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

[Guest]

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?

[GMAT 2007]

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
[editor: this is wrong. the sign of a variable has nothing to do with addition and subtraction.
it is only MULTIPLICATION AND DIVISION that are affected by the sign of the quantity.

there's a much worse problem here: you CAN'T SUBTRACT INEQUALITIES that face the same way. you can add them, but you can't subtract them. see below.]

[Guest]

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!

[StaceyKoprince]

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

[anoo.anand]

Ok then what about statement 2 ?

Please help , how do we derive from there ?


should we plugin for these cases ??

[lordee78]

Stacey,
In the case above, could we have subtracted if we were told that W, X, and Y are positive?

[RonPurewal]

Ok then what about statement 2 ?

Please help , how do we derive from there ?


should we plugin for these cases ??

if you don't have an approach, then you should immediately start plugging in. you should do ANYTHING to ensure that you're not just sitting there staring at a problem.

--

statement (2) is mostly a bag of hot air.

all you need is y < w, which is EXACTLY equivalent to w - y > 0.
there are two ways you could figure this out:
(1) just think about what w - y > 0 would mean. (when would you subtract two numbers and get a positive answer? if the first number is bigger.)
(2) subtract y from both sides of y < w to give 0 < w - y.

so #2 is sufficient. they're just including x in there to try to get you to waste your time.

[RonPurewal]

Stacey,
In the case above, could we have subtracted if we were told that W, X, and Y are positive?

no. you cannot subtract two inequalities that face the same way.

think about this:
x < 10
y < 10
if you try to subtract these, then you'll get x - y (?) 0.
but that clearly doesn't work, since you could create possibilities for "<" (e.g. x = 7, y = 8); "=" (e.g., x = y = 8); or ">" (e.g., x = 8, y = 7).

incidentally, if two inequalities face in OPPOSITE ways, then you can subtract them. but if that's the case, it's easier to just multiply one of them by -1 and then add them.

--

by the way, if you're referring to the "GMAT2007" post above, that post is in error. see the edit.