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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 04 Jan 2009, 18:17
If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0

Interested in seeing efficient approach for this. My approach of trying every combination takes way too long. Thanks!
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Re: Absolutes and Inequality confusion [#permalink] New post 04 Jan 2009, 20:02
Is it the OA is E ?

I tried the no. also but when see the problem like this
I usaully assume that the no. in absolute is zero
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Re: Absolutes and Inequality confusion [#permalink] New post 04 Jan 2009, 20:31
GMATpp wrote:
Is it the OA is E ?

I tried the no. also but when see the problem like this
I usaully assume that the no. in absolute is zero



Not sure if I understand your method.. Can you elaborate. Do you assume a and b = 0 ??
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Re: Absolutes and Inequality confusion [#permalink] New post 04 Jan 2009, 21:34
I assume B = 0 according to l a l > l b l
so it would be easy to think about value of a.

then try the numbers
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Re: Absolutes and Inequality confusion [#permalink] New post 04 Jan 2009, 22:06
I also got E with the following approach:

From the question |a| > |b| or, a^2 > b^2
or, (a-b)(a+b) > 0 and this means, either a > b and a > -b or, a < b and a < -b

Now, a > b and a > -b is possible only if a and b are both positive
and a < b and a < -b is possible only if a < 0.

Now, if a > 0 then a.|b| > 0 and a-b > 0 but, a.|b| < a-b may not be true.
Similarly, if a < 0 then both a.|b| and a-b will be < 0 but again, inequality may not be true.

Now stmt1 does not give any extra information. Insufficient.
Stmt2 also does not give any extra information. Insufficient.
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Re: Absolutes and Inequality confusion [#permalink] New post 07 Jan 2009, 10:36
scthakur wrote:
I also got E with the following approach:

From the question |a| > |b| or, a^2 > b^2
or, (a-b)(a+b) > 0 and this means, either a > b and a > -b or, a < b and a < -b

Now, a > b and a > -b is possible only if a and b are both positive
and a < b and a < -b is possible only if a < 0.

Now, if a > 0 then a.|b| > 0 and a-b > 0 but, a.|b| < a-b may not be true.
Similarly, if a < 0 then both a.|b| and a-b will be < 0 but again, inequality may not be true.

Now stmt1 does not give any extra information. Insufficient.
Stmt2 also does not give any extra information. Insufficient.



When you say that a > b and a > -b is possible only if a and b are both positive, does that mean in all cases or only in some? If a =2 and b =-1 it holds true as well.
Re: Absolutes and Inequality confusion   [#permalink] 07 Jan 2009, 10:36
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