Problem:
Joey and his five brothers are ages , and . One afternoon two of his brothers whose ages sum to went to the movies, two brothers younger than went to play baseball, and Joey and the -year-old stayed home. How old is Joey?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The -year-old and the two brothers who went to play baseball account for three of the four brothers who are younger than . Because the only age pairs that sum to are and , and , and and , the brothers who went to the movies must be and years old. Hence the -year-old and -year-old brothers went to play baseball, and Joey is .
The problems on this page are the property of the MAA's American Mathematics Competitions