Question

代数课上的所有学生都参加了一次满分 $100$ 分的考试。五名学生得了 $100$ 分，每名学生至少得 $60$ 分，平均分为 $76$ 。这个班最少可能有多少名学生？

All the students in an algebra class took a $100$ -point test. Five students scored $100,$ each student scored at least $60,$ and the mean score was $76.$ What is the smallest possible number of students in the class?

$10$

$11$

$12$

$13$

$14$

答案：D

知识点：平均数极限情形界定

难度评级：1440

小提示：

把每个分数看成与平均分 $76$ 的差。

Measure each score as its deviation from the mean $76$

大提示：

五个 $100$ 分一共比平均分高 $120$ 分；每个其他学生最多比平均分低 $16$ 分。

The five $100$ s are $120$ points above the mean; each other student is at most $16$ below it

解答：

每个 $100$ 分比平均分 $76$ 高 $24$ 分，所以五个学生共高出 $120$ 分。这些必须由低于平均分的分数抵消，而每个剩余学生最多低 $76 - 60 = 16$ 分。因此至少需要 $\dfrac{120}{16} = 7.5$ ，即 $8$ 名额外学生，总数为 $13$ 。五个 $100$ 分和八个 $61$ 分可以达到这一情况。

因此正确答案是 D。

Each score of $100$ is $24$ above the mean, so the five contribute $120$ points above $76.$ These must be balanced by points below the mean, and each remaining student is at most $76 - 60 = 16$ below. So at least $\dfrac{120}{16} = 7.5,$ hence $8$ more students are needed, for a total of $13.$ Five $100$ s and eight $61$ s achieve this.

Thus, the correct answer is D.

2004 AMC 12B 第 11 题

答案：D

难度评级：1440

小提示：

大提示：

解答：

其他年份的第 11 题