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

Revision as of 09:36, 8 April 2023

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

2015 AMC 12B (Problems • Answer Key • Resources)
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 13: / Line 13: @@
 <cmath>-, \text{Nabeel}, \text{Rahul}, -, \text{Rafsan}, \text{Arabi}, -, \text{Marzuq}, -, \text{Lian}, -, -</cmath>
-Thus the 8th place runner is <math>\textbf{(B)}\; \text{Marzuq}</math>.
+Thus the 8th place runner is <math>\boxed{\textbf{(B)}\; \text{Marzuq}}</math>.
 ==Solution 2==

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

Revision as of 09:36, 8 April 2023

Contents

Note

Problem

Solution 1

Solution 2

See Also