Data Sufficiency

I have a query
we have a positive number X when divided by positive integer D gives remainder R.
Now we have a factor of D say m
when X is divided by m what would be the remainder?

one thing i have checked through number trials that it may not be R but we get the constant remainder and it can be determined. but would request for a logic behind this?

Dear Rich
I believe my post is not clear my apology, yes the same is aftermath of a question in the forum so i extended the same to see what i get.

the problem is like this

i am given a remainder and the divisor but not the actual dividend.
will i be able to calculate a remainder if a get a new divisor which is a factor of earlier divisor.

so in the illustration i get a divisor 8 and remainder 6 and now i have to find out what is the remainder when the same no is divided by 4.
I would get a 2 every time no matter what is the dividend.
i could not get the concept why this is happening and when i can get the same remainder 6.

The question you're asking is one that belongs to the field of modular arithmetic: if you're really curious about this topic, here's a fantastic introduction. (If you're not that curious, here's a much shorter introduction.) I love number theory, so I highly recommend the topic.

To answer your specific question, let's consider a somewhat general example.

Suppose I give you the divisor 15 and the remainder 3. The quotient is unknown, so we'll call it q. This tells us that the dividend is of the form 15q + 3.

Now I want you to tell me the remainder when that same dividend is divided by 5 (a factor of the original divisor). The dividend is 15q + 3, and the divisor is 5. (15q + 3)/5, in the remainder system, gives 3q + 3, so the remainder remains the same.

Now suppose that I screwed up! The divisor was 15, but the remainder was actually 11. This time, the dividend is of the form 15q + 11. When we go to find the remainder when divided by 5, we'll get (15q + 11)/5, which gives us 3*(q+2) + 1, or a remainder of 1. Uh oh!

As we can see, the remainders are not consistent. I'd be happy to explain why, but delving much further into the topic would demand introducing a concepts irrelevant to the GMAT, however, so if you're curious I'd check it out after you finish this test!