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

Question

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

Bunuel · Accepted Answer

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.

sumit88 · Answer

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.

EMPOWERgmatRichC · Answer

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:  A

GMAT assassins aren't born, they're made,
Rich

HanoiGMATtutor · Answer

n = 26k + 13 = 13(k+2), so n is divisible by 13, and consequently 2n is also divisible by 13.

Answer choice A.

BrentGMATPrepNow · Answer

----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

Abhishek009 · Answer

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

Kinshook · Answer

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

ScottTargetTestPrep · Answer

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

Answer: A

MathRevolution · Answer

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

bumpbot · Answer

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

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

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