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

(Solution 1)
(Solution 2)
Line 16: Line 16:
  
 
<cmath>1 - </cmath>
 
<cmath>1 - </cmath>
<cmath>2 R </cmath>
+
<cmath>2 Nabil </cmath>
<cmath>3 T </cmath>
+
<cmath>3 Rahul </cmath>
 
<cmath>4 - </cmath>
 
<cmath>4 - </cmath>
<cmath>5 J </cmath>
+
<cmath>5 Rafsan </cmath>
<cmath>6 M </cmath>
+
<cmath>6 Arabi </cmath>
 
<cmath>7 - </cmath>
 
<cmath>7 - </cmath>
<cmath>8 H </cmath>
+
<cmath>8 Marzuq </cmath>
  
Thus our answer is <math>\fbox{\textbf{(B)}\; \text{Hikmet}}</math>.
+
Thus our answer is <math>\fbox{\textbf{(B)}\; \text{Marzuq}}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2015|ab=B|num-a=5|num-b=3}}
 
{{AMC12 box|year=2015|ab=B|num-a=5|num-b=3}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 04:01, 15 February 2021

Problem

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

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

Solution 1

Let $-$ denote any of the 6 racers not named. Then the correct order following all the logic looks like:

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

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.


\[1 -\] \[2 Nabil\] \[3 Rahul\] \[4 -\] \[5 Rafsan\] \[6 Arabi\] \[7 -\] \[8 Marzuq\]

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

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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