In order for the condition to hold, a and b must be the same sign. If they are the same sign, they will be on the same quadrant regardless of their value.
So the first step would be to think about what the question is asking you. The question is asking you two things:
are 'x' and 'y' the same sign, and if so, are they the same sign as 'a' and 'b'.
xy> 0 tells you 'x' and 'y' are the same sign but gives you no clue about whether they are the same sign as 'a' and 'b'. So it is no sufficient.
ax>0 alone tells you 'a' and 'x' are the same sign, but still doesnt answer whether 'x' and 'y' are the same sign.
Taken together, you know that 'a', 'b', 'x', and 'y' all have the same sign therefore they must be in the same quadrant.
The answer is C.