Check the below link,

https://www.beatthegmat.com/number-prope ... tml#313012

If you still have doubts,please let us know.

I totally agree with your explanation. However, is there any solution instead of putting numbers in equation?

nubu wrote:I totally agree with your explanation. However, is there any solution instead of putting numbers in equation?

Ok,i agree shortcuts are hard to comeby when you are running in the race(in prep tests)
any way i think a different method would be

Question may be rearranged as
is n/m integer? (for eg,12/3...means 4 students in each class..)

Now
possible values of n--any thing greater than 13
possible values of m--from 4 to 12

so st 1
3(n/m)=integer
we have to check can 3 X (non-integer) be integer? as 3 X int=int(is clear take n=16 and m=4)
now
take n=16,m=6
3X(16/6)=8 is integer but 16/6 is not integer ie 16 students cannot be divided equally in 6 classes

so double case in sufficient

now here is the trap you start thinking same for B and think answer is E
but twist is 13 in st 2
13 (n/m)=integer and m<13
so there is no chance of m cancelling 13 as m is less than 13
so m must evenly divide n to 13 x (n/m) to be integer
so sufficient

So B
I was suspicious when it gave that >3 and less than 13 thing and initially thought it may be C when i looked question only.
so it was B so no need to test C