2015 AMC 8 Problem 20
Attempt Problem 20 of the 2015 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
Ralph went to the store and bought pairs of socks for a total of . Some of the socks he bought cost a pair, some of the socks he bought cost a pair, and some of the socks he bought cost a pair. If he bought at least one pair of each type, how many pairs of socks did Ralph buy?
Answer: D
Small hint:
Let the numbers of and pairs be variables.
Big hint:
Subtract the pair-count equation from the cost equation.
Video solution:
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Written solution:
Let and be the numbers of and pairs, respectively. Then
Subtracting gives Since at least one pair of each type was bought, and Also so Modulo the equation gives even, so
Then so and
Thus, D is the correct answer.
Problem 20 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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