2020 AMC 8 Problem 13
Attempt Problem 13 of the 2020 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 2020 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
Jamal has a drawer containing green socks, purple socks, and orange socks. After adding more purple socks, Jamal noticed that there is now a chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?
Answer: B
Small hint:
The non-purple socks stay at
Big hint:
If purple is , non-purple is
Video solution:
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Written solution:
Suppose Jamal adds purple socks. Then, there will be purple socks.
Also, since there are total socks to begin with, we have socks after adding the socks.
Since we have a chance of choosing a purple sock afterwards, we know
Solving for yields:
Therefore, socks are added.
Thus, the correct answer is B.
Problem 13 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
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
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