MathDB
Typical school of High

Source: 2017 AMC 10B #11 / AMC 12B #10

February 16, 2017
AMC 10AMC 12ratios

Problem Statement

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?
<spanclass=latexbold>(A)</span>10%<spanclass=latexbold>(B)</span>12%<spanclass=latexbold>(C)</span>20%<spanclass=latexbold>(D)</span>25%<spanclass=latexbold>(E)</span>3313%<span class='latex-bold'>(A) </span> 10\%\qquad <span class='latex-bold'>(B) </span> 12\%\qquad <span class='latex-bold'>(C) </span> 20\%\qquad <span class='latex-bold'>(D) </span> 25\%\qquad <span class='latex-bold'>(E) </span> 33\frac{1}{3}\%