Abs Value a - Abs Value b >= Abs Value a - b 1) b>a 2) : GMAT Data Sufficiency (DS)
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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
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Kudos [?]: 46 [0], given: 19

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

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28 Jul 2010, 12:14
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Difficulty:

55% (hard)

Question Stats:

70% (02:21) correct 30% (01:11) wrong based on 10 sessions

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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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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

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

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

$$|a-b| = |-3+2| = 1$$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
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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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Kudos [?]: 1621 [0], given: 235

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29 Jul 2010, 12:51
math-absolute-value-modulus-86462.html#p651947

check this out !!!
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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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