Difference between revisions of "2015 AMC 10B Problems/Problem 5"

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==Problem==
 
==Problem==
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NOTE: this problem is supposedly the same as this question: https://artofproblemsolving.com/wiki/index.php/2015_AMC_12B_Problems/Problem_4
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but somehow the names are all different
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David, Hikmet, Jack, Marta, Rand, and Todd were in a <math>12</math>-person race with <math>6</math> other people. Rand finished <math>6</math> places ahead of Hikmet. Marta finished <math>1</math> place behind Jack. David finished <math>2</math> places behind Hikmet. Jack finished <math>2</math> places behind Todd. Todd finished <math>1</math> place behind Rand. Marta finished in <math>6</math>th place. Who finished in <math>8</math>th place?
 
David, Hikmet, Jack, Marta, Rand, and Todd were in a <math>12</math>-person race with <math>6</math> other people. Rand finished <math>6</math> places ahead of Hikmet. Marta finished <math>1</math> place behind Jack. David finished <math>2</math> places behind Hikmet. Jack finished <math>2</math> places behind Todd. Todd finished <math>1</math> place behind Rand. Marta finished in <math>6</math>th place. Who finished in <math>8</math>th place?
  

Revision as of 20:30, 5 November 2021

Problem

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

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

https://youtu.be/61oSoeT0ULA

~savannahsolver

See Also

2015 AMC 10B (ProblemsAnswer KeyResources)
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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