem 28
Attempt Problem 28 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).
28.
If the arithmetic mean of and is double their geometric mean, with then a possible value for the ratio to the nearest integer, is:
none of these
Answer: D
Small hint:
Set and divide the mean equation by
Big hint:
The equation becomes quadratic after squaring
Solution:
Let The condition gives so The root greater than is whose nearest integer is
Therefore, the correct answer is D.
Problem 28 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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- 1961 AMC 12
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- 1963 AMC 12
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