AMC12 2010 B

AMC12 2010 B · Q6

AMC12 2010 B · Q6. It mainly tests Averages (mean), Casework.

At the beginning of the school year, $50\%$ of all students in Mr. Well's class answered "Yes" to the question "Do you love math", and $50\%$ answered "No." At the end of the school year, $70\%$ answered "Yes" and $30\%$ answered "No." Altogether, $x\%$ of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of $x$?

在学年开始时，Wells先生班上所有学生中有$50\%$对问题“你爱数学吗”回答“是”，另有$50\%$回答“否”。在学年结束时，$70\%$回答“是”，$30\%$回答“否”。总共有$x\%$的学生在学年开始和结束时给出了不同的答案。$x$的最大可能值与最小可能值之差是多少？

(A) 0 0

(B) 20 20

(D) 60 60

(E) 80 80

Answer

Correct choice: (D)

正确答案：（D）

Solution

The minimum possible value would be $70 - 50 = 20\%$. The maximum possible value would be $30 + 50 = 80\%$. The difference is $80 - 20 = \boxed{\textbf{(D) }60}$.

$x$的最小可能值为$70-50=20\%$。$x$的最大可能值为$30+50=80\%$。差为$80-20=\boxed{\textbf{(D) }60}$。

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