For all distinct non-zero values of x and y, is x > y?

(1) x - y > -y
(2) 1/x>1/y

Statement 1: adding y to both sides of x - y > -y, gives us x > 0. Tells us nothing about y. Not Sufficient.

Statement 2: pick some easy numbers. If x = 2 and y = 3, we satisfy the condition, because 1/2 > 1/3. And the answer to the question is NO, x is not bigger than y ,as 2 is not greater than 3.

If x = 2 and y = -3, we satisfy the condition, because 1/2 > -(1/3). And the answer to the question is YES, x is bigger than y, as 2 is greater than -3.
Because we can get a NO and a YES, this is not sufficient.

Together, also not sufficient. Both of the scenarios we used in statement 2 involved a positive x, so we can reuse those scenarios when testing the statements together. Because we can get a NO and a YES, together the statements are still not sufficient.

Answer is E

Thanks David,
can't we write the second eqn as Y>X.?is it wrong>I chose B because of this.

can't we write the second eqn as Y>X.?is it wrong>I chose B because of this.

If we take the reciprocal of both sides of an inequality, we must flip the inequality sign if both sides of the inequality are positive or if both sides of the inequality are negative.

For example, 3 < 4, but 1/3 > 1/4
And -3 > -4, but -(1/3) < -(1/4)

However, if one side is positive and one side is negative, we do not flip the inequality sign when taking the reciprocal. 4 > -2, and 1/4 > -(1/2)

In this case, even when testing the statements together, we only know that x is positive. y could be positive or negative.