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The remainder when the positive integer m is divided by n is
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24 Mar 2018, 05:18
24 Mar 2018, 05:18
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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)
(A) r
(B) 2r
(C) 2n
(D) m – nr
(E) 2(m – nr)
Re: The remainder when the positive integer m is divided by n is
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25 Mar 2018, 02:07
25 Mar 2018, 02:07
2
-> m = q(n)+ r1
q = (m-r1)/n
where q = quotient and r1 = remainder
-> So, if both n &m get multiplied by 2, quotient won't change and hence,
2m = q*(2n) + r2
2m = (m-r1)/n* 2n + r2
therefore,
2m = 2m - 2r1 + r2
therefore
2r1 = r2
q = (m-r1)/n
where q = quotient and r1 = remainder
-> So, if both n &m get multiplied by 2, quotient won't change and hence,
2m = q*(2n) + r2
2m = (m-r1)/n* 2n + r2
therefore,
2m = 2m - 2r1 + r2
therefore
2r1 = r2
Re: The remainder when the positive integer m is divided by n is
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31 May 2019, 07:50
31 May 2019, 07:50
4
taking on number, for the 2m/2n case -
we see that 10/3 leaves remainder 1, and 20/6 leaves remainder 2 ( i.e. double )
again, 8/6 leaves remainder 2, and 16/12 leaves remainder 4 ( again double)
also, 15/7 leaves remainder 1, and 30/14 leaves remainder 2.
So, inference is that 2m/2n leaves 2*r remainder.
we see that 10/3 leaves remainder 1, and 20/6 leaves remainder 2 ( i.e. double )
again, 8/6 leaves remainder 2, and 16/12 leaves remainder 4 ( again double)
also, 15/7 leaves remainder 1, and 30/14 leaves remainder 2.
So, inference is that 2m/2n leaves 2*r remainder.
