Maths Olympiad Prep

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Combinatorics Difficulty 2.0 Junior Find the answer

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

Pick one

Solution

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

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.