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# If a and b are integers, and |a| > |b|, is a |b| < a

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Director
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If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

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29 Jun 2008, 21:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0
Manager
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Re: If a and b are integers, and |a| > |b|, is a · |b| < a – b? [#permalink]

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29 Jun 2008, 21:44
D for me.

|a| > |b| is possible when

a>b (3,2)
-a>-b (-3,-2)
-a>b (-3,2)

1 says a<0.
we have two possiblities.
(-3,-2) for this a-|b|=-5 and (a-b)=-1
Inequality does not hold
For (-3,2)
a-|b| = -5 and (a-b)= -5
The inequality does not hold, SUFF

Option 2 says ab>0
Two possibilities
a>0, b>0 (3,2)
OR
a<0, b<0 (-3,-2)
Inequality does not hold

Suff
Hence D

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Re: If a and b are integers, and |a| > |b|, is a · |b| < a – b? [#permalink]

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29 Jun 2008, 22:24
E

a=-2, b=-1 --> true (-2<-1)
a=-100, b=-0.1 --> false (-10<-99.9)
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Director
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Kudos [?]: 185 [0], given: 0

Re: If a and b are integers, and |a| > |b|, is a · |b| < a – b? [#permalink]

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29 Jun 2008, 22:30
Sorry zeenie, the OA is E.

The OE is attached:
Attachments

Abominable-ABs.jpg [ 222.93 KiB | Viewed 910 times ]

CEO
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Re: If a and b are integers, and |a| > |b|, is a · |b| < a – b? [#permalink]

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29 Jun 2008, 22:45

a|b| < a-b --> a(|b|-1) < -b

from both statement: a and b are negative.
if |b|>1 ---> negative * positive < small positive --> true
if |b|<1 ---> negative * negative < small positive --> positive < positive --> we can choose a huge negative value of a in order to get larger positive number of a(|b|-1) than -b.

This is a key to construct our examples.
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Manager
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Re: If a and b are integers, and |a| > |b|, is a · |b| < a – b? [#permalink]

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30 Jun 2008, 00:26
oops !!! Read the question wrong !!

a-|b| < a – b?
apology !!
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Re: If a and b are integers, and |a| > |b|, is a · |b| < a – b? [#permalink]

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30 Jun 2008, 07:45
gmatnub wrote:
If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0

i get E..

pick a=1 or -1 b=10, -10

1*10<1-10 NO

-1*10 < -1-10 NO
-1*10<-1+10 Yes
-1*10<-1-10 NO..

ab>=0

ok so pick b=0

-1*0>-1-0 No

and the above example..

E
Re: If a and b are integers, and |a| > |b|, is a · |b| < a – b?   [#permalink] 30 Jun 2008, 07:45
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