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If 3 < m < 13 < n,

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If 3 < m < 13 < n,

by ska7945 » Fri Aug 22, 2008 11:19 pm
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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by abcdefg » Wed Jul 15, 2009 10:12 pm
anyone have any good quick solutions to this? thanks
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by tohellandback » Wed Jul 15, 2009 10:24 pm
The solution in itself is pretty quick but explanation might be lengthy.

To get equal number of student in each class n must be multiple of m

1) basically it tells you that 3n is a multiple of m. From this we can't be sure whether n is a multiple of m.
for ex, take m=6
now when n is a multiple of 6 we can have equal number of students in each class(both for 3n and n)
but when n=2,4,810,...3n satisfies the condition but n does not.
INSUFFICIENT

2) its just telling you that 13n is a multiple of m
now for any number 3<m<13, if 13 n is divisible by m, then n is divisible by m
In other words, n must have all the factors of m because 13>m
SUFFICIENT
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by viju9162 » Thu Jul 16, 2009 5:50 am
Dear Friend,

I didnt really get the explaination. Is it possible to brief more about it?

Thanks,
Viju
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by GmatAggie » Thu Jul 16, 2009 6:41 am
First of all, this is my first post on this blog and I am NOT sure if I how I explain this is correct or not but here's my logic:

The Question:
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?

Once we break down the question it basically tells us that there are no less than 3 class rooms or no more than 13 classrooms to which the students can be assigned to. It also says that n is infinite.

Statement one tells us that 3n is a multiple of m. But if you look at 3n. you can see that there are multiple possibles for it to be m, and since the statement told us that 3<m<13. We have at least 3 possibilities: 6, 9, and 12. From 3(2), 3(3), and 3(4). Since we get 3 possibile possibilities in the inequality and we don't get a definite answer, this statement is INSUFFICIENT.

Statement 2 on the other hand tells us that 13n is a multiple of m, and since the in equality states that 3<m<13. We know that there cannot be multiple answers in the inequality for m, since 13n is a mulitple. This gives us a definite answer. That makes this answer SUFFICIENT.

Please reply if you agree or disagree with my reasoning.

Thank you.
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by Patrick_GMATFix » Tue Jun 08, 2010 6:18 am
[This question is also discussed here]

This is a pretty tough divisibility question. It basically asks whether we can distribute n kids into m equal groups. In other words, REPHRASE: Is n divisible by m?

This is #128 in OG12. Detailed solution and take-away are attached below.

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