riteshgupta wrote:

Can any one provide a much elaborate solution, did not understand the above's....

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?Basically the question asks whether

n (# of students) is a multiple of

m (# of classrooms), or whether

\frac{n}{m}=integer, because if it is then we would be able to assign students to classrooms so that each classroom has the same number of students assigned to it.

Given:

3<m<13<n.

(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 -->

\frac{3n}{m}=integer, from this we can not say whether

\frac{n}{m}=integer. For example

n indeed might be a multiple of

m (

n=14 and

m=7) but also it as well might not be (

n=14 and

m=6). Not sufficient.

(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 -->

\frac{13n}{m}=integer, now as given that

3<m<13 then 13 (prime number) is not a multiple of

m, so

\frac{13n}{m} to be an integer the

n must be multiple of

m. Sufficient.

Answer: B.

Hope its' clear.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-school-admin-will-assign-each-student-in-a-group-of-n-127509.html In case of any questions please post there.

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