Question

Antonette 在一场有 $10$ 道题的测试中得分率为 $70 \%$ ，在一场有 $20$ 道题的测试中得分率为 $80 \%$ ，在一场有 $30$ 道题的测试中得分率为 $90 \%$ 。如果三次测试合并成一场有 $60$ 道题的测试，哪个百分数最接近她的总成绩？

Antonette gets $70 \%$ on a $10$ -problem test, $80 \%$ on a $20$ -problem test and $90 \%$ on a $30$ -problem test. If the three tests are combined into one $60$ -problem test, which percent is closest to her overall score?

$40$

$77$

$80$

$83$

$87$

答案：D

知识点：平均数百分数

难度评级：1100

解答：

Antonette 第一次测试答对 $0.7\cdot 10=7$ 题。类似地，她第二、三次测试分别答对 $0.8\cdot 20=16$ 题和 $0.9\cdot 30=27$ 题。

总共答对 $50$ 题。合并测试成绩为 $100\cdot \dfrac{50}{60}=83\frac{1}{3}\%$ ，最接近 $83\%$ 。

所以正确答案是 D。

Antonette got $0.7\cdot 10=7$ questions right on the first test. Similarly, she got $0.8\cdot 20=16$ and $0.9\cdot 30=27$ problems right on her second and third tests.

Adding these up yields $50$ correct questions. Her score on the combined test would have been $100\cdot \dfrac{50}{60}=83\frac{1}{3}\%$ , closest to $83\%$ .

Thus, D is the correct answer.

2006 AMC 8 第 12 题

答案：D

难度评级：1100

解答：

其他年份的第 12 题