# Difference between revisions of "2015 AMC 12B Problems/Problem 4"

## 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 following all the logic looks like:

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

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

## Solution 2

We can list these out vertically to ensure clarity, starting with Marta and working from there.

$$1 -$$ $$2 Nabeel$$ $$3 Rahul$$ $$4 -$$ $$5 Rafsan$$ $$6 Arabi$$ $$7 -$$ $$8 Marzuq$$

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