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

This problem is also problem number 4 on the 2015 AMC 12B, just with different names. This is the link.

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

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