Walkabout wrote:

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

The answer has to be a factor of 27, the only option that's a factor of 27 is 3.

Sice

(10x + y) - (10y + x) = 27, you can simplify this relationship by subtracting with a common factor --> 9x - 9y = 27 ---> 9(x - y) = 27 ---> here, you already notice that the difference has to be a factor of both 9 and 27, but you can simplify further ---> x - y = 3, and thus we have the answer.

But these last steps are superfluous if you already notice that the answer has to be a factor of 27, this way you save time without having to calculate.