GMAT-Zenith wrote:Is 1/x-y < y-x ?
(1) y is positive.
(2) x is negative.

Can it be solved in this way


Reprahsing the given statement
1> x^2+Y^2

Statement 1 irrespective of the sign of x and y , x^2+Y^2 will be greater than 1 because of even exponents. The answer should be D.

The given correct answer in GMAT bible is C.

Please tell me where i am wrong

Hi GMAT-Zenith:

A couple of things:

1. First of all to get x^2+y^2, you need (x+y)^2-2xy. we have (y-x)*(x-y).
2. Second, and more importantly, unless we know the signs of the numbers, we CANNOT cross multiply in an inequality.
That's why it didn't work.

Now for the question:

Is 1/(x-y) < y-x ?

(1) y is positive.
If y=1, x=0, 1/(-1) is less than 1-0.
If y=1, x=2, 1/(2-1) is greater than 1-2.
Insufficient

(2) x is negative.
If x=-1, y=0, 1/(-1) is less than 0+1.
If x=-1, y=-2, 1/(-1+2) is greater than -2+1.

Together:
x<0, y>0
then x-y <0.

Hence

1/(x-y) is negative.
y-x is positive.
Therefore 1/(x-y) < (y-x). Sufficient.

Hence C is correct.

Let me know if this helps

Thanks for your help.
I didnt recall, without knowing the sign we cannot multiply in inequalities.Careless errors. Need to work on these
But,(y-x)(x-y) gives x^2+Y^2.

Also, your target date is Aug 18. how your preparation has been and your practice score.
I have my date on 23rd Aug but will need to postponed it.

GMAT-Zenith wrote:Thanks for your help.
I didnt recall, without knowing the sign we cannot multiply in inequalities.Careless errors. Need to work on these
But,(y-x)(x-y) gives x^2+Y^2.

Hi G-Z:
You might be doing a sign error somewhere. Here's the expansion:

(y-x)(x-y) = y(x-y) -x(x-y) = yx -y^2 -x^2 +xy = 2xy - (x^2+y^2) = -( x^2 + y^2 -2xy) = -(x-y)^2.

Another way (y-x)(x-y) = -(x-y)(x-y) = - (x-y)^2.

Thank you. Now i got it.

How is your preparation

GMAT-Zenith wrote:Is 1/x-y < y-x ?
(1) y is positive.
(2) x is negative.

-1/(y-x) < y-x?
To answer this question, we need to know the sign of y-x.
To illustrate:
If y-x = 1, then -1/1 < 1, and the answer is YES.
If y-x = -1, then -1/-1 > -1, and the answer is NO.
y-x is positive if y>x.

Question rephrased: Is y>x?

Statement 1: No information about x. INSUFFICIENT.
Statement 2: No information about y. INSUFFICIENT.
Statements combined: Since y>0 and x<0, we know that y>x. SUFFICIENT.

The correct answer is C.

Here is an approach(see attached image)that rephrases the question in the main stem. Many of the official GMAT questions are amenable to such approach. Certainly it can be done using examples and numbers, but GMAT is not about plugging numbers, although that is a useful backup.

Dabral