DS problem - How to solve absolute inequalities?

[praveen_gmat]

Is 1 / (a-b) < (b-a)?
(1) a < b
(2) 1 < |a-b|

For statement 1:
a,b = 2,3
a,b = -2,3
a,b = -10,-3
For all above pairs, I always get a YES for the question.

For statement 2:
I can rephrase the inequality as in 2 cases ( based on the approach stated in Manhattan book )
a-b > 1 or b-a < 1
For both cases, I took a and b as
a,b = 6,4
a,b = 3,-2
For all above pairs, I always get a NO for the question.

Is my approach in re-phrasing statement 2 wrong? GMAT Instructors, Please help.

[GmatKiss]

IMO:A

[praveen_gmat]

@GmatKiss, Appreciate if you could answer MY QUESTION. I know the answer.

[leonswati]

Is 1 / (a-b) < (b-a)?
(1) a < b
(2) 1 < |a-b|

For statement 1:
a,b = 2,3
a,b = -2,3
a,b = -10,-3
For all above pairs, I always get a YES for the question.

For statement 2:
I can rephrase the inequality as in 2 cases ( based on the approach stated in Manhattan book )
a-b > 1 or b-a < 1
For both cases, I took a and b as
a,b = 6,4
a,b = 3,-2
For all above pairs, I always get a NO for the question.

Is my approach in re-phrasing statement 2 wrong? GMAT Instructors, Please help.

The way You solved statement 1 you can be sure that if a<b we will always get a yes...
Now lets solve statement 2:
We can assume any value of |a-b|>1 , so let |a-b| = 2
therefore we can say that either
a-b = -2 ororororororor a-b = 2
a = b-2 orororororororo a = b+2
a<b orororororororororor a>b

So according to this the answer is either yes or no.....

So answer is A

[praveen_gmat]

Thank you leonswati !
Got it .. I did not consider a case where a<b

[sam2304]

Its quite easier without substituting values.

Is 1 / (a-b) < (b-a)?

A. a < b

we can rewrite this as a-b < 0 => b-a > 0

so 1/-ve < +ve - true

SUFF

B. 1< |a-b|

this gives 2 inequalities

1 < a-b or 1 < -(a-b) = 1 < b-a = -1 > a-b

a-b > 1 or a-b < -1

If a-b > 1 => a-b is +ve, then b-a is -ve

So 1/+ve < -ve is false

If a-b < -1 => a-b is -ve, then b-a is +ve

So 1/-ve < +ve is true

INSUFF

So A