FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 1
Revision as of 13:57, 19 November 2020 by Icematrix2 (talk | contribs) (Created page with "==Problem== If <math>x</math> and <math>y</math> are positive integers such that their product is <math>64,</math> what is the sum of all distinct values for <math>xy+x+y?</ma...")
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
2019 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by First problem |
Followed by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by FidgetBoss 4000's Mock American Mathematics Competitions.