2017 AMC 12B Problem 10

Question

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?

10\%

12\%

20\%

25\%

33\tfrac{1}{3}\%

Students who like dancing but say they dislike it are

60\% \cdot 20\%

of all students

Divide that group by the total who say they dislike dancing

Students who like dancing but say they dislike it make up

60\% \cdot 20\% = 12\%

of all students. Students who dislike dancing and say so make up

40\% \cdot 90\% = 36\%.

Among everyone who says they dislike dancing, the fraction who actually like it is

\frac{12}{12 + 36} = \frac{12}{48} = \frac{1}{4} = 25\%.

Thus, the correct answer is D.

Problem 10 in other years