A school administrator will assign each student in a group of n students to one 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?

(1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.

(2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.


I could easily understand how statement (1) is not sufficient, however, I have a doubt. The OG explained that if we can show an example which proves that 3n is divisible by m and n alone is not then we can say that the statement is not sufficient.

As for statement (2), after reading the explanation in the OG I felt that the solution there might not strike me intuitively under exam pressure. I preferred the solution explained by the Grockit OG TV, they simply explained that if 13n is divisible by m then m has to be a factor of 13n (as we know m cannot be a factor of 13, subsequently, it is pretty easy to see that n has to be divisible by m.)

Ideally, this should be it and I can move forward to reviewing the next question, but I am not convinced. What if I apply the same logic to statement (1)? That is, if 3n is divisible by m then as we know m cannot be 3 and, also as 3 is a prime number, n should be divisible by m but IT IS NOT.

Could some one throw some light and make things clearer?

Thanks in advance.

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