Difference between revisions of "2017 AMC 12B Problems/Problem 10"

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==Solution==
 
==Solution==
Let there be <math>100</math> students. <math>60</math> of them like dancing, and <math>40</math> do not. Of those who like dancing, <math>20\%</math>, or <math>12</math> of them say they dislike dancing. Of those who dislike dancing, <math>90\%</math>, or <math>36</math> of them say they dislike it. Thus, <math>\frac{12}{12+36} = \frac{12}{48} = \frac{1}{4} = 25\% \boxed{\textbf{(D)}}</math>
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WLOG, let there be <math>100</math> students. <math>60</math> of them like dancing, and <math>40</math> do not. Of those who like dancing, <math>20\%</math>, or <math>12</math> of them say they dislike dancing. Of those who dislike dancing, <math>90\%</math>, or <math>36</math> of them say they dislike it. Thus, <math>\frac{12}{12+36} = \frac{12}{48} = \frac{1}{4} = 25\% \boxed{\textbf{(D)}}</math>
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2017|ab=B|num-b=9|num-a=11}}
 
{{AMC12 box|year=2017|ab=B|num-b=9|num-a=11}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 22:38, 2 March 2017

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?

$\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ \frac{100}{3}\%$

Solution

WLOG, let there be $100$ students. $60$ of them like dancing, and $40$ do not. Of those who like dancing, $20\%$, or $12$ of them say they dislike dancing. Of those who dislike dancing, $90\%$, or $36$ of them say they dislike it. Thus, $\frac{12}{12+36} = \frac{12}{48} = \frac{1}{4} = 25\% \boxed{\textbf{(D)}}$

See Also

2017 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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 12 Problems and Solutions

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