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

[RonPurewal]

do you mean we can not use subtraction on two inequalities?

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.

[RonPurewal]

I rephrased the question:

w+x < 0
0 < w-y
-----------
w+ x < w-y ---> x < -y or x+y < 0

so the rephrased question becomes is x+y < 0

1) Clearly solves this problem . Sufficient

2) is an obvious one . Sufficient

Why is this method wrong?

whoa, no. you can't combine statements with the question prompt!

here's a quick example of why not:
let's say the question prompt is
if x > 2, is y > 3?
under your approach, if you add these, you'll get is x + y > 5?
if you look at, say, x = 4 and y = 1, that's a "no" to the original prompt question, but a "yes" to the modified one. not good.

[RonPurewal]

I agree with Kweku. Even I get D.

Well B is sufficient (obvious).

Well A is also sufficient because:

Question stem tells us (1) that w+x<0. (2) Asks us is w-y>0 (Yor N)

In part (2) if we multiply both sides by -1 we get (2A) -w+y<0

Now if we add (1) and 2A: (because the signs are facing the same direction)

w+x<0
-w+y<0
_________
x+y<0

In other words, w-y>0 holds true (given w+x<0 ) as long as x+y<0. Rephrase: (2) hold true given (1) as long as the following equation is satisifed x+y<0.

Now Statement 1 gives us this equation.

Therefore, it should be D.

Can any instructor please help as to why answer is B only.

same mistake as kweku's.

the explanations are earlier in this thread, in my posts and in others' posts.

but, whether you see the explanations or not, just make sure that you get the important takeaway:
YOU CANNOT COMBINE STATEMENTS WITH THE QUESTION PROMPT. EVER.

[RonPurewal]

I agree with Kweku. Even I get D.

Well B is sufficient (obvious).

Well A is also sufficient because:

Question stem tells us (1) that w+x<0. (2) Asks us is w-y>0 (Yor N)

In part (2) if we multiply both sides by -1 we get (2A) -w+y<0

Now if we add (1) and 2A: (because the signs are facing the same direction)

w+x<0
-w+y<0
_________
x+y<0

In other words, w-y>0 holds true (given w+x<0 ) as long as x+y<0. Rephrase: (2) hold true given (1) as long as the following equation is satisifed x+y<0.

Now Statement 1 gives us this equation.

Therefore, it should be D.

Can any instructor please help as to why answer is B only.

same mistake as kweku's.

the explanations are earlier in this thread, in my posts and in others' posts.

but, whether you see the explanations or not, just make sure that you get the important takeaway:
YOU CANNOT ADD/SUBTRACT EQUATIONS TO/FROM THE QUESTION PROMPT. EVER.

you can SUBSTITUTE INTO the question prompt, but that is another matter entirely. (note that you can't substitute one inequality into another inequality, so that issue is moot here.)