1957 AMC 12 Problem 29
Attempt Problem 29 of the 1957 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 1957 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
29.
The relation is true only for:
Here means that can take on all values greater than and the value equal to while has a corresponding meaning with “less than.”
Answer: D
Small hint:
The factor is positive except at
Big hint:
Away from zero, the sign is controlled by
Solution:
At the product is zero. For the factor is positive, so the product is nonnegative exactly when or or Including the isolated value gives the set in choice D.
Thus, the correct answer is D.
Problem 29 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
- 1964 AMC 12
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- 1972 AMC 12
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- 1999 AMC 12