Data Sufficiency

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

Let a be students assigned per class

1) ma = 3n

so a =3n/m now here m may divide n evenly then it will be possible, however m may be something like 6,9 i,e it has a factor 3, which divides 3 & the other factor divides n, e.g n=20, m=6, howver if m=5 then it divides n

INSUFF

2) ma =13n

so a= 13n/m, now since m is between 3 < m < 13 < n so it will not divide 13 hence for a to be an integer it should divide n

Suff.