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

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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?
 
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?
  
<math>\textbf{(A) } \text{Arn}\qquad\textbf{(B) }\text{Bob}\qquad\textbf{(C) }\text{Cyd}\qquad\textbf{(D) }\text{Dan}\qquad \textbf{(E) }\text{Eve}</math>
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==Solution==
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The five numbers which cause people to leave the circle are <math>7, 14, 17, 21, and 27.</math>
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Arn counts <cmath>7 (assuming they start at </cmath>1) 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,  \textbf{(D)}<math> -scrabbler94
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</math>\textbf{(A) } \text{Arn}\qquad\textbf{(B) }\text{Bob}\qquad\textbf{(C) }\text{Cyd}\qquad\textbf{(D) }\text{Dan}\qquad \textbf{(E) }\text{Eve}$
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2018|num-b=2|num-a=4}}
 
{{AMC8 box|year=2018|num-b=2|num-a=4}}
  
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 13:35, 21 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?


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, \textbf{(D)}$-scrabbler94$\textbf{(A) } \text{Arn}\qquad\textbf{(B) }\text{Bob}\qquad\textbf{(C) }\text{Cyd}\qquad\textbf{(D) }\text{Dan}\qquad \textbf{(E) }\text{Eve}$

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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