2017 AMC 10B Problems/Problem 11

Revision as of 00:09, 7 January 2021 by Math teen (talk | contribs) (Video Solution & Solution)

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?

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

Video Solution & Solution

https://youtu.be/93lThricxLE

~savannahsolver

The number of people who say they dislike dancing but actually like dancing is, $60%*20% = 12%$ (Error compiling LaTeX. ! Missing $ inserted.). Then the number of people who say they dislike dancing and actually do dislike dancing is, $40%*90% = 36%$ (Error compiling LaTeX. ! Missing $ inserted.). After this, we would want to find out what percent of the whole school says they dislike dancing but like it, so we would have $\frac{12%}{12% + 36%}$ (Error compiling LaTeX. ! File ended while scanning use of \frac .) which would then be $\frac{12%}{48%}$ (Error compiling LaTeX. ! File ended while scanning use of \frac .) which is $\frac{1}{4}$ or $\boxed{\textbf{(D)}\ 25%}$ (Error compiling LaTeX. ! File ended while scanning use of \boxed.)

See Also

2017 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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 AMC 10 Problems and Solutions

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