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# If a is positive, what is the value of b?

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Manager
Joined: 25 Nov 2011
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If a is positive, what is the value of b? [#permalink]

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25 Feb 2012, 22:30
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If a is positive, what is the value of b?

(1) ab = 2ab

(2) |a + b| = |a − b|

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-Aravind Chembeti

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Re: If a is positive, what is the value of b? [#permalink]

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25 Feb 2012, 22:51
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If a is positive, what is the value of b?

(1) ab = 2ab --> $$ab=0$$ --> since given that $$a>0$$ then $$b=0$$. Sufficient.

(2) |a + b| = |a − b| --> the distance between $$a$$ and $$b$$ is the same as distance between $$a$$ and $${-b}$$ --> again since given that $$a>0$$ then $$b=0$$ (if $$a$$ is not zero then --0----a---- and $$b$$ must be 0: --(b=0)----a----). Or since both parts of the expression are positive we can safely apply squaring: ($$a+b)^2=(a-b)^2$$ --> $$(a+b)^2-(a-b)^2=0$$ --> $$(a+b-a+b)(a+b+a-b)=0$$ --> $$2b*2a=0$$ --> $$ab=0$$. The same info as above: since given that $$a>0$$ then $$b=0$$. Sufficient.

Hope it helps.
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Joined: 23 Aug 2014
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GMAT Date: 11-29-2014
If a is positive, what is the value of b? [#permalink]

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07 Nov 2014, 22:47
Bunuel
Thank you for all your posts. They've been helping me a lot.

I am a little confused here. I did not quite get the first sentence of your S2 explanation.
I know that absolute value is the number's distance from 0, in which case a+b and a-b are equidistant from 0. But that is all I know.

Also, you squared the equation because...? is it because the signs could then be ignored?

what about two cases a+b=a-b or a+b = -a+b ? can anything be done with this?

Thanks a lot
D
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Joined: 02 Sep 2009
Posts: 45423
Re: If a is positive, what is the value of b? [#permalink]

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09 Nov 2014, 05:34
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deeuk wrote:
Bunuel
Thank you for all your posts. They've been helping me a lot.

I am a little confused here. I did not quite get the first sentence of your S2 explanation.
I know that absolute value is the number's distance from 0, in which case a+b and a-b are equidistant from 0. But that is all I know.

Also, you squared the equation because...? is it because the signs could then be ignored?

what about two cases a+b=a-b or a+b = -a+b ? can anything be done with this?

Thanks a lot
D

|a - b| is the distance between a and b. Similarly |a + b|, or which is the same as |a - (-b)| is the distance between a and -b.

As for squaring, it allows us to get rid of the modulus, so it simplifies the expression to manipulate with it further.

Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

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Re: If a is positive, what is the value of b? [#permalink]

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02 Jan 2015, 07:21
Chembeti wrote:
If a is positive, what is the value of b?

(1) ab = 2ab

(2) |a + b| = |a − b|

We dont have to solve it.

1) Equation, eventually we will get the value

2) modulas equation has two values but since we know the sign of b this will eventually will give us the value
Intern
Joined: 12 Jun 2016
Posts: 5
Re: If a is positive, what is the value of b? [#permalink]

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18 Aug 2016, 00:19
Bunuel wrote:
If a is positive, what is the value of b?

(1) ab = 2ab --> $$ab=0$$ --> since given that $$a>0$$ then $$b=0$$. Sufficient.

(2) |a + b| = |a − b| --> the distance between $$a$$ and $$b$$ is the same as distance between $$a$$ and $${-b}$$ --> again since given that $$a>0$$ then $$b=0$$ (if $$a$$ is not zero then --0----a---- and $$b$$ must be 0: --(b=0)----a----). Or since both parts of the expression are positive we can safely apply squaring: ($$a+b)^2=(a-b)^2$$ --> $$(a+b)^2-(a-b)^2=0$$ --> $$(a+b-a+b)(a+b+a-b)=0$$ --> $$2b*2a=0$$ --> $$ab=0$$. The same info as above: since given that $$a>0$$ then $$b=0$$. Sufficient.

Hope it helps.

I did not get |a + b| = |a − b| --> the distance between $$a$$ and $$b$$ is the same as distance between $$a$$ and $${-b}$$ --> again since given that $$a>0$$ then $$b=0$$ (if $$a$$ is not zero then --0----a---- and $$b$$ must be 0: --(b=0)----a----). part of the explanation?
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Re: If a is positive, what is the value of b? [#permalink]

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18 Aug 2016, 07:35
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Ashreya95 wrote:
Bunuel wrote:
If a is positive, what is the value of b?

(1) ab = 2ab --> $$ab=0$$ --> since given that $$a>0$$ then $$b=0$$. Sufficient.

(2) |a + b| = |a − b| --> the distance between $$a$$ and $$b$$ is the same as distance between $$a$$ and $${-b}$$ --> again since given that $$a>0$$ then $$b=0$$ (if $$a$$ is not zero then --0----a---- and $$b$$ must be 0: --(b=0)----a----). Or since both parts of the expression are positive we can safely apply squaring: ($$a+b)^2=(a-b)^2$$ --> $$(a+b)^2-(a-b)^2=0$$ --> $$(a+b-a+b)(a+b+a-b)=0$$ --> $$2b*2a=0$$ --> $$ab=0$$. The same info as above: since given that $$a>0$$ then $$b=0$$. Sufficient.

Hope it helps.

I did not get |a + b| = |a − b| --> the distance between $$a$$ and $$b$$ is the same as distance between $$a$$ and $${-b}$$ --> again since given that $$a>0$$ then $$b=0$$ (if $$a$$ is not zero then --0----a---- and $$b$$ must be 0: --(b=0)----a----). part of the explanation?

Before attempting questions you should make sure that your fundamentals are clear. You should understand what an absolute value is. After that start with easier questions on modulus and move to harder ones.

Hope it helps.
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Re: If a is positive, what is the value of b? [#permalink]

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21 Sep 2017, 22:14
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Re: If a is positive, what is the value of b?   [#permalink] 21 Sep 2017, 22:14
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