2020 AMC 8 Problem 6
Attempt Problem 6 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).
6.
Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the last car. Aaron sat directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car?
Aaron
Darren
Karen
Maren
Sharon
Answer: A
Small hint:
Maren is fixed in the last car
Big hint:
Test the possible adjacent positions for Sharon and Aaron
Video solution:
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Written solution:
Maren is in the last car. Since Aaron is directly behind Sharon and Darren is in front of Aaron, the possible placements of Darren, Sharon, and Aaron before Maren are limited.
If Sharon and Aaron were in cars and Darren could not be in front of Aaron. If they were in cars and then Darren and Karen would have to occupy cars and which are adjacent.
Thus Sharon and Aaron must be in cars and Darren is then in car Karen is in car and Aaron is in the middle car.
Thus, the correct answer is A.
Problem 6 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
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- 1998 AMC 8
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