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DS - Arithmetic, Algebra ------- Problem

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by minihobel » Wed Jun 10, 2015 4:54 am
Hi!

I just ran over this question in OG - QR: DS part question 120.:

Is 1/a-b < b-a ?

(1) a < b
(2) never mind

It's just about (1)

They say: From this, it is known that 1/a-b is negative and b-a is positive. Therefore, 1/a-b < b-a SUFFICIENT.

BUT:
it is not said that a and/or b is positive/negative, so let's assume:
a= -50
b=-100

=> 1/a-b = 1/(-50)-(-100) = 1/50
=> b-a = (-100) - (-50) = -50


So how is (1) sufficient? Thanks in advance!
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by DavidG@VeritasPrep » Wed Jun 10, 2015 5:14 am
Is 1/a-b < b-a ?

(1) a < b
(2) never mind

It's just about (1)

They say: From this, it is known that 1/a-b is negative and b-a is positive. Therefore, 1/a-b < b-a SUFFICIENT.

BUT:
it is not said that a and/or b is positive/negative, so let's assume:
a= -50
b=-100
You have to abide by the condition of the statement. We're told that a<b, so we wouldn't be allowed to test a = -50 and b = -100, because a would be greater in this case. Think of it this way. If a<b, we can subtract b from both sides to get a-b<0. If you multiply both sides by (-1) the sign will flip, and we'll have b - a> 0.

If a- b< 0, 1/(a-b) will be negative. Obviously, this will be less than b -a, which we know is positive.
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by Brent@GMATPrepNow » Wed Jun 10, 2015 6:42 am
Is 1/(a-b) < b-a?

1) a < b

Target question: Is 1/(a-b) < b-a?

Statement 1: a < b
If a < b, then a-b is negative, which means 1/(a-b) is NEGATIVE.
Also, if a < b, then b-a is POSITIVE.
A NEGATIVE number is always less than a POSITIVE number, so it must be the case that 1/(a-b) < b-a
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by minihobel » Wed Jun 10, 2015 6:47 am
after reading this, i feel pretty stupid right now.
Sorry for the question... I should have read more carefully.

Thanks guys. Your help is much appreciated!!
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by nikhilgmat31 » Fri Jun 12, 2015 3:40 am
what is Case 2 in this question ?
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by DavidG@VeritasPrep » Fri Jun 12, 2015 3:56 am
what is Case 2 in this question ?
Statement 2: 1<|a-b|

(And you can see pretty quickly that this statement alone will not be sufficient.)
Case 1: a=4 b = 2; 1/(a-b) is greater than b-a, so answer is YES.
Case 2: a = 2 b = 4 1/(a-b) is not greater than b-a, so answer is NO.
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