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DS problem - How to solve absolute inequalities?

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by praveen_gmat » Sun Oct 16, 2011 5:43 am
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.
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Source: — Data Sufficiency |
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by GmatKiss » Sun Oct 16, 2011 6:47 am
IMO:A
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by praveen_gmat » Sun Oct 16, 2011 6:51 am
@GmatKiss, Appreciate if you could answer MY QUESTION. I know the answer.
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by leonswati » Sun Oct 16, 2011 7:58 am
praveen_gmat wrote: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
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by praveen_gmat » Sun Oct 16, 2011 8:16 am
Thank you leonswati !
Got it .. I did not consider a case where a<b
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by sam2304 » Sun Oct 16, 2011 8:37 am
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
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