2013 AMC 10A Problems/Problem 6
Contents
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
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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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