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

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Manager
Joined: 13 Aug 2009
Posts: 115
WE 1: 4 years in IT
Is 1/(a-b) < b - a?  [#permalink]

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28 Feb 2010, 10:12
4
00:00

Difficulty:

(N/A)

Question Stats:

64% (01:48) correct 36% (02:10) wrong based on 98 sessions

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Is $$\frac{1}{a-b}<b-a$$?

(1) $$a<b$$
(2) $$1<|b-a|$$

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Joined: 02 Sep 2009
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Is 1/(a-b) < b - a?  [#permalink]

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01 Mar 2010, 01:23
Is $$\frac{1}{a-b}<b-a$$?

Simplify: $$b-a+\frac{1}{b-a}>0$$ --> Is $$\frac{(b-a)^2+1}{b-a}>0$$? As numerator is always positive, question becomes: is, denominator, $$b-a>0$$? Or is $$b>a$$?

(1) $$a<b$$. Directly gives us the answer. Sufficient.

(2) $$1<|b-a|$$. Clearly insufficient to conclude whether $$b>a$$.

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Re: Is 1/(a-b) < b - a?  [#permalink]

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01 Mar 2010, 08:15
Bunuel wrote:
Is $$\frac{1}{a-b}<b-a$$? Simplify: $$b-a+\frac{1}{b-a}>0$$ --> Is $$\frac{(b-a)^2+1}{b-a}>0$$? As numerator is always positive, question becomes: is, denominator, $$b-a>0$$? Or is $$b>a$$?

Nice explanation!

I was thinking 1<(b-a)(a-b) , 1<2ab-a^2-b^2 and got lost!
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Re: Is 1/(a-b) < b - a?  [#permalink]

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02 Mar 2010, 15:32
swethar wrote:
I was thinking 1/(a-b)< b-a , 1<(b-a)(a-b) , 1<2ab-a^2-b^2 and got lost!

Never do the expression highlighted in red - unless you know for sure (a-b) > 0
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Re: Is 1/(a-b) < b - a?  [#permalink]

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07 Sep 2017, 09:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is 1/(a-b) < b - a?   [#permalink] 07 Sep 2017, 09:47
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