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More than 100 students signed up to participate in the Geography Bowl competition. If teams of 2 could be made with no students left out, and teams of 13 could also be made with no students left out, what is the fewest number of students who could have signed up for the Geography Bowl?

 May 13, 2023
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1 - LCM(2, 13) ==26. So, you could have 13 teams of 2 students each, or 2 teams of 13 students each.

 

But, the question says "more than 100 students signed up to participate in GB competition."

 

So, we have to find number > 100 that is divisible by both 2 and 13. 102 is not divisible by 13. Next 104 is divisible by both 2 and 13, because: 104 mod 13==0

 

Therefore, the fewest number of students that signed up was: 104 students.

 May 13, 2023

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