2024 AMC 8 Problem 19
Attempt Problem 19 of the 2024 AMC 8 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 2024 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Jordan owns pairs of sneakers. Three fifths of the pairs are red and the rest are white. Two thirds of the pairs are high-top and the rest are low-top. The red high-top sneakers make up a fraction of the collection. What is the least possible value of this fraction?
Answer: C
Small hint:
There are red pairs and high-top pairs
Big hint:
To minimize red high-tops, make as many white pairs high-top as possible
Solution:
Jordan has pairs of red sneakers and pairs of white sneakers. Moreover, are high-top and are low-top. If we want to minimize the number of red high-top sneakers, then we can set all white sneakers to be high-top, leaving red sneakers as high-top. Hence, the fraction of red high-top sneakers would be .
Thus, C is the correct answer.
Problem 19 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
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- 1991 AMC 8
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