1971 AMC 12 Problem 27
Attempt Problem 27 of the 1971 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 1971 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
A box contains chips, each of which is red, white, or blue. The number of blue chips is at least half the number of white chips and at most one-third the number of red chips. The number which are white or blue is at least The minimum number of red chips is:
Answer: E
Small hint:
Let the counts be and translate every condition into an inequality
Big hint:
From and , find the least possible integer
Solution:
Let the counts be The conditions give Hence so and Equality is possible with so the minimum is
Therefore, 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
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- 1961 AMC 12
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- 1963 AMC 12
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- 1972 AMC 12
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