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

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by Jay@ManhattanReview » Thu Sep 12, 2019 3:18 am
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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by Brent@GMATPrepNow » Thu Sep 12, 2019 5:43 am
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.
-------------------------------

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
Brent Hanneson - Creator of GMATPrepNow.com
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by ELatour » Thu Sep 12, 2019 8:57 am
The easiest solution is to pick a number that meets the requirements of the problem. I chose 13 (but you could just have easily picked 39 or 65).

13 divided by 26 = 0 R 13
So 2(13) divided by 26 = 1 R 0
(A)

If you chose 39 then:
39 divided by 26 = 1 R 13
So 2(39) divided by 26 = 78 / 26 = 3 R 0
(A)

If you're doing algebra... you're probably doing something wrong.
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by Scott@TargetTestPrep » Wed Sep 18, 2019 8:50 am
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
We can let n = 13 since 13/26 = 0 remainder 13. Thus, 2n = 26 and 26/13 = 2 remainder 0.

Answer: A

Scott Woodbury-Stewart
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