1958 AMC 12 Problem 28
Attempt Problem 28 of the 1958 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 1958 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
A -quart radiator is filled with water. Four quarts are removed and replaced with pure antifreeze liquid. Then four quarts of the mixture are removed and replaced with pure antifreeze. This is done a third and a fourth time. The fractional part of the final mixture that is water is:
Answer: B
Small hint:
Each removal takes away the same fraction of whatever water remains
Big hint:
After one replacement, of the previous water remains
Solution:
Each removal takes one-fourth of the well-mixed radiator contents, so it leaves three-fourths of the water then present. After four replacements, the water fraction is
Therefore, the correct answer is B.
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
- 1957 AMC 12
- 1959 AMC 12
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