Question

几名学生参加三场赛跑。每场比赛第一名得 $5$ 分，第二名得 $3$ 分，第三名得 $1$ 分。没有并列名次。一个学生在三场比赛中至少要得到多少分，才能保证他的总分高于任何其他学生？

Several students are competing in a series of three races. A student earns $5$ points for winning a race, $3$ points for finishing second, and $1$ point for finishing third. There are no ties. What is the smallest number of points that a student must earn in the three races to be guaranteed of earning more points than any other student?

$9$

$10$

$11$

$13$

$15$

答案：D

知识点：极端原理

难度评级：1090

解答：

总分 $11$ 并不能保证第一，例如 $5+5+1$ 可能被另一个学生也得到 $11$ 分。

但如果一个学生得到 $5+5+3 = 13$ 分，那么剩下的名次使任何其他学生最多得到 $3+3+5 = 11$ 分。因此 $13$ 分能保证领先。

所以正确答案是 D。

A total of $11$ (for example $5+5+1$ ) does not guarantee first place, since another student could also reach $11.$

But if one student scores $5+5+3 = 13,$ the remaining places give every other student at most $3+3+5 = 11.$ So $13$ points guarantees the lead.

Thus, the correct answer is D .

1991 AMC 8 第 14 题

答案：D

难度评级：1090

解答：

其他年份的第 14 题