Difference between revisions of "FidgetBoss 4000's 2019 AMC 12B Problems/Problem 1"
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==See also== | ==See also== | ||
| − | {{AMC12 box|year=2019|ab=B|before=First problem|after=[[FidgetBoss 4000's Mock AMC 12B Problems/Problem 2]]}} | + | {{AMC12 box|year=2019|ab=B|before=First problem|after=[[FidgetBoss 4000's Mock AMC 12B Problems/Problem 2|Problem 2]]}} |
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| + | [[Category:Introductory Algebra Problems]] | ||
{{FidgetBoss Notice}} | {{FidgetBoss Notice}} | ||
Revision as of 13:53, 19 November 2020
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. 
