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

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Manager
Joined: 09 Dec 2009
Posts: 122
Followers: 4

Kudos [?]: 31 [0], given: 19

Abs Value a - Abs Value b >= Abs Value a - b 1) b>a 2) [#permalink]  28 Jul 2010, 12:14
00:00

Difficulty:

55% (hard)

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

_________________

G.T.L. - GMAT, Tanning, Laundry

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

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 208

Kudos [?]: 1339 [2] , given: 235

Re: Abs Value Rephrasing [#permalink]  28 Jul 2010, 12:42
2
KUDOS
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

$$b= -2 , a = -3$$

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

$$|a-b| = |-3+2| = 1$$answer 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
Followers: 4

Kudos [?]: 31 [0], given: 19

Re: Abs Value Rephrasing [#permalink]  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.
_________________

G.T.L. - GMAT, Tanning, Laundry

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

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 208

Kudos [?]: 1339 [0], given: 235

Re: Abs Value Rephrasing [#permalink]  29 Jul 2010, 12:51
Manager
Joined: 14 Jul 2010
Posts: 72
Followers: 3

Kudos [?]: 18 [0], given: 2

Re: Abs Value Rephrasing [#permalink]  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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