2017 AMC 10B Problems/Problem 11

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

2017 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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2017 AMC 10B Problems/Problem 11

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