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

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===Note===
 
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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
 
 
==Problem==
 
==Problem==
 
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?
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~Education, the Study of Everything
 
~Education, the Study of Everything
  
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==Video Solution==
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==Video Solution 2==
 
https://youtu.be/61oSoeT0ULA
 
https://youtu.be/61oSoeT0ULA
  
 
~savannahsolver
 
~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
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2015|ab=B|num-b=4|num-a=6}}
 
{{AMC10 box|year=2015|ab=B|num-b=4|num-a=6}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 00:03, 31 August 2022

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

See Also

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

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

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