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

Question

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

BrentGMATPrepNow · Accepted Answer

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

Answer: B

RELATED VIDEO 
 https://www.youtube.com/watch?v=XCxgIR042tE

sb0541 · Answer

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 .

broall · Answer

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

Abhishek009 · Answer

Plug in some numebrs and check -

m = 5
n = 3
r = 2

2m = 10
2n = 6

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

2r = 4
  
Thus, answer must be (B) 2r

amitsah · Answer

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.

guialain · Answer

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

less than 10 secondes actually.

gracie · Answer

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

SidKan · Answer

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 .

BrushMyQuant · Answer

The remainder when the positive integer m is divided by n is r

Theory: Dividend = Divisor*Quotient + Remainder

m -> Dividend
n -> Divisor
a -> Quotient (Assume)
r -> Remainders
=> m = n*a + r = an + r ...(1)

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

2m = 2*(an + r) (from (1))
=> 2m = 2an + 2r = 2n*a + 2r
=> 2m when divided by 2n gives a as quotient and 2r as remainder

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

Emily1122 · Answer

BrushMyQuant 
 BrentGMATPrepNow

if we use the equation 2m = 2an + 2r = 2n*a + 2r
=> 2m when divided by 2n gives a as quotient and 2r as remainder

why the 2 is not canceled out when divided by 2n, so the reminder is r?
I understand if we test numbers, the reminder is 2r, just want to learn how the equation works. Thanks!

BrushMyQuant · Answer

Emily1122

2m = 2n*a + 2r
Now if we cancel 2 from both the sides we will get

m = na + r
=> m when divided by n gives a as quotient and r as remainder, which is true.

Ex: 14 = 4*3 + 2
=> 14 when divided by 4 gives 3 as quotient and 2 as remainder

If we cancel 2 from both the sides we get
7 = 2*3 + 1
=> 7 when divided by 2 gives 3 as quotient and 1 as remainder

Hope it helps!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards