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|a-b|=?

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Math Revolution GMAT Instructor
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V
Joined: 16 Aug 2015
Posts: 7240
GMAT 1: 760 Q51 V42
GPA: 3.82
|a-b|=?  [#permalink]

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New post 25 May 2016, 03:53
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (02:19) correct 41% (01:58) wrong based on 83 sessions

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|a-b|=?
1) |a+b|=5
2) ||a|-|b||=5

*An answer will be posted in 2 days.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Math Revolution GMAT Instructor
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Re: |a-b|=?  [#permalink]

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New post 26 May 2016, 17:18
There are 2 variables in the original condition (a and b), and in order to match the number of variables to the number of equations, we need 2 equations. Hence, there is high chance that C is the correct answer. Using the condition 1) and the condition 2), we get (a,b)=(0,5),(-1,6). The answer is unique and the condition is not sufficient. Hence, the correct answer is E.
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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Re: |a-b|=?  [#permalink]

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New post 27 May 2016, 04:15
1
Question asks whether with given values we can get unique value of |a-b|

Statement 1
|a+b|=5
a= 3, b = 2 , |a+b|=5, |a-b| = 1

a= -6, b = 1 , |a+b|=5, |a-b| = 7

So Statement 1 is not sufficient

Statement 2
||a|-|b||=5

a= -6, b = 1 , ||a|-|b||=5, |a-b| = 7
a= -7, b = 2 , ||a|-|b||=5, |a-b| = 9

So Statement 2 is not sufficient

Combining Statement 1 and 2
a= -6, b = 1

||a|-|b||=5 and |a+b|=5. Then |a-b| = 7

a= 7, b = -2

||a|-|b||=9 and |a+b|=5. Then |a-b| = 9


Even after Combining Statement 1 and 2, we get different values for |a-b|

So (E) is the correct option
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Re: |a-b|=?  [#permalink]

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New post 22 Aug 2017, 01:38
yup, the easiest and fastest way to solve this question is to give random numbers to a, b. I lose 4 min to try every way by applying different math formulas and concepts.
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Re: |a-b|=?   [#permalink] 22 Aug 2017, 01:38
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