This question appeared on one of the GMATPrep practice tests and I cannot figure out the solution. Thanks in advance for the help.

If w+x<0, is w-y>0?

1) x+y<0
2) y<x<w

The answer is B. However, if you subtract statement 1 from the question stem, you get "w-y<0" which provides you with a definitive "No" to the question. Am I doing something incorrect here?

You cannot substract (1) from question stem because variables(x,y,w) could be -ve or +ve. So the result could either be -ve or +ve.

I prefer Picking numbers if the values are not known. If you pick numbers you will know (2) is sufficient but (1) is not. So the answer is (B)

Hope it helps.

GMAT 2007

I understand your point. However, in the MGMAT course, we had the following problem:

If x+y+z>0, is z>1?

1) z>x+y+1
2) x+y+1<0

We were told that as long as the inequality signs are in the same direction, you can add them (perhaps you cannot subtract them and this is the issue with the method I proposed in my original post). Taking that approach, if you add the question stem with statement 1, you get z>0.5 (not sufficient). If you add statement 2 to the question stem you get z>1 (sufficient). Is this approach totally misguided, or is it that you can only ADD inequalities, but cannot SUBTRACT them?

Thanks!

Yep, you can add with signs in the same direction, but don't subtract. (Technically, to subtract you have to have opposite signs and then things get much more complicated because now you have to know which sign to carry through, and you may not if you only have variables - so just don't do it that way.)

You can, if you like, multiply an inequality by -1 and then add them, for example:
-1(x+y<0) =
-x -y > 0 =
0 < -x-y
plus
w+x < 0 =
w + x < -x-y =
w + y < -2x which tells me nothing - insufficient