Difference between revisions of "2021 JMPSC Invitationals Problems/Problem 3"
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+ | ==See also== | ||
+ | #[[2021 JMPSC Invitational Problems|Other 2021 JMPSC Invitational Problems]] | ||
+ | #[[2021 JMPSC Invitational Answer Key|2021 JMPSC Invitational Answer Key]] | ||
+ | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
+ | {{JMPSC Notice}} |
Revision as of 16:26, 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 Invitational Problems
- 2021 JMPSC Invitational Answer Key
- All JMPSC Problems and Solutions
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.