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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) [#permalink] New post 28 Jul 2010, 12:14
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A
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C
D
E

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Question Stats:

70% (02:21) correct 30% (01:11) wrong based on 10 sessions
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] New post 28 Jul 2010, 12:42
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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
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Re: Abs Value Rephrasing [#permalink] New post 29 Jul 2010, 05:26
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

Round 2: 07/10/10 - This time it's personal.

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 178

Kudos [?]: 926 [0], given: 235

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Re: Abs Value Rephrasing [#permalink] New post 29 Jul 2010, 12:51
Manager
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Re: Abs Value Rephrasing [#permalink] New post 01 Aug 2010, 21:56
|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, 21:56
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