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#128 in OG 12 DS A school administrator will assign each...

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by beyondenim1 » Mon Feb 14, 2011 10:02 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.


I'm stumped with this one. I've browsed this question already and still I cant fully grasp the concept in #2.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon Feb 14, 2011 10:17 pm
The question can be rephrased as "If 3 < m < 13 < n, is n/m an integer?"

(1) The information in statement 1 implies that 3n/m is an integer. Now we have find whether n/m is an integer.
Given that 3 < m < 13 < n, if n = 36 and m = 6, then n/m is an integer.
On the other hand if n = 40 and m = 6, then n/m is not an integer.
Since we don't get a unique answer, so (1) is NOT SUFFICIENT.

(2) According to the statement, 13n/m is an integer.
3 < m < 13 < n implies that m lies between 3 and 13 but is not 13, so 13n/m can be integer only if n/m is an integer.
So, (2) is SUFFICIENT.

The correct answer is B.
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by Night reader » Mon Feb 14, 2011 10:19 pm
two ways to tackle this question simple arithmetic if n cab be divided by m or combinatoric principle
st(1) 3nCm only possible when 3! can be factored in the denominator m. When m=6, 3n can be factored, but when m=5 it's difficult, or even 11 :( Not Sufficient
st(2) 13nCm, 13n can never be factored in m as m<13 and 13 is a prime factor. So we answer no with st(2) and Sufficient

IOM B
beyondenim1 wrote: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'm stumped with this one. I've browsed this question already and still I cant fully grasp the concept in #2.
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