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If the remainder is 13 when the integer n is divided by 26

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eybrj2
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If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   21 Mar 2012, 00:05
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If the remainder is 13 when the integer n is divided by 26, what is the remainder when 2n is divided by 13?

A. 0
B. 2
C. 3.25
D. 6.5
E. 13
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A
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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   21 Mar 2012, 00:09
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eybrj2 wrote:
If the remainder is 13 when the integer n is divided by 26, what is the remainder when 2n is divided by 13?

A. 0
B. 2
C. 3.25
D. 6.5
E. 13


Given: n=26q+13. Clearly n is divisible by 13 (since both 26q and 13 are), so 2n will also be divisible by 13, which means the remainder will be zero.

Answer: A.
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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   17 Nov 2013, 13:11
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If the remainder is 13 when the integer n is divided by 26, what is the remainder when 2n is divided by 13?

A. 0
B. 2
C. 3.25
D. 6.5
E. 13

we have the following equation as follows:
Assume x is quotient here,
n = 26x+13 --------------------(1)
ie n=13(2x+1)
It clearly disible by 13 so of course 2n is also divisible by 13 perfectly. So,the remainder is 0.
Answe (a) is the right choice.
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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   09 Apr 2015, 13:06
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Hi All,

This is a great 'concept' question, but it can also be answered by TESTing VALUES.

We're told that N is in integer and that when N is divided by 26 the remainder is 13. We're asked for the remainder when 2n is divided by 13.

IF...
N = 39
39/26 = 1r13

Thus, 2N = 78
When 78/13, we get 6r0

Final Answer:
Show Spoiler
A


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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   12 Sep 2019, 06:57
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eybrj2 wrote:
If the remainder is 13 when the integer n is divided by 26, what is the remainder when 2n is divided by 13?

A. 0
B. 2
C. 3.25
D. 6.5
E. 13


----ASIDE----------------------
When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
-------------------------------

GIVEN: When n is divided by 26, the remainder is 13
So, some possibles value of n are: 13, 39, 65, 91, ...etc
We can use any of these possible n-values to answer the question.

GIVEN: What is the remainder when 2n is divided by 13?
If n = 13, then 2n = 2(13) = 26, and 26 divided by 26 leaves a remainder of 0

Answer: A

Cheers,
Brent
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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   12 Sep 2019, 08:29
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eybrj2 wrote:
If the remainder is 13 when the integer n is divided by 26, what is the remainder when 2n is divided by 13?

A. 0
B. 2
C. 3.25
D. 6.5
E. 13


Given: The remainder is 13 when the integer n is divided by 26

Asked: What is the remainder when 2n is divided by 13?

n = 26k + 13
2n = 13* 4k + 26 = 13(4k + 2)

2n has remainder 0 when divided by 13.

IMO E
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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   13 Sep 2019, 16:40
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eybrj2 wrote:
If the remainder is 13 when the integer n is divided by 26, what is the remainder when 2n is divided by 13?

A. 0
B. 2
C. 3.25
D. 6.5
E. 13


We can let n = 13 since 13/26 = 0 remainder 13. Thus, 2n = 26 and 26/13 = 2 remainder 0.

Answer: A
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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   05 Oct 2020, 08:30
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Remainder is 13 when the integer n is divided by 26 => n = 26 * p + 13 , so n = 39 , 65, ......

Remainder when 2n is divided by 13=> 2(39) = 78 divided by 13 , remainder is '0'.

Answer A
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If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   26 Jun 2016, 01:40
n = 26k + 13 = 13(k+2), so n is divisible by 13, and consequently 2n is also divisible by 13.

Answer choice A.
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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   12 Sep 2019, 08:21
eybrj2 wrote:
If the remainder is 13 when the integer n is divided by 26, what is the remainder when 2n is divided by 13?

A. 0
B. 2
C. 3.25
D. 6.5
E. 13


Plug in any value of n , let n = 13+26 = 39 , which when divided by 26 leaves a remainder of 13....

Now, 2n/13 will yeild remainder as 0 as 26 is divisibly by 13 , 2*26/13 is 0

Thus, Answer must be (A) 0
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Re: If the remainder is 13 when the integer n is divided by 26 [#permalink] New post   19 Nov 2023, 10:38
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