Is x + y > 0 ?

(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.
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Statement 1:

x>y

If both x and y are positive then YES

If both x and y are negative then NO

Insufficient

Statement 2:

(x+y)(x-y)>0

If x-y>0, then YES

If x-y<0, then NO

Insufficient

Statement 1&2:

x-y>0,

then x+y>0

Sufficient

C


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I am not sure your approach is correct.

You could have a gigantic positive x e a tiny negative y and still hold the conditions true.

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

Combining we can say x+y>0.. So Answer is C

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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