Abs Value a - Abs Value b >= Abs Value a - b 1) b>a 2)

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Abs Value a - Abs Value b >= Abs Value a - b 1) b>a 2) [#permalink]

28 Jul 2010, 13:14

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62% (02:26) correct

37% (01:11) wrong

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Abs Value a - Abs Value b >= Abs Value a - b

1) b>a
2) a>0

How do I rephrase this question and then attack it?

[Reveal] Spoiler: OA

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Re: Abs Value Rephrasing [#permalink]

28 Jul 2010, 13:42

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TheSituation wrote:

Abs Value a - Abs Value b >= Abs Value a - b

1) b>a
2) a>0

How do I rephrase this question and then attack it?

question : is |a| - |b| >= |a-b|

we know |a| - |b| <= |a-b|
now the above question becomes |a| - |b| = |a-b| this is only possible when |b| < |a|

1. b>a

b= 4 ,a = 3 => |a| - |b| = 3-4 = -1 <> |4-3| answer is no

b= -2 , a = -3

|a| - |b| = 3 -2 = 1

|a-b| = |-3+2| = 1answer is yes

2.a >0

b= 4 ,a = 5 => |a| - |b| = 5-4

= |5-4|answer is yes

b = -5 , a = 4 => |a| - |b| = 4 - 5 = - 1

|a-b| = |4+5| = 9 answer is no

Combine together, when a>0 and b>a the answer is NO hence C
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Manager

Joined: 09 Dec 2009

Posts: 122

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Re: Abs Value Rephrasing [#permalink]

29 Jul 2010, 06:26

TheSituation wrote:

question : is

we know
now the above question becomes this is only possible when

This is the part I'm having trouble with, could you elaborate on how/why you could make these assumptions?

Thanks.
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Round 1: 05/12/10 handling-a-grenade-thesituation-s-official-debrief-94181.html

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CEO

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Joined: 12 Oct 2009

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Location: Malaysia

Concentration: Marketing, Entrepreneurship

Schools: Anderson '15 (D), INSEAD Jan '14

GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35

Followers: 124

Kudos [?]: 634 [0], given: 221

Re: Abs Value Rephrasing [#permalink]

29 Jul 2010, 13:51

math-absolute-value-modulus-86462.html#p651947

check this out !!!
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Re: Abs Value Rephrasing [#permalink]

01 Aug 2010, 22:56

|a|-|b|>=|a|-b

what I notice here is that this equation will not valid if B will be less than 0. So B should definitely be bigger than 0.

Re: Abs Value Rephrasing [#permalink] 01 Aug 2010, 22:56

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Abs Value a - Abs Value b >= Abs Value a - b 1) b>a 2)

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Abs Value a - Abs Value b >= Abs Value a - b 1) b>a 2)

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