If x does not equal -y, is (x-y)/(x+y) > 1?

1. x>0
2. y>0

Answer: E.

I got B. I multiplied both sides by the denominator and then subtracted x from both sides leaving me with:
-y>y? So my rephrase was, is y negative?

Can you please tell me how this is wrong? The official answer is E.

If x does not equal -y, is (x-y)/(x+y) > 1?

1. x>0
2. y>0

Rephrase:
x-y > x+y (x not equal to -y)

ADBCE Grid:-p
1) X>0; Does not say about y. Hence Insuff
2) Y>; Does not say about x. Hence Insuff
1 and 2: x>0, y>0 x= 1, y=1; 0> 2. No
x= 4, y=1; 3 > 5 No
x=1 y=-4; 1-(-4) > 1-4
= 5 >-3 yes.

Insuff.

Hence E.

Thanks

nope.

if that were a proper rephrase, then you could subtract x from both sides, giving the same rephrase found in the original post. in this case, (2) would be sufficient, because y>0 necessarily means -y is not > y.

but ... that's not a proper rephrase. see below.

yeah, you can't do that. this is a common rookie mistake, but it's a BIG mistake. to wit:
do not ever multiply or divide an inequality by a variable or expression, UNLESS you KNOW THE SIGN of that variable or expression.
the reason is something you undoubtedly know, but just haven't connected to this situation: if you multiply or divide by a positive quantity, then the sign doesn't flip; if you multiply or divide by a negative quantity, then the sign does flip.

the issue here, then, is that you don't know the sign of (x + y) in this problem.

you can verify that (1) and (2) are each insufficient alone with the following plug-ins (x, y):
(1, 1) --> no
(2, -1) --> yes
(-2, 1) --> yes
the first and second statements show that (1) is insufficient; the first and third show that (2) is insufficient.

but here's my big problem: (1) and (2) together ARE sufficient, so the answer should be c.
justification:
if x + y is positive, then you can definitively multiply by it, giving 'is x - y > x + y ?' then, as in the original post, you can subtract x, giving 'is -y > y ?', which is equivalent to 'is y negative?'

another way of arriving at the same result:
if x and y are both positive, then x + y is a positive denominator. if a fraction with a positive denominator is to be greater than 1, there's only one way to accomplish that: the numerator must also be positive, and it must be BIGGER than the denominator. but, since y is positive, that's impossible, because we have left numerator = x - y < x + y = right denominator.

so answer = c, unless something in the problem has been copied incorrectly.

I agree with Ron the answer would be C; Unless the following was asked

The answer would be E, if the qustion was Is (x-y)/x+y >0 and xis not equal to -y
I agree with the first two statements why Stat 1 and stat 2 alone would be insufficient.

But together 1 and 2 are still insufficient because:
If x and y >0 and x>y
Then (x-y)/(x+y)
If x=4 and y=1
3/5 >0

If x<y,
x=1 and y=4
Then (x-y)/(x+y) =-3/5 <0 So insufficient

I find this one in my set and statement 2 is supposed to say "y<0" NOT "y>0" as typed above! Try it again - this should clear things up. :)

A humble request to post the official answer as a reply to the question, or at the far bottom of the question. It is of little use to try a problem knowing the correct answer right away.
Thanks

That's a good point, Aragorn. I'll raise this issue to the other instructors on the forum. Thanks.

Rey

one small doubt, the question doesn't say x>y, therefore both can be positive (according to 1 & 2), but if y>x, wouldn't my answer be E?

I guess everyone agrees that we can rule out answers A and B.

Combining statements 1 and 2, where x and y are both positive we can evaluate the question with x=y=1 and you will arrive at 0 > 1 which is FALSE. Therefore with statements 1 and 2 TRUE, there is still a possibility that the answer to the question can be TRUE or FALSE which means statements 1 and 2 are insufficient together.

My answer is E.

nope. if y > x, the number is negative, and so it's still less than 1.
the way the problem is currently written on this thread, it's always less than 1 if you take both statements together.

it turns out there actually has been a transcription error - statement 2 is supposed to say y < 0, not y > 0. in that case, the answer is indeed (e).

nope.

to give answer choice (e), the QUESTION PROMPT must still be able to generate both YES and NO answers (so that the overall answer is "MAYBE"), even if both statements are taken to be true.

as you have demonstrated, it's possible for the answer to the question to be "NO" if both statements are true.
however, with the problem as written in this thread (with "greater than" in both statements), it's actually impossible for the answer to be "YES" if both statements are true. try it - you won't be able to do it (read my longer post above if you aren't convinced).

you can't count the truth of statements (1) and (2) as a Yes answer to the question!!!!