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DS - Number problem

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DS - Number problem

by AJ1440 » Sun Oct 09, 2011 5:12 pm
HI All .. posting one DS problem from GMAT official .. though I know the answer, plz help in understanding how logic works for this one

128. 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.

Thanks in Advance!
AJ
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Oct 09, 2011 7:30 pm
AJ1440 wrote:HI All .. posting one DS problem from GMAT official .. though I know the answer, plz help in understanding how logic works for this one

128. 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.

Thanks in Advance!
AJ
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 AJ1440 » Sun Oct 09, 2011 10:00 pm
many thanks .. u r amazing!!
do u think difficulty level for this questions can be considered as high for GMAT?
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by parul9 » Sun Oct 09, 2011 11:08 pm
B!

We have to find if n is a multiple of m.
From stmt 1 - 3n is a multiple of m and m is b/w 4 and 12.
If m is 6 or 12, we can't derive from this info whether n too would be a multiple of m.
So NOT SUFFICIENT.

From stmt 2 - 13n is a multiple of m.
since m is less than 13, it follows that n would be a multiple of m.
So, this is SUFFICIENT.

Answer would be B.
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