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

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

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

(1) ab = 2ab

(2) |a + b| = |a − b|
[Reveal] Spoiler: OA

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

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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.

Answer: D.

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

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

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New post 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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New post 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

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

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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.

Answer: D.

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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New post 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.

Answer: D.

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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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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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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