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a*b#0. Is |a|/|b|=a/b?

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a*b#0. Is |a|/|b|=a/b? [#permalink] New post 12 Feb 2012, 21:00
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a*b#0. Is |a|/|b|=a/b?

(1) |a*b|=a*b
(2) |a|/|b|=|a/b|
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Dec 2012, 01:52, edited 3 times in total.
Edited the question and OA
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Re: abs value II [#permalink] New post 12 Feb 2012, 21:05
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devinawilliam83 wrote:
a*b#0. Is |a|/|b|=a/b?
(1) |a*b|=a*b
(2) |a|/|b|=|a/b|

the OA is D, how is 2 sufficient to answer the question?


It's not. You're right answer is A, not D.

a*b#0. Is |a|/|b|=a/b?

|a|/|b|=a/b is true if and only a and b have the same sign, meaning a/b is positive.

(1) |a*b|=a*b, means a and b are both positive or both negative, as LHS is never negative (well in this case LHS is positive as neither a nor b equals to zero). So, a/b is positive in any case. Hence |a|/|b|=a/b. Sufficient.

(2) |a|/|b|=|a/b|, from this we can not conclude whether they have the same sign or not: consider a=1, b=1 and a=1, b=-1 to see that these two sets give different answer to the question. Not sufficient.

Answer: A.
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Re: a*b#0. Is |a|/|b|=a/b? [#permalink] New post 11 Nov 2014, 18:57
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Re: a*b#0. Is |a|/|b|=a/b?   [#permalink] 11 Nov 2014, 18:57
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