Difference between revisions of "2015 AMC 12B Problems/Problem 4"
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+ | ===Note=== | ||
+ | NOTE: this problem is supposedly the same as this question: https://artofproblemsolving.com/wiki/index.php/2015_AMC_10B_Problems/Problem_5 | ||
+ | but somehow the names are all different | ||
==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? | |
− | <math>\textbf{(A)}\; \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== | + | ==Solution 1== |
− | Let <math>-</math> denote any of the 6 racers not named. Then the correct order following all the logic | + | 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{ | + | Clearly the 8th place runner is <math>\fbox{\textbf{(B)}\; \text{Marzuq}}</math>. |
+ | |||
+ | ==Solution 2== | ||
+ | We can list these out vertically to ensure clarity, starting with Marta and working from there. | ||
+ | |||
+ | |||
+ | <cmath>1 - </cmath> | ||
+ | <cmath>2 Nabeel </cmath> | ||
+ | <cmath>3 Rahul </cmath> | ||
+ | <cmath>4 - </cmath> | ||
+ | <cmath>5 Rafsan </cmath> | ||
+ | <cmath>6 Arabi </cmath> | ||
+ | <cmath>7 - </cmath> | ||
+ | <cmath>8 Marzuq </cmath> | ||
+ | |||
+ | 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 20:32, 5 November 2021
Contents
Note
NOTE: this problem is supposedly the same as this question: https://artofproblemsolving.com/wiki/index.php/2015_AMC_10B_Problems/Problem_5 but somehow the names are all different
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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