Question

Joey 和他的五个兄弟年龄分别为 $3$ 、 $5$ 、 $7$ 、 $9$ 、 $11$ 和 $13$ 。一天下午，两个年龄和为 $16$ 的兄弟去看电影，两个小于 $10$ 岁的兄弟去打棒球，Joey 和 $5$ 岁的兄弟留在家里。Joey 几岁？

Joey and his five brothers are ages $3,$ $5,$ $7,$ $9,$ $11,$ and $13.$ One afternoon two of his brothers whose ages sum to $16$ went to the movies, two brothers younger than $10$ went to play baseball, and Joey and the $5$ -year-old stayed home. How old is Joey?

$3$

$7$

$9$

$11$

$13$

答案：D

知识点：逻辑推理分类讨论

难度评级：1140

解答：

年龄和为 $16$ 的配对有 $(3,13)$ 、 $(5,11)$ 、 $(7,9)$ 。

$5$ 岁的人留在家里，所以看电影的不能是 $(5,11)$ 。若 $7$ 岁和 $9$ 岁的兄弟去看电影，则剩下小于 $10$ 岁的只有 $3$ 岁的兄弟，不够两人去打棒球。

因此看电影的是 $(3,13)$ ，打棒球的是 $(7,9)$ ，剩下的 Joey 是 $11$ 岁。

所以正确答案是 D。

The age pairs that sum to $16$ are $(3,13)$ , $(5,11)$ , and $(7,9)$ .

The $5$ -year-old stayed home, so the movie pair cannot be $(5,11)$ . If $7$ and $9$ went to the movies, then the only remaining brother younger than $10$ would be the $3$ -year-old, not enough for baseball.

Thus the movie pair was $(3,13)$ , the baseball pair was $(7,9)$ , and Joey is the remaining brother, age $11$ .

Thus, D is the correct answer.

2013 AMC 10A 第 6 题

答案：D

难度评级：1140

解答：

其他年份的第 6 题