When the positive integer M is divided by 7 the remainder is 4?

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

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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)

Source: Nova GMAT
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Originally posted by vikasp99 on 03 Mar 2017, 01:02.
Last edited by Sajjad1994 on 15 Jul 2019, 00:02, edited 1 time in total.

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

Updated on: 17 May 2021, 06:40

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) + 2Likewise, 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 2rAnswer: BRELATED VIDEO _________________

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

03 Mar 2017, 03:25

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

Answer is B .

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

03 Mar 2017, 07:57

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 \(2r\).The answer is B _________________

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

03 Mar 2017, 10:01

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 = 5n = 3r = 2

Quote:

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

2m = 102n = 6So, Remainder when 2m is divided by 2n is = 4 2r = 4

Thus, answer must be (B) 2r

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

03 Mar 2017, 12:31

best way to solve this is to insert numbers and decide.e.g 5/2 rem. = 110/4 rem. = 217/3 rem = 234/6 rem. = 4

so on. hence 2r is the answer.

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

27 Mar 2017, 02:14

Plugging number works pretty well here.5 by 2 remainder is 110 by 4 remainder is 2less than 10 secondes actually. _________________

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

29 Mar 2018, 14:04

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 remainderwe know the quotients are equalr=m-nqx=2m-2nq➡x/2=m-nqthus, x/2=r➡x=2r

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