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Re: The remainder when the positive integer m is divided by n is r. What i
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03 Mar 2017, 06:22

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2

vikasp99 wrote:

The remainder when the positive integer m is divided by n is r. What is the remainder when 2m is divided by 2n ?

(A) r

(B) 2r

(C) 2n

(D) m – nr

(E) 2(m – nr)

Another approach:

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 2rgreater than some multiple of 2n. So if we divide 2m by 2r, the remainder must be 2r

Re: The remainder when the positive integer m is divided by n is r. What i
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27 Mar 2017, 02:14

Plugging number works pretty well here. 5 by 2 remainder is 1 10 by 4 remainder is 2

less than 10 secondes actually.
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