If the remainder is 13 when the integer \(n\) is divided by

AAPL wrote:GMAT Paper Tests

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

OA A

Say n = 26q + 13, where q = any positive integer

Thus, 2n = 52n + 26

=> 2n/13 = 52n/13 + 26/13 = 4n + 2, completely divisible. The remainder is 0.

The correct answer: A

Hope this helps!

-Jay
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AAPL wrote:GMAT Paper Tests

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.
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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