2020 AMC 8 Problems/Problem 6

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?

$\textbf{(A) }\text{Aaron} \qquad \textbf{(B) }\text{Darren} \qquad \textbf{(C) }\text{Karen} \qquad \textbf{(D) }\text{Maren}\qquad \textbf{(E) }\text{Sharon}$

Solution 1

The following arrangement works, if Darren is $D$ , Aaron is $A$ , Karen is $K$ , Maren is $M$ , and Sharon is $S$ : $DSAKM$ .

Thus the answer is $\textbf{(A) }\text{Aaron}$

~Windigo

Solution 2

Let the carts look like $\_,\_,\_,\_,\_$ where the left is the back and the right is the front. Using all the information given, it is not too hard to construct $\text{M,K,A,S,D}$ so the answer is $\textbf{(A) }\text{Aaron}$ .

-franzliszt

Video Solution

https://youtu.be/G04TnUc5iAA

~savannahsolver

2020 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AJHSME/AMC 8 Problems and Solutions

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2020 AMC 8 Problems/Problem 6

Contents

Problem 6

Solution 1

Solution 2

Video Solution

See also