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

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Manager
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If a and b are integers, and |a| > |b|, is a |b| < a [#permalink] New post 14 Oct 2009, 06:22
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If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0
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Re: Wed Q3 - AB [#permalink] New post 14 Oct 2009, 06:54
hogann wrote:
If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0


1. a< 0 . We know that |b|> =0 if b is +/- any number or 0

lets consider a = -2 and b = 0 then we get -2 · 0 < -2 -0 which is incorrect
lets consider a = -2 and b = -3 then we get -2·|-3|< -2 - (-3) which is correct. Hence A is insuff

2. ab >= 0
for ab =0 b will be 0 as we have |a| > |b|
now if b =0 and a =-2 then -2· |0| < -2 -0 which is incorrect
now if b = 3 and a = 4 then ab = 12 and 4· 3< 4-3 is incorrect
now if b = 10 and a = -2 then -2·10< -2 -10 which is correct hence insuff

now consider both a<0 and ab >=0 , for this we can have b =0 and -ve
if a=-2 and b= 0 then a<0,ab=0 and -2·0< -2-0 which is incorrect
if a = -2 and b = -3 then a<0, ab>0 and -2.3 < -2 - (-3) which is correct

Hence insuff.

Ans E
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Re: Wed Q3 - AB [#permalink] New post 14 Oct 2009, 17:12
Hey hogann - I asked the same thing a week ago. More here:
absolute-values-85086.html
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Re: Wed Q3 - AB [#permalink] New post 14 Oct 2009, 18:36
E .

Take 2 numbers like a = -1 and B -4 ..
that will solve the solution :)
Re: Wed Q3 - AB   [#permalink] 14 Oct 2009, 18:36
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