Difference between revisions of "2015 AMC 12B Problems/Problem 4"
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==Problem== | ==Problem== | ||
− | Lian, Marzuq, Rafsan, Arabi, | + | 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? |
− | <math>\textbf{(A)}\; \text{Lian} \qquad\textbf{(B)}\; \text{Marzuq} \qquad\textbf{(C)}\; \text{Rafsan} \qquad\textbf{(D)}\; \text{ | + | <math>\textbf{(A)}\; \text{Lian} \qquad\textbf{(B)}\; \text{Marzuq} \qquad\textbf{(C)}\; \text{Rafsan} \qquad\textbf{(D)}\; \text{Nabeel} \qquad\textbf{(E)}\; \text{Rahul}</math> |
==Solution 1== | ==Solution 1== | ||
Let <math>-</math> denote any of the 6 racers not named. Then the correct order following all the logic looks like: | Let <math>-</math> denote any of the 6 racers not named. Then the correct order following all the logic looks like: | ||
− | <cmath>-, \text{ | + | <cmath>-, \text{Nabeel}, \text{Rahul}, -, \text{Rafsan}, \text{Arabi}, -, \text{Marzuq}, -, \text{Lian}, -, -</cmath> |
Clearly the 8th place runner is <math>\fbox{\textbf{(B)}\; \text{Marzuq}}</math>. | Clearly the 8th place runner is <math>\fbox{\textbf{(B)}\; \text{Marzuq}}</math>. | ||
Line 16: | Line 16: | ||
<cmath>1 - </cmath> | <cmath>1 - </cmath> | ||
− | <cmath>2 | + | <cmath>2 Nabeel </cmath> |
<cmath>3 Rahul </cmath> | <cmath>3 Rahul </cmath> | ||
<cmath>4 - </cmath> | <cmath>4 - </cmath> |
Latest revision as of 04:51, 15 February 2021
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 following all the logic looks like:
Clearly the 8th place runner is .
Solution 2
We can list these out vertically to ensure clarity, starting with Marta and working from there.
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 |
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