If x and y are integers, is x > y?

This is a moderately difficult question on Inequalities, with the second statement being slightly tricky to analyse. So you will have to be slightly careful in interpreting it. Option B is one of the trap answers here.

We know that x and y are integers, but we do not know their signs. We are trying to ascertain if x>y. In other words, we are trying to ascertain if (x-y)>0.
From statement I alone, we only know that (x+y) > 0. This is hardly sufficient to uniquely answer whether (x-y)>0.

If x = 3 and y = 2, (x+y) = (3+2) = 5 which is definitely greater than 0; also, for these values of x and y, x>y and the answer to the main question will be a YES.
If x = -1 and y = 2, (x+y) = (-1+2) = 1 which is definitely greater than 0; but, for these values of x and y, x<y and the answer to the main question will be a NO.
Therefore, statement I alone is insufficient. So, answer options A and D can be ruled out. The possible answer options are B, C or E.

From statement II alone, we know that \(y^x\) < 0 which means \(y^x\) is negative. So, we can surely say that y has to be negative i.e. y<0. But we cannot say anything about the sign of x.
If y = -3 and x = 1, \((-3)^1\) <0. Here, x>y; if y = -3 and x = -5, \((-3)^-5\)<0, here x<y.
Therefore, statement II alone is insufficient. So, answer option B can be ruled out. The possible answer options are C or E.

Using the data from statements I and II, from the second statement, we know that y is negative, but x can be positive or negative. But, both x and y cannot be negative since x+y>0. Hence, x has to be positive and y has to be negative.
Therefore, we can surely say that x>y. So, the correct answer option is C.

As mentioned earlier, you have to exercise a fair degree of caution while interpreting statement II, because it can trick you into assuming that x has to be positive. Also, trying out simple values while evaluating the inequalities will help analyse them better..

Hope this helps!