2015 AMC 12B Problems/Problem 4

Revision as of 22:40, 20 January 2018 by Flyhawkeye (talk | contribs) (Solution)

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 $\fbox{\textbf{(B)}\; \text{Hikmet}}$.

See Also

2015 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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 AMC 12 Problems and Solutions

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