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GMAT Word Problem and Inequality

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by abhi75 » Mon Jun 23, 2008 6:39 pm
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.
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Source: — Data Sufficiency |
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by beeparoo » Thu Jun 26, 2008 10:07 am
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?
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by navalpike » Thu Jun 25, 2009 7:18 pm
good solution beeparoo.

Does anyone also have an algebraic solution? Never hurts to know multiple ways to solve these problems.
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by ketkoag » Sun Jun 28, 2009 8:05 am
Yeah, B it is.. this question has been posted many times on this forum..
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by aj5105 » Sun Jun 28, 2009 9:22 pm
Very nice solution beeparoo.
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by berserk » Sat Nov 28, 2009 8:17 pm
very good explanation!
I hv gotten struggled for this Q for an hour.
Thanks...
My goal is just 700
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