Difference between revisions of "2017 AMC 10B Problems/Problem 11"
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<math>\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%</math> | <math>\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%</math> | ||
==Solution== | ==Solution== | ||
| − | <math>60\% \cdot 20\% = 12\%</math> of the people that claim that they | + | <math>60\% \cdot 20\% = 12\%</math> of the people that claim that they like dancing actually dislike it, and <math>40\% \cdot 90\% = 36\%</math> of the people that claim that they dislike dancing dislike it. Therefore, the answer is <math>\frac{12\%}{12\%+36\%} = \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 22:33, 26 August 2020
Problem
At Typico High School, 
of the students like dancing, and the rest dislike it. Of those who like dancing, 
say that they like it, and the rest say that they dislike it. Of those who dislike dancing, 
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?
Solution
of the people that claim that they like dancing actually dislike it, and 
of the people that claim that they dislike dancing dislike it. Therefore, the answer is 
.
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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