# 2015 AMC 12B Problems/Problem 4

## Problem

David, Hikmet, Jack, Marta, Rand, and Todd were in a 12-person race with 6 other people. Rand finished 6 places ahead of Hikmet. Marta finished 1 place behind Jack. David finished 2 places behind Hikmet. Jack finished 2 places behind Todd. Todd finished 1 place behind Rand. Marta finished in 6th place. Who finished in 8th place? $\textbf{(A)}\; \text{David} \qquad\textbf{(B)}\; \text{Hikmet} \qquad\textbf{(C)}\; \text{Jack} \qquad\textbf{(D)}\; \text{Rand} \qquad\textbf{(E)}\; \text{Todd}$

## Solution 1

Let $-$ denote any of the 6 racers not named. Then the correct order following all the logic looks like: $$-, \text{Rand}, \text{Todd}, -, \text{Jack}, \text{Marta}, -, \text{Hikmet}, -, \text{David}, -, -$$

Clearly the 8th place runner is $\fbox{\textbf{(B)}\; \text{Hikmet}}$.

## Solution 2

We can list these out vertically to ensure clarity, starting with Marta and working from there. $$1 -$$ $$2 R$$ $$3 T$$ $$4 -$$ $$5 J$$ $$6 M$$ $$7 -$$ $$8 H$$

Thus our answer is $\fbox{\textbf{(B)}\; \text{Hikmet}}$.

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