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

Solution 2

Assume WLOG that there are 100 people. Then 60 of them like dancing, 40 dislike dancing. Of the ones that like dancing, 48 say they like dancing and 12 say they dislike it. Of the ones who dislike dancing, 36 say they dislike dancing and 4 say they like it. We want the ratio of students like it but say they dislike it to the total amount of students that say they dislike it. This is $\frac{12}{12+36}=\frac{12}{48}=\frac{1}{4}$ . We choose $\boxed{\textbf{(D) } 25\%}$

Video Solution

https://youtu.be/93lThricxLE

~savannahsolver

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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Problem

Solution

Solution 2

Video Solution

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