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Tough Number Properties question ! Need help

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by waggrave » Mon Aug 15, 2011 8:52 am
Hello,

I found this question in OG12, and I'm not really satisfied with the explanation given.
Could anyone help me to understand it ?

Thanks a lot...

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.
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Source: — Data Sufficiency |
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by gmatboost » Mon Aug 15, 2011 9:50 am
Translation of question:
Is n evenly divisible by m?
(Or, if you prefer: Is m a factor of n?)


Statement 1: 3n is divisible by m / m is a factor of 3n.
This does NOT necessarily mean that m is a factor of n, since the 3 in 3n could be part of m.
For example, m = 6 (contains 3), n = 20 (does not contain 3).

Statement 2: 13n is divisible by m / m is a factor of 13n.
This DOES necessarily mean that m is a factor of n, since m<13 and therefore does not contain 13 as a factor.

Answer is B.
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by waggrave » Mon Aug 15, 2011 1:30 pm
Thank you very much for your really clear answer. It's not in fact such a hard question, i feel stupid ! Thanks aniway :)
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