Is x + y 0 ? (1) x - y 0 (2) x^2 - y^2 0

Question

Is x + y > 0 ?

(1) x - y > 0
(2) x^2 - y^2 > 0

Bunuel · Answer

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.

OptimusPrepJanielle · Answer

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 Correct Option: C

acegmat123 · Answer

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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felippemed · Answer

Posted from my mobile device

Maybe a better approach is theoretically.

Posted from my mobile device

felippemed · Answer

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.

acegmat123 · Answer

Is it in Statement 1 or 2 or 1&2 taken together?

sai897 · Answer

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

felippemed · Answer

The answer is C, but the approach is a bit more complex. Otherwise the right choice is by luck.

Here is a conceptual solution to the problem

BillyZ · Answer

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 .

sujoykrdatta · Answer

It's pretty clear that individual statements aren't sufficient We can take values to check S1: x=3,y=1 => x+y>0 x=3,y=-4 => x+y<0 S2: x=3,y=1 => x+y>0 x=-4,y=-3 => x+y<0 Combining: divide S2 by S1: x+y > 0 - sufficient Ans C

Is x + y > 0 ? (1) x - y > 0 (2) x^2 - y^2 > 0

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