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by ketkoag » Sat Mar 28, 2009 2:23 am
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.

OA: B
Please explain how to tackle this problem.
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Source: — Data Sufficiency |
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by DanaJ » Sat Mar 28, 2009 4:12 am
What the question is really asking is whether n is divisible by m: if it is the case, then there will be n/m students in each classroom.

1. this stmt tells you that 3n is divisible by m. But that does not mean that n is also divisible by m: think of n = 14 and m = 6. On the other hand, take n = 15 and m = 5 and n is divisible by m.

2. this stmt tells you that 13n is divisible by m. Since 3 < m < 13 < n, n must be divisible by m (because 13 is prime). So 2 is sufficient.
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