IF W + X <0, IS W -Y >0?

[MBA Applicant 2007/8]

IF W + X <0, IS W -Y >0?

(1) X + Y <0
(2) Y<X<W

I chose answer D. My reasons were as follows:

(1)
W+X < 0 ---1
Y+X < 0 ---2
-----------
W - Y < 0 -----(1-2)

SUFF

(2) Y = -5, X = -3 & W = -1

Then, W > Y --- YES
SUFF


However, the answer is B. Can you please explain?

[StaceyKoprince]

The way you've manipulated statement 1 shows only 1 possibility. The problem with eliminating the variable x from the inequalities is that we don't see circumstances in which the sign of x makes the difference (in terms of w and y).

Picking numbers might illustrate this best.

First, let's make x = -100, w = 10, and y = 5. In this case, w+x < 0 is true, x+y < 0 is true, and w-y > 0 is true.
Now, let's make x = -100, w = 10, and y = 20. In this case, w+x < 0 is true, x+y < 0 is true, but w-y > 0 is false. Because we've shown two contradictory options here, the statement is insufficient.

Just remember that whenever you combine inequalities to eliminate variables, you are likely to lose some possibilities. A better way to deal with this type of question on the test is to pick easy-to-work-with but extreme values and try to both prove and disprove the given question.