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Difference between revisions of "2017 AMC 10B Problems/Problem 11"

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<math>\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%</math>
 
<math>\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%</math>
 
==Solution==
 
==Solution==
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<math>60\% \cdot 20\% = 12\%</math> of the people that claim that they dislike dancing actually like it, and <math>40\% \cdot 90\% = 36\%</math>. Therefore, the answer is <math>\frac{12\%}{12\%+36\%} = \boxed{\textbf{(D) } 25\%}</math>.
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<math>60\% \cdot 20\% = 12\%</math> of the people that claim that they dislike dancing actually like it, and <math>40\% \cdot 90\% = 36\%</math> of the people that claim that they dislike dancing dislike it. Therefore, the answer is <math>\frac{12\%}{12\%+36\%} = \boxed{\textbf{(D) } 25\%}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2017|ab=B|num-b=10|num-a=12}}
 
{{AMC10 box|year=2017|ab=B|num-b=10|num-a=12}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 22:22, 11 January 2020

Problem

At Typico High School, $60\%$ of the students like dancing, and the rest dislike it. Of those who like dancing, $80\%$ say that they like it, and the rest say that they dislike it. Of those who dislike dancing, $90\%$ say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?

$\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%$

Solution

$60\% \cdot 20\% = 12\%$ of the people that claim that they dislike dancing actually like it, and $40\% \cdot 90\% = 36\%$ of the people that claim that they dislike dancing dislike it. Therefore, the answer is $\frac{12\%}{12\%+36\%} = \boxed{\textbf{(D) } 25\%}$.

See Also

2017 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 10 		Followed by
Problem 12
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All AMC 10 Problems and Solutions

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