2015 AMC 12B Problems/Problem 4

Contents

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 $\boxed{\textbf{(B)}\; \text{Marzuq}}$.