Difference between revisions of "2018 AMC 8 Problems/Problem 3"

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The five numbers which cause people to leave the circle are <math>7, 14, 17, 21,</math> and <math>27.</math>
 
The five numbers which cause people to leave the circle are <math>7, 14, 17, 21,</math> and <math>27.</math>
  
Arn counts <math>7</math> (assuming they start at <math>1</math>) so he leaves first. Then Cyd counts <math>14</math>, as there are <math>7</math> numbers to be counted from this point. Then Fon, Bob, Eve, so last one standing is Dan, hence meaning the answer would be <math>\textbf{(D)}</math>
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Arn counts <math>7</math> (assuming they start at <math>1</math>) so he leaves first. Then Cyd counts <math>14</math>, as there are <math>7</math> numbers to be counted from this point. Then Fon, Bob, Eve, so last one standing is Dan, hence meaning the answer would be <math>\boxed{\textbf{(D)}Dan}</math>
  
 
==See Also==
 
==See Also==

Revision as of 15:43, 23 November 2018

Problem 3

Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle?

$\textbf{(A) } \text{Arn}\qquad\textbf{(B) }\text{Bob}\qquad\textbf{(C) }\text{Cyd}\qquad\textbf{(D) }\text{Dan}\qquad \textbf{(E) }\text{Eve}$

Solution

The five numbers which cause people to leave the circle are $7, 14, 17, 21,$ and $27.$

Arn counts $7$ (assuming they start at $1$) so he leaves first. Then Cyd counts $14$, as there are $7$ numbers to be counted from this point. Then Fon, Bob, Eve, so last one standing is Dan, hence meaning the answer would be $\boxed{\textbf{(D)}Dan}$

See Also

2018 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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 AJHSME/AMC 8 Problems and Solutions

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