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(1) x - y > 0 --> x > y. One number is greater than another. From this we cannot say whether their sum is positive. Not sufficient.

(2) x^2 - y^2 > 0 --> x^2 > y^2 --> |x| > |y|. One number is further from 0 than another. From this we cannot say whether their sum is positive. Not sufficient.

(1)+(1) From (2) (x - y)(x + y) > 0 (x + y and x - y have the same sign) and from (1) x - y > 0, thus x + y > 0. Sufficient.

Statement 1: x – y > 0 This means x > y Case 1: x = 2, y = 1 Here x + y > 0 Case 2: x = -10, y = -11 Here x + y < 0 Insufficient

Statement 2: \(x^2 – y^ 2 > 0\) Or \(x^2 > y^ 2\) From this too, we cannot say anything about x + y Case 1: x = 4, y = 1 x + y > 0 Case 2: x = -4, y = 1 x + y < 0 Insufficient

Statement 1 and 2 Combined: From statement 1, x - y > 0 From statement 2, \(x^2 – y^ 2 > 0\) or (x+y)(x-y) >0 Since we already know that (x-y) > 0 from statement 1, Therefore x + y > 0 Sufficient

1)x-y>0 is insufficient as it will show x>y but if x and y are negative then x+y can't be greater than 0. (Insufficient) 2)(x+y)(x-y)>0 is insufficient as we can't say whether x+y>0 or not

We can rephrase the question by subtracting y from both sides of the inequality: Is \(x > -y\) ?

(1) INSUFFICIENT: If we add y to both sides, we see that x is greater than y. We can use numbers here to show that this does not necessarily mean that \(x > -y\). If \(x = 4\) and \(y = 3\), then it is true that \(x\) is also greater than \(-y\). However if \(x = 4\) and \(y = -5\), \(x\) is greater than \(y\) but it is NOT greater than \(-y\).

(2) INSUFFICIENT: If we factor this inequality, we come up \((x + y)(x – y) > 0\). For the product of \((x + y)\) and \((x – y)\) to be greater than zero, the must have the same sign, i.e. both negative or both positive. This does not help settle the issue of the sign of \(x + y\).

(1) AND (2) SUFFICIENT: From statement 2 we know that \((x + y)\) and \((x – y)\) must have the same sign, and from statement 1 we know that \((x – y)\) is positive, so it follows that \((x + y)\) must be positive as well.

The correct answer is C.
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(1) x - y > 0 --> x > y. One number is greater than another. From this we cannot say whether their sum is positive. Not sufficient.

(2) x^2 - y^2 > 0 --> x^2 > y^2 --> |x| > |y|. One number is further from 0 than another. From this we cannot say whether their sum is positive. Not sufficient.

(1)+(1) From (2) (x - y)(x + y) > 0 (x + y and x - y have the same sign) and from (1) x - y > 0, thus x + y > 0. Sufficient.

Answer: C.

Hi Bunuel

A little help plz. This is how i did statement 2. x^2 - y^2 > 0 --> (x+y) (x-y) > 0 --> if we divide both sides by x-y we get x+y > 0 Hence sufficient. Can you please help me fill gaps in my understanding here ?