2013 AMC 10A Problem 6

Problem 6 of 25Easier

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?

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Solution

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.