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

Question

If a and b are integers, and |a| > |b|, is a · |b| = 0

Interested in seeing efficient approach for this. My approach of trying every combination takes way too long. Thanks!

GMATpp · Answer

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

kman · Answer

Not sure if I understand your method.. Can you elaborate. Do you assume a and b = 0 ??

GMATpp · Answer

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

scthakur · Answer

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.

snowy2009 · Answer

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 is possible only if a and b are both positive
and a 0 then a.|b| > 0 and a-b > 0 but, a.|b| 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.

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

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