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# The remainder when the positive integer m is divided by n is r. What i

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Senior Manager
Joined: 02 Jan 2017
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The remainder when the positive integer m is divided by n is r. What i [#permalink]

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03 Mar 2017, 02:02
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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)
Manager
Joined: 13 Apr 2010
Posts: 90
Re: The remainder when the positive integer m is divided by n is r. What i [#permalink]

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03 Mar 2017, 04:25
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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)

We can plug in numbers and test this .
Example . Take m =10 , n= 3 , r = 1 ; m=20 , n=6 , r = 2

Take m = 7 , n =5 , r = 2 ; m =14 , n= 10 , r = 4

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Joined: 12 Sep 2015
Posts: 2466
Re: The remainder when the positive integer m is divided by n is r. What i [#permalink]

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03 Mar 2017, 07:22
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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 2r greater than some multiple of 2n. So if we divide 2m by 2r, the remainder must be 2r

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Re: The remainder when the positive integer m is divided by n is r. What i [#permalink]

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03 Mar 2017, 08:57
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)

We have $$m=k\times n + r$$ with $$0 \leq r < n$$

Hence $$2m= k \times (2n) + 2r$$. Since $$0 \leq 2r < 2n$$, we could say that the remainder when $$2m$$ is divided by $$2n$$ is $$2r$$.

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Re: The remainder when the positive integer m is divided by n is r. What i [#permalink]

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03 Mar 2017, 11:01
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)

Plug in some numebrs and check -

m = 5
n = 3
r = 2

Quote:
What is the remainder when 2m is divided by 2n ?

2m = 10
2n = 6

So, Remainder when 2m is divided by 2n is = 4

2r = 4

Thus, answer must be (B) 2r

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Intern
Joined: 25 Sep 2016
Posts: 16
The remainder when the positive integer m is divided by n is r. What i [#permalink]

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03 Mar 2017, 13:31
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best way to solve this is to insert numbers and decide.
e.g

5/2 rem. = 1

10/4 rem. = 2

17/3 rem = 2

34/6 rem. = 4

so on. hence 2r is the answer.
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Re: The remainder when the positive integer m is divided by n is r. What i [#permalink]

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27 Mar 2017, 03:14
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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Director
Joined: 07 Dec 2014
Posts: 998
The remainder when the positive integer m is divided by n is r. What i [#permalink]

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29 Mar 2018, 15:04
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)

let x=2m/2n remainder
we know the quotients are equal
r=m-nq
x=2m-2nq
➡x/2=m-nq
thus, x/2=r
➡x=2r
B
Intern
Joined: 02 Oct 2016
Posts: 25
Re: The remainder when the positive integer m is divided by n is r. What i [#permalink]

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08 Apr 2018, 07:06
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We can plug in numbers and test this .
Example . Take m =10 , n= 3 , r = 1 ; m=20 , n=6 , r = 2

Take m = 7 , n =5 , r = 2 ; m =14 , n= 10 , r = 4

Re: The remainder when the positive integer m is divided by n is r. What i   [#permalink] 08 Apr 2018, 07:06
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