Difference between revisions of "2015 AMC 12B Problems/Problem 4"
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===Note=== | ===Note=== | ||
| − | + | This problem is also problem number 5 on the [[2015 AMC 10B]]. | |
| − | + | [https://artofproblemsolving.com/wiki/index.php/2015_AMC_10B_Problems/Problem_5] | |
| + | |||
==Problem== | ==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? | 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? | ||
Revision as of 09:31, 8 April 2023
Contents
Note
This problem is also problem number 5 on the 2015 AMC 10B. [1]
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 following all the logic looks like:
![\[-, \text{Nabeel}, \text{Rahul}, -, \text{Rafsan}, \text{Arabi}, -, \text{Marzuq}, -, \text{Lian}, -, -\]](http://latex.artofproblemsolving.com/e/c/3/ec364be22d6d93081d6a952a2a475fea025d3694.png)
Clearly the 8th place runner is 
.
Solution 2
We can list these out vertically to ensure clarity, starting with Marta and working from there.
![\[1 -\]](http://latex.artofproblemsolving.com/1/0/5/105aa601b74d255fdec68cea63a561c4634d492d.png)
![\[2 Nabeel\]](http://latex.artofproblemsolving.com/f/7/2/f721a5b009d17bdf473b8944f860e5118b860d7c.png)
![\[3 Rahul\]](http://latex.artofproblemsolving.com/0/5/c/05c991ab9ec67e5b408ad328f3fb83c40ed8b7d9.png)
![\[4 -\]](http://latex.artofproblemsolving.com/3/4/d/34dde0e8318825de00c6c696b1c5e715454d4420.png)
![\[5 Rafsan\]](http://latex.artofproblemsolving.com/b/b/c/bbc8eb8fb4eca84c52ebaa9998651c2499f9ace9.png)
![\[6 Arabi\]](http://latex.artofproblemsolving.com/c/e/1/ce16a03a4e7f138594cb581ee42ba189623aa0c1.png)
![\[7 -\]](http://latex.artofproblemsolving.com/1/4/f/14fa5dbaae18d5eaff20f23b696f5eac2a6254be.png)
![\[8 Marzuq\]](http://latex.artofproblemsolving.com/8/8/e/88eef4f42e9ecb7c6834e8e77e0b7b9613916639.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. 
