Data Sufficiency

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

1. x>0
2. y<0>

This is how i solved:

->x-y > x + y ??
-> y< 0 ??

so the answer should be B. But it turns out that my solution is wrong.. anyone know why we can't solve like this ?

I assume that the question was:

IS (x-y)/(x+y) > 1?

(Please clearly post the question, makes our lives easier when trying to help.)

You made a classic inequality mistake. We CANNOT simply "move over" variables if we don't know the signs of what we're "moving".

Let's examine what you did:

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

->x-y > x + y

to get to this inequality, you must have multiplied both sides by (x+y). However, we have to remember that if we ever multiply or divide both sides of an inequality by a negative, the inequality flips directions.

So, we end up with TWO solutions:

If (x+y) is positive, then we get:

Is x-y > x+y?

But, if (x+y) is negative we get:

Is x-y < x+y?

And, of course, each of those simplifies to different questions.

So, when going through the statements, we really need to pay attention to the signs.

Back to our originally scheduled program:

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

(1) x > 0

We know nothing about y, so just knowing that x is positive doesn't allow us to answer the question. We could pick numbers to make the left side either positive or negative.

(2) y < 0

We know nothing about x, so just knowing that y is negative doesn't allow us to answer the question. We could pick numbers to make the left side either positive or negative.

Together:

If we know that x is positive and y is negative, we know that the top of our fraction is:

(+) - (-) = +

and the bottom of our fraction is:

(+) + (-) = ?? (depends on the actual numbers).

So, even together we have no clue if the left side is positive or negative: choose (e).