The sum of the two digit numbers above is a three digit number PQ5, wh

ok, so we have
XY+
YX
= PQ5, where all the digits are distinct.
from this, we can conclude that X+Y is equal to either a 1 digit number or a 2 digit number, the units digit of which would be 5.

from the given possibilities:
I x = 7, then we must have Y equal to 8 so that the units digit would be 5.
78+87 = 165 - since all the digits are distinctive, then yes, X can be 7.

II x = 8, this works the same way as I. if x =8 then y = 7, and we get 87+78 = 165. again, this satisfies the conditions.
If we stumble and don't know what to do next, we can just eliminate A, B, and C, and try to make a smart guess with a chance of getting the right answer 1/2.

III x = 9, let's see, if X =9, then Y must be 6.
96+69 = 165. Same thing as I and II right? no! it is not. The condition is that X, Y, P, and Q are distinct digits, which mean that no digit should be repeated. In this case we have Q has the same digit as Y. This does not satisfy the condition, and thus, the answer is D.