2017 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 11 Easy

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? (2017 AMC 10B Problem, Question#11)

  • A.

    10\%

  • B.

    12\%

  • C.

    20\%

  • D.

    25\%

  • E.

    33\dfrac{1}{3}\%

Answer:D

60\%\cdot20\%=12\% of the people that claim that they dislike dancing actually like it,and 40\%\cdot90\%=36\%. Therefore, the answer is \dfrac{12\%}{12\%+36\%}=\rm (D)25\%.

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