Question

在一场数学竞赛中， $57$ 名学生穿蓝色衬衫，另外 $75$ 名学生穿黄色衬衫。这 $132$ 名学生被分成 $66$ 对。其中恰有 $23$ 对中两名学生都穿蓝色衬衫。有多少对中两名学生都穿黄色衬衫？

At a math contest, $57$ students are wearing blue shirts, and another $75$ students are wearing yellow shirts. The $132$ students are assigned into $66$ pairs. In exactly $23$ of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts?

$23$

$32$

$37$

$41$

$64$

答案：B

知识点：数对计数

难度评级：960

视频讲解：

Click to load, then click again to play

文字解答：

蓝蓝配对用掉 $2\cdot 23 = 46$ 名穿蓝色衬衫的学生。因此还有 $57-46=11$ 名穿蓝色衬衫的学生在混合配对中，也就恰有 $11$ 名穿黄色衬衫的学生在混合配对中。

剩下只有 $64$ 名穿黄色衬衫的学生与另一名穿黄色衬衫的学生配对，所以黄黄配对数为 $\dfrac{64}2 = 32$ 。

所以答案是 B。

There are $2\cdot 23 = 46$ students with blue shirts that are in a pair with just blue shirts. This means there are $57-46=11$ students in blue shirts who are paired with someone wearing a yellow shirt, meaning exactly $11$ people wearing yellow shirts are paired with someone wearing a blue shirt.

This leaves just $64$ students wearing a yellow shirt who are paired with someone else wearing a yellow shirt. This yields $\dfrac{64}2 = 32$ pairs.

Thus, the answer is B .

2021 AMC 10B Spring 第 4 题

答案：B

难度评级：960

视频讲解：

文字解答：

其他年份的第 4 题