Difference between revisions of "2015 AMC 12B Problems/Problem 4"
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==Problem== | ==Problem== | ||
Revision as of 13:54, 23 November 2023
- The following problem is from both the 2015 AMC 10B #5 and 2015 AMC 12B #4, so both problems redirect to this page.
Contents
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?
Solution 1
Let --- denote any of the 6 racers not named. Then the correct order looks like this:
![\[-, \text{Nabeel}, \text{Rahul}, -, \text{Rafsan}, \text{Arabi}, -, \text{Marzuq}, -, \text{Lian}, -, -\]](http://latex.artofproblemsolving.com/e/c/3/ec364be22d6d93081d6a952a2a475fea025d3694.png)
Thus the 8th place runner is 
.
Solution 2
We list the people out vertically for clarity, starting with Marzuq and working from there.
![\[1 -\]](http://latex.artofproblemsolving.com/1/0/5/105aa601b74d255fdec68cea63a561c4634d492d.png)
![\[2 \text{Nabeel}\]](http://latex.artofproblemsolving.com/9/c/a/9ca6eb51f0291777cc58c5cdc75bf68be108dd8e.png)
![\[3 \text{Rahul}\]](http://latex.artofproblemsolving.com/c/8/2/c82430f899e43f0cad590dcf4eafdf1108b223d1.png)
![\[4 -\]](http://latex.artofproblemsolving.com/3/4/d/34dde0e8318825de00c6c696b1c5e715454d4420.png)
![\[5 \text{Rafsan}\]](http://latex.artofproblemsolving.com/b/d/b/bdb4b9bf130d25b99559442531adf9a9abefb547.png)
![\[6 \text{Arabi}\]](http://latex.artofproblemsolving.com/2/4/f/24f1a33d2d70f22868b48630b47539e4b1a81b2f.png)
![\[7 -\]](http://latex.artofproblemsolving.com/1/4/f/14fa5dbaae18d5eaff20f23b696f5eac2a6254be.png)
![\[8 \text{Marzuq}\]](http://latex.artofproblemsolving.com/0/9/5/0953657fbaedfaf8e896893c01bb26f7173899c9.png)
Thus our answer is .
See Also
| 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. 
