It might be tempting to try a series of numbers until you find something that works, but there must be a deeper pattern the GMAT is asking you to discover.

Let's say the tens digit of A is x and the units of A is y. So if A is 73, x = 7 and y = 3. Algebraically, A = 10x + y. If the digits are reverse to create B, x is the units digit of B and y is the tens digit of B, meaning that B = 10y + x.

We can add those together:
A + B
= (10x + y) + (10y + x)
= 11x + 11y
= 11(x + y)

Since x and y are digits, they must be integers, so the sum of x and y must be an integer. 11 times any integer is a multiple of 11, so we're looking for the choice that is a multiple of 11. You aren't expected to know multiples of 11 off the top of your head, so start with an easy one, like 110. Add 11: 121. Add 11 again: 132. That's choice (C), which is correct.