AMC10 2021 B

AMC10 2021 B · Q4

AMC10 2021 B · Q4. It mainly tests Arithmetic misc, Basic counting (rules of product/sum).

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?

在一场数学竞赛中，有 $57$ 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。在恰好 $23$ 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？

(A) 23 23

(B) 32 32

(D) 41 41

(E) 64 64

Answer

Correct choice: (B)

正确答案：（B）

Solution

There are $46$ blue students paired with a blue partner. The other $11$ students wearing blue shirts must each be paired with a partner wearing a shirt of the opposite color. There are $64$ yellow students remaining. Therefore the requested number of pairs is $\tfrac{64}{2}=\boxed{\textbf{(B)} ~32}$

有 $46$ 名穿蓝色衬衫的学生与蓝色伙伴配对。其余 $11$ 名穿蓝色衬衫的学生必须各自与穿不同颜色衬衫的伙伴配对。剩余 $64$ 名穿黄色衬衫的学生。因此，所求对数为 $\tfrac{64}{2}=\boxed{\textbf{(B)} ~32}$

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