2006 AMC 8 第 12 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
12.
Antonette 在一场有 道题的测试中得分率为 ，在一场有 道题的测试中得分率为 ，在一场有 道题的测试中得分率为 。如果三次测试合并成一场有 道题的测试，哪个百分数最接近她的总成绩？
Antonette gets on a -problem test, on a -problem test and on a -problem test. If the three tests are combined into one -problem test, which percent is closest to her overall score?
小提示：
把每次测试百分比转化为答对题数。
Convert each test percentage into a number of correct answers.
大提示：
这是按题目数量加权的平均，不是三个百分比的普通平均。
This is a weighted average by number of problems, not a plain average of the three percentages.
解答：
Antonette 第一次测试答对 题。类似地，她第二、三次测试分别答对 题和 题。
总共答对 题。合并测试成绩为 ，最接近 。
所以正确答案是 D。
Antonette got questions right on the first test. Similarly, she got and problems right on her second and third tests.
Adding these up yields correct questions. Her score on the combined test would have been , closest to .
Thus, D is the correct answer.
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