2013 AMC 10A Problems/Problem 6
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[hide]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?
Solution 1
Because the -year-old stayed home, we know that the -year-old did not go to the movies, as the -year-old did not and . Also, the -year-old could not have gone to play baseball, as he is older than . Thus, the -year-old must have stayed home, so Joey is
Solution 2
There are only kids who are under but since the -year old stayed home, the only possible ages who went to play baseball are the brothers who are , either or is but since we need kids to go to baseball who are under , must have been the pair to go to the movies and must have went to baseball, so only the -year old is left, which is answer choice
See Also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AMC 10 Problems and Solutions |
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