2015 AMC 10B Problems/Problem 5

Problem

David, Hikmet, Jack, Marta, Rand, and Todd were in a $12$ -person race with $6$ other people. Rand finished $6$ places ahead of Hikmet. Marta finished $1$ place behind Jack. David finished $2$ places behind Hikmet. Jack finished $2$ places behind Todd. Todd finished $1$ place behind Rand. Marta finished in $6$ th place. Who finished in $8$ th place?

$\textbf{(A) } \text{David} \qquad\textbf{(B) } \text{Hikmet} \qquad\textbf{(C) } \text{Jack} \qquad\textbf{(D) } \text{Rand} \qquad\textbf{(E) } \text{Todd}$

Solution

Because Marta was $6$ th, Jack was $5$ th, so Todd was $3$ rd. Thus, Rand was $2$ nd and the 8th place finisher was $\boxed{\mathbf{(B)}\ \mathrm{Hikmet}}$

Video Solution 1

https://youtu.be/sNdfksIblfs

~Education, the Study of Everything

Video Solution 2

https://youtu.be/61oSoeT0ULA

~savannahsolver

Note

NOTE: this problem is supposedly the same as this question: https://artofproblemsolving.com/wiki/index.php/2015_AMC_12B_Problems/Problem_4 but somehow the names are all different

2015 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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