Difference between revisions of "2021 JMPSC Invitationals Problems/Problem 3"
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Revision as of 16:30, 11 July 2021
Problem
There are exactly 
even positive integers less than or equal to 
that are divisible by 
. What is the sum of all possible positive integer values of ?
Solution
must have exactly 5 even multiples less than . We have two cases, either is odd or even. If is even, then 
. We solve the inequality to find 
, but since must be an integer we have x = 18, 20. If is odd, then we can set up the inequality 
. Solving for the integers must be 
. The sum is 
or 
~Grisham
See also
- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition. 
