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Difference between revisions of "2017 AMC 10B Problems/Problem 11"

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~savannahsolver
 
~savannahsolver
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The number of people who say they dislike dancing but actually like dancing is, <math>60%</math> times <math>20%</math> which is <math>12%</math>. Then the number of people who say they dislike dancing and actually do dislike dancing is, <math>40%</math> times <math>90%</math> which is <math>36%</math>. 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 <math>\frac{12%}{12% + 36%}</math> which would then be <math>\frac{12%}{48%} = \frac{1}{4}</math> or
 
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<math>\boxed{\textbf{(D) }\ 25%}</math>
 
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2017|ab=B|num-b=10|num-a=12}}
 
{{AMC10 box|year=2017|ab=B|num-b=10|num-a=12}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 23:15, 6 January 2021

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

See Also

2017 AMC 10B (Problems • Answer Key • Resources)
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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