2015 AMC 12B Problems/Problem 4

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Note

This problem is also problem number 5 on the 2015 AMC 10B, just with different names. This is the link.

Problem

Lian, Marzuq, Rafsan, Arabi, Nabeel, and Rahul were in a 12-person race with 6 other people. Nabeel finished 6 places ahead of Marzuq. Arabi finished 1 place behind Rafsan. Lian finished 2 places behind Marzuq. Rafsan finished 2 places behind Rahul. Rahul finished 1 place behind Nabeel. Arabi finished in 6th place. Who finished in 8th place?

$\textbf{(A)}\; \text{Lian} \qquad\textbf{(B)}\; \text{Marzuq} \qquad\textbf{(C)}\; \text{Rafsan} \qquad\textbf{(D)}\; \text{Nabeel} \qquad\textbf{(E)}\; \text{Rahul}$

Solution 1

Let --- denote any of the 6 racers not named. Then the correct order looks like this:

\[-, \text{Nabeel}, \text{Rahul}, -, \text{Rafsan}, \text{Arabi}, -, \text{Marzuq}, -, \text{Lian}, -, -\]

Thus the 8th place runner is $\boxed{\textbf{(B)}\; \text{Marzuq}}$.

Solution 2

We list the people out vertically for clarity, starting with Marzuq and working from there.


\[1 -\] \[2 \text{Nabeel}\] \[3 \text{Rahul}\] \[4 -\] \[5 \text{Rafsan}\] \[6 \text{Arabi}\] \[7 -\] \[8 \text{Marzuq}\]

Thus our answer is $\boxed{\textbf{(B)}\; \text{Marzuq}}$.

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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