FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 1
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Problem
If and
are positive integers such that their product is
what is the sum of all distinct values for
Solution 1
Use Simon's Favorite Factoring Trick to deduce . We know
and
are positive integers and
. So, we have the following possibilities for the pair
. Note that we do not have to account for flipping
and
because the question asks for only the
values for
. If
, then
. If
, then
. If
, then
. If
, then
. The sum of these distinct values is
.
See also
FidgetBoss 4000's 2019 Mock AMC 12B (Problems • Answer Key • Resources) | |
Preceded by First problem |
Followed by Problem 2 |
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All AMC 12 Problems and Solutions |
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