Number Properties Disguised - OG12 (challening)

[GMATMadeEasy]

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.

Could someone explain why this question can be translated to n/m as an integer ? Especially when we are saying that each room should have same number of students.

also the solution for each statements please.

[selango]

Given,

3<m<13<n

Question can be rephrased as,

Is n is multiple of m or n is divisible by m?

stmt1,

3n=a*m

3n/m=a [where a is an integer]

Let m=6,n=16,n is not divisible by m

Let m=6,n=12,n is divisible by m

Insuff

stmt2,

13n=a*m

13*n/m=a [where a is an integer]

Note that 3<m<13.Whatever m values,13 is not divisible by m.

-->Only n is divisible by m.

Suff

Pick B

[Geva@EconomistGMAT]

Could someone explain why this question can be translated to n/m as an integer ? Especially when we are saying that each room should have same number of students.

Try a few numerical examples to wrap your head around it. if we have m=4 and n=16, we'd be able to place 4 students in each class and have an equal number of students per class. This is because 16 is divisible by 4: if we take 16 and divide it by 4, we get an integer result (which is the number of students per class).
Let's say that m=4 and n is 15 - is it possible to assign an equal number of students in each of the four classes? start assigning students :
1st student in class A, B, C, D - total assigned 4 students out of 15
2nd student in class A, B, C, D - total assigned 8 students out of 15
3rd student in class A, B, C, D - total assigned 12 students out of 15
4th student in class A, B, C - and we've run out.

we're left with 3 classes with 4 students, and one class with only 3 - there's no way to divide 15 among 4 classes and get the same integer result for all, since 15 is not divisible by 4.

The question is really asking "is n divisible by m?". This can be translated into "is n/m = integer result?"

[waltz2salsa]

selango wrote:

Let m=6,n=8,n is not divisible by m

Let m=6,n=12,n is divisible by m

Well i completely agree with your reasoning but in context of the problem, the example quoted is incorrect. ( as n>13 , but same reasoning can be applied for m=6, n= 16 and m=6, n=24)

[clawhammer]

Can anyone tell me the reason behind they put the information about n>13 in this question?

- I seem to got it correct without considering this factor, but there could be some logic I'm missing to check!

[goyalsau]

Given,

3<m<13<n

Question can be rephrased as,

Is n is multiple of m or n is divisible by m?

stmt1,

3n=a*m

3n/m=a [where a is an integer]

Let m=6,n=8,n is not divisible by m

Let m=6,n=12,n is divisible by m

Insuff

stmt2,

13n=a*m

13*n/m=a [where a is an integer]

Note that 3<m<13.Whatever m values,13 is not divisible by m.

-->Only n is divisible by m.

Suff

Pick B

Good work Buddy,,,,,,
Nice explanation,