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If |a+1|=|b-1|, what is the value of a-b? (1) ab>0

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If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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New post Updated on: 18 Feb 2017, 06:21
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Challenging Question!



If \(|a+1|=|b-1|\), what is the value of \(a-b\) ?

(1) \(ab>0\)

(2) \(\frac{a}{b}≠ -1\)

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Originally posted by hazelnut on 18 Feb 2017, 05:15.
Last edited by hazelnut on 18 Feb 2017, 06:21, edited 2 times in total.
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Re: If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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New post 18 Feb 2017, 08:09
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Re: If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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New post 18 Feb 2017, 09:28
Either of the statements is sufficient.
If |a+1|=|b-1| then there can be two cases
1. a and b both are of same sign, in this case the difference a-b will be -2 always
2. a and b are of different sign, in this case absolute value of a and b will be same

Now let's look at statements:
1. ab>0: so a and b are of same sign (both positive or negative)
- sufficient
2. Frac{a}{b}!= -1: so a and b are of same sign
- sufficient

So either statement is sufficient


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Re: If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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New post 18 Feb 2017, 10:00
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ziyuenlau wrote:

Challenging Question!



If \(|a+1|=|b-1|\), what is the value of \(a-b\) ?

(1) \(ab>0\)

(2) \(\frac{a}{b}≠ -1\)



Hi...

Let us solve \(|a+1|=|b-1|\)...
Square both sides.. \(a^2+2a+1=b^2-2b+1\)..
\(a^2-b^2+2a+2b=0.....(a-b)(a+b)+2(a+b)=0.....(a-b+2)(a+b)=0\)..
So either (a-b)=-2 OR a=-b or both..

Let's see the statements..
(1) \(ab>0\)
So both a and b are of same sign..
If they are of same sign, a-b=-2..
Sufficient

(2) \(\frac{a}{b}≠ -1\)[/quote]
So a ≠ -b..
As per conditions if a is not equal to b, a-b=-2..
Sufficient

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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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New post 25 Mar 2017, 15:52
Hello Chetan,

Unable to understand how S-1 and S-2 are sufficient. From question I infer a-b = -2 or a+b =0. But not sure how to relate this to S-1, S-2. It looks I am skipping a simple point. Request your help.
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Re: If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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New post 25 Mar 2017, 20:01
coolkl wrote:
Hello Chetan,

Unable to understand how S-1 and S-2 are sufficient. From question I infer a-b = -2 or a+b =0. But not sure how to relate this to S-1, S-2. It looks I am skipping a simple point. Request your help.


Hi

There are two possiblities as you have also mentioned..
1) a-b=-2
2) a=-b

Now SI tells us that ab>0, so both a and b are of same sign that is either BOTH are NEGATIVE or both are POSITIVE..
So a=-b is not TRUE...
Only possibility left is a-b=-2, so we can say a-b is -2 & this is what we have to find this sufficient

SII tells us a/b \(\neq{-1}\) or \(a \neq{-b}\)
So only second case possible is a-b=-2, again we can tell what a-b is..

Hope it helps
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If |a+1|=|b-1|, what is the value of a-b? (1) ab>0 &nbs [#permalink] 25 Mar 2017, 20:01
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