Difference between revisions of "2020 AMC 8 Problems/Problem 6"
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| + | ==Video Solution== | ||
| + | https://youtu.be/G04TnUc5iAA | ||
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| + | ~savannahsolver | ||
==See also== | ==See also== | ||
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Revision as of 11:36, 19 November 2020
Problem 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?
Solution 1
The following arrangement works, if Darren is 
, Aaron is 
, Karen is 
, Maren is 
, and Sharon is 
: 
.
Thus the answer is 
~Windigo
Solution 2
Let the carts look like ![\[\_,\_,\_,\_,\_\]](http://latex.artofproblemsolving.com/c/3/b/c3b07417003fca341e144e85191ef9975c911b1c.png)
where the left is the back and the right is the front. Using all the information given, it is not too hard to construct ![\[\text{M,K,A,S,D}\]](http://latex.artofproblemsolving.com/1/e/e/1eee8cfcddef62f09eb36f329cfe80f7f08c46ef.png)
so the answer is .
-franzliszt
Video Solution
~savannahsolver
See also
| 2020 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
