salma wrote:Hi,
Can you plz help me with this question:
Is X+Y>0
1)X^2 - Y^2>1
2)X/Y +1>0

The actual answer is that the 2 statements together are not sufficient!!!!
My answer was B: from statement 2 we can get X/Y > -1, then X>-Y, then X+Y>0. Why is it wrong???

Thanks

If we don't know the sign of a variable, we have to be very careful about manipulating inequalities.

Your first step was fine:

x/y + 1 > 0 ===> x/y > -1

However, to do the next step what you're actually doing is multiplying both sides by "y". If y is negative, that will flip the inequality.

So, if y is positive, we get:

x > -y
x + y > 0

However, if y is negative, we get:

x < -y
x + y < 0

Therefore, statement (2) is insufficient.

Statement (1) can be simplified as:

(x+y)(x-y) > 1

so, both terms could be + or both could be -. Also insufficient.

Even after combining, x+y could be greater or less than 0, so not enough information: choose (E).

I would say the correct answer would be E.
Both the statement is insufficent to conclude a finite answer.

And for your clarification when you had X/Y >-1, you cant multiply Y on
Both sides as we don’t know whether Y is +ve or -ve.
For +ve Y, X>-Y and for -ve Y, X <-Y [property of inequalities]

Moved to DS section