A school administrator will assign each student

A school administrator will assign each student in a group of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?

2 Explanations

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Varun S Nair

But 3 is also a prime number. Why can't I extend the same logic of statement 2 to statement 1 and conclude that statement 1 is also not sufficient?

I'm talking about the case when I use n = 100 & m = 26. Please explain.

Sep 16, 2019 • Comment

Adam

First of all, statement 1 is not sufficient. Statement 2 is sufficient. And m must be less than 13, so the example is when n = 100 and m = 6.

The idea here is that, according to statement 1, 3*(n/m) = an integer. This is true when n/m is an integer (yes to the prompt), or when m is a multiple of 3. So, if m = 9 and n = 24, then n/m is not an integer, but 3n/m is. Hence, insufficient.

Similarly, for statement 2, 13*(n/m) is an integer when n/m is an integer, or when m is a multiple of 13. However, m is less than 13, so it can't be a multiple of 13. That's why statement 2 is sufficient.

Sep 24, 2019 • Reply

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Mike McGarry, Magoosh Tutor