GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 31 May 2020, 02:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 02 Jan 2017
Posts: 288
The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

Updated on: 15 Jul 2019, 00:02
1
10
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:12) correct 33% (00:52) wrong based on 216 sessions

### HideShow timer Statistics

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
Difficulty Level: 600

Originally posted by vikasp99 on 03 Mar 2017, 01:02.
Last edited by SajjadAhmad on 15 Jul 2019, 00:02, edited 1 time in total.
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4879
GMAT 1: 770 Q49 V46
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

03 Mar 2017, 06:22
1
Top Contributor
4
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

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
##### General Discussion
Manager
Joined: 13 Apr 2010
Posts: 86
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

03 Mar 2017, 03:25
1
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

Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1295
Location: Viet Nam
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

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 $$2r$$.

_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4992
Location: India
GPA: 3.5
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

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 = 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

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Joined: 25 Sep 2016
Posts: 16
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

03 Mar 2017, 12:31
1
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.
Manager
Joined: 01 Dec 2016
Posts: 99
Concentration: Finance, Entrepreneurship
GMAT 1: 650 Q47 V34
WE: Investment Banking (Investment Banking)
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

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.
_________________
What was previously considered impossible is now obvious reality.
In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them
VP
Joined: 07 Dec 2014
Posts: 1252
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

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 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: 23
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

08 Apr 2018, 06:06
1
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

Non-Human User
Joined: 09 Sep 2013
Posts: 15024
Re: The remainder when the positive integer m is divided by n is r. What i  [#permalink]

### Show Tags

03 Jul 2019, 07:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The remainder when the positive integer m is divided by n is r. What i   [#permalink] 03 Jul 2019, 07:41