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

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10 00:00

Difficulty:   95% (hard)

Question Stats: 40% (02:01) correct 60% (02:18) wrong based on 138 sessions

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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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Joined: 02 Aug 2009
Posts: 7969
Re: If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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2
1
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

D
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Math Expert V
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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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ziyuenlau wrote:

Challenging Question!

If $$|a+1|=|b-1|$$, what is the value of $$a-b$$ ?

(1) $$ab>0$$

(2) $$\frac{a}{b}≠ -1$$

Similar question: https://gmatclub.com/forum/x-2-y-2-what ... 72994.html
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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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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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If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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

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chetan2u wrote:
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

Hi chetan2u,

This looks wrong. I believe the correct answer is A (ie. only statement (1) is sufficient alone).

The Q states: $$|a+1|=|b-1|$$

If $$\frac{a}{b}≠−1$$, then there are two solutions, either $$a-b=-2$$ or $$a-b=0$$

Example,$$a=3$$ and$$b=5$$, then both the original condition $$|3+1|=|5-1|$$ and$$\frac{3}{5}≠−1$$are satisfied.

But also consider $$a=b=0$$: $$|0+1|=|0-1|$$ is satisfied. $$\frac{0}{0}≠−1$$ is also satisfied, as $$\frac{0}{0}$$ is indeterminate.

Hence statement 2 is not sufficient independently, as you do not have a unique solution for ($$a-b$$).
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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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chetan2u - Can we multiply a variable in an inequality?.. i suppose not
and then a/b!= -1 could be lot of things

Statement A should only be sufficient

Posted from my mobile device
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Posts: 7969
Re: If |a+1|=|b-1|, what is the value of a-b? (1) ab>0  [#permalink]

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dushyanta wrote:
chetan2u - Can we multiply a variable in an inequality?.. i suppose not
and then a/b!= -1 could be lot of things

Statement A should only be sufficient

Posted from my mobile device

Hi,

Yes, we cannot multiply inequality --< or >--, but we can always do it for = or $$\neq$$

For example $$\frac{a}{b}\neq{-1}$$
when is $$\frac{a}{b}=-1$$... ONLY when a=-b.
Now, opposite of above when will a/b NOT be -1 --- when a is NOT equal to -b
SO, if a =2, then for $$\frac{a}{b}\neq{-1}$$, b should not be -(2) or -(a) or -a
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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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ngmat12 wrote:
chetan2u wrote:
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

Hi chetan2u,

This looks wrong. I believe the correct answer is A (ie. only statement (1) is sufficient alone).

The Q states: $$|a+1|=|b-1|$$

If $$\frac{a}{b}≠−1$$, then there are two solutions, either $$a-b=-2$$ or $$a-b=0$$

Example,$$a=3$$ and$$b=5$$, then both the original condition $$|3+1|=|5-1|$$ and$$\frac{3}{5}≠−1$$are satisfied.

But also consider $$a=b=0$$: $$|0+1|=|0-1|$$ is satisfied. $$\frac{0}{0}≠−1$$ is also satisfied, as $$\frac{0}{0}$$ is indeterminate.

Hence statement 2 is not sufficient independently, as you do not have a unique solution for ($$a-b$$).

In GMAT, we deal with ONLY real numbers...
That is why you will never see a case in GMAT when the denominator is 0... Although, the statement II could have mentioned $$b\neq{0}$$
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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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Hi! Can anyone explain this with plotting the number line approach?
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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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hazelnut wrote:

Challenging Question!

If $$|a+1|=|b-1|$$, what is the value of $$a-b$$ ?

(1) $$ab>0$$

(2) $$\frac{a}{b}≠ -1$$

We can also solve by making use of the below concept:

if |a|=|b| , then a=b OR a=-b

Applying the above concept we get:

|a+1|=|b-1|

a+1=b-1 OR a+1=1-b
=> a-b=-2----1) OR a=-b------2)

now, first says: ab>0, thus eqn 2 cannot satisfy as both are of opposite signs and hence eqn 1 suffices. -- Sufficient
second says : a/b not equal to -1, thus eqn 2 again cannot satisfy and hence eqn 1 suffices here too-- Sufficient.
D it is.
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