Problem Solving

Hi,

This is a fairly simple question but even I would please like to have an explanation for the same.

Q. If j is divisible by 12 and 10 then is j divisible by 24?

What I have done is:
12 = 2 x 2 x 3 and 10 = 2 x 5
24 = j x 2 x 2 x 2 x 3

If we look at 12 and 10 then clearly we can say that we have sufficient information to prove that j is divisible by 24. Isn't it? But answer mentions it to be - 'Can't be determined'.

Thanks,
Kaushik K

Hi Kaushik,

I think you have picked up this problem from MGMAT Number properties. Going by their own explanation when you convert them in to their prime factors.

12 - 2 X 2 X 3
10 - 2 X 5

For J to be divisible by 24 it should have 2 X 2 X 2 X 3

From the above factorization we identify that there are two "2" and one "3". The two in 10 might be redundant. it is already counted in the two "2" represented by 12. So we cannot be sure if 24 can divide j. Hence the answer cannot be determined.

@ Anurag@Gurome Thanks for the alternative approach