AMC10 2013 A

AMC10 2013 A · Q6

AMC10 2013 A · Q6. It mainly tests Casework, Logic puzzles.

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?

乔伊和他的五个兄弟的年龄分别是3、5、7、9、11和13岁。一天下午，两个年龄和为16岁的兄弟去看电影，两个小于10岁的兄弟去打棒球，乔伊和5岁的兄弟留在家里。乔伊多大年龄？

(A) 3 3

(B) 7 7

(D) 11 11

(E) 13 13

Answer

Correct choice: (D)

正确答案：（D）

Solution

The 5-year-old and the two brothers who went to play baseball account for three of the four brothers who are younger than 10. Because the only age pairs that sum to 16 are 3 and 13, 5 and 11, and 7 and 9, the brothers who went to the movies must be 3 and 13 years old. Hence the 7-year-old and 9-year-old brothers went to play baseball, and Joey is 11.

5岁的孩子和去打棒球的两个兄弟占了小于10岁四个兄弟中的三个。因为唯一年龄和为16的配对是3和13、5和11、7和9，去看电影的兄弟一定是3岁和13岁。因此7岁和9岁的兄弟去打棒球，乔伊是11岁。

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