# Difference between revisions of "2021 JMPSC Invitationals Problems/Problem 3"

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+ | #[[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]] | ||

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## Revision as of 17:26, 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

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