GMAT Word Problem and Inequality

[abhi75]

A school administrator will assign each student in a group of n students to one of the 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 the 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 the m classrooms so that each classroom has the same number of students assigned to it.

[beeparoo]

Here's my crack at it.

Question is asking: Is n/m is an integer? Yes or No?

Statement (1): 3n/m = integer. Here, m can be a multiple of 3 or be one of n's factors.
If m is 6, while n is say, 14, then n/m will not result in an integer. Ans is NO.
But if m is 7, while n is 14, then indeed, the answer is YES.
INSUFFICIENT

Statement (1): 13n/m = integer.
Since m < 13, m is not a multiple of this prime number. Therefore, m must be a factor of n, and n/m must be an integer. SUFFICIENT

I choose B. What is the OA?

[navalpike]

good solution beeparoo.

Does anyone also have an algebraic solution? Never hurts to know multiple ways to solve these problems.

[ketkoag]

Yeah, B it is.. this question has been posted many times on this forum..

[aj5105]

Very nice solution beeparoo.

[berserk]

very good explanation!
I hv gotten struggled for this Q for an hour.
Thanks...