There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

------NOW ONTO THE QUESTION------------------------

The remainder when the positive integer m is divided by n is r.
We're not told the quotient here (i.e., the Q value), so let's say the quotient is k
In other words, "m is divided by n equals k with remainder r."
We can write: m = nk + r

What is the remainder when 2m is divided by 2n ?
If m = nk + r, then 2m = 2(nk + r)
Expand to get: 2m = 2nk + 2r

Or we can say: 2m = (k)2n + 2r
This tells us that 2m is 2r greater than some multiple of 2n. So if we divide 2m by 2r, the remainder must be 2r

Answer: B

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