The positive two-digit integers x and y have the same digits

[BTGmoderatorDC]

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

OA D

Source: Official Guide

[Ian Stewart]

If AB is a two digit number, where A is the tens digit and B the units digit, then the number is equal to 10A + B.

Here we are adding AB and BA, which is the same as adding 10A+B and 10B + A. Adding those we get 11A + 11B, which clearly has 11 as a factor.

[Brent@GMATPrepNow]

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

Another approach is to test some values for x and y that satisfy the given information.

Positive two-digit integers x and y have the same digits, but in reverse order
So, it COULD be the case that x = 12 and y = 21

Which of the following must be a factor of x + y?
x + y = 12 + 21 = 33

Now check the answer choices...
(A) 6 is NOT a factor of 33. ELIMINATE
(B) 9 is NOT a factor of 33. ELIMINATE
(C) 10 is NOT a factor of 33. ELIMINATE
(D) 11 is a factor of 33. KEEP
(E) 14 is NOT a factor of 33. ELIMINATE

Answer: D

Cheers,
Brent