12th OG: DS #128

[thatsku]

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?

I. 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.

II. 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 <--- Highlight to see the OA


iblurker comments

[thatsku]

Answer explanation will follow after discussion.....

[farooq]

I'm unable to crack this question. I don't know how I will take my GMAT exam

[touche]

m ..classrooms---4 to 12
n...students>13
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? Implies is n divisible by m?
I. 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

3n is a multiple of m,,... insuff

II. 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.
13 n is divisible by m.... implies that n is divisible by m... suff
B

[nverma]

IMO D..

Let n=14, so 3n=42 and 13n= 182..

Statement 1:
Is 42 divisible by m, where m=4,5,6,7,8,910,11,12
yes it is divisible by 6 and 7..SUFF.

Statement 2:
Is 182 divisible by m, where m=4,5,6,7,8,910,11,12
yes it is divisible by 7..SUFF

[sk_gmat]

given: 3 < m < 13 < n

I. 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.

II. 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.

Stmt I: 3n/m is an integrer, is n/m an integer?
3n/m = 3(n/m) m varies from 4 to 12. 3 can divide some values between this range, hence 3(n/m) may reduce to a fraction or an integer and hence we can not be sure if n/m would be a fraction or an integer. Hence insufficient

Stmt II: 13n/m is an integrer, is n/m an integer?
13n/m = 13(n/m) and m varies from 4 to 12. since 13 can NEVER divide any value of m, n/m is an integer to make 13(n/m) an integer. Sufficient

Hence B

[junoon]

IMO B