2017 AMC 12B 第 10 题

Question

在 Typico 高中，

60\%

的学生喜欢跳舞，其余学生不喜欢。在喜欢跳舞的学生中，

80\%

说自己喜欢跳舞，其余说自己不喜欢。在不喜欢跳舞的学生中，

90\%

说自己不喜欢跳舞，其余说自己喜欢。在所有说自己不喜欢跳舞的学生中，实际喜欢跳舞的学生占多少比例？

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}\%

喜欢跳舞但说自己不喜欢的学生占全体学生的

60\% \cdot 20\%

。

Students who like dancing but say they dislike it are

60\% \cdot 20\%

of all students

用这一组人数除以所有说自己不喜欢跳舞的人数

Divide that group by the total who say they dislike dancing

喜欢跳舞但说自己不喜欢的学生占全体学生的

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

。不喜欢跳舞且如实这么说的学生占

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

。在所有说自己不喜欢跳舞的人中，实际喜欢跳舞的比例为

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

所以正确答案是 D。

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.

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