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Is 2ab > ab ?

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Is 2ab > ab ? [#permalink]

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New post Updated on: 14 Apr 2018, 00:41
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Is 2ab > ab ?

(1) \(\frac{a^4}{b^3}<-17\)

(2) \((ab)^3<(ab)^4\)
[Reveal] Spoiler: OA


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Originally posted by summer101 on 05 Aug 2013, 05:44.
Last edited by Bunuel on 14 Apr 2018, 00:41, edited 3 times in total.
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Re: Is 2ab > ab ? [#permalink]

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New post 05 Aug 2013, 05:54
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Is 2ab > ab ?
or is \(2ab-ab=ab>0\)? The question asks if a,b have the same sign (and are non zero numbers).

1. \(\frac{a^4}{b^3}<-17\)
The sign of \(a^4\) is \(+\), and because the fraction is less than a negative number => \(b\) must be negative. No info about \(a\), not sufficient.

2. \((ab)^3<(ab)^4\)
or \((ab)^4-(ab)^3>0\), \((ab)^3(ab-1)>0\). The first \((ab)^3\) is positive if \(ab>0\), the second term is positive if \(ab>1\), so overall that equation is positive is \(ab>1\) or \(ab<0\). Not sufficient

(1+2) From statement 1 we know that the sign of b is -, but we cannot say anything about the sign of a (that can be positive or negative as long as the conditions of statement 2, \(ab>1\) or \(ab<0\), are respected).
Not sufficient

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Re: Is 2ab > ab ? [#permalink]

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New post 14 Apr 2018, 03:36
summer101 wrote:
Is 2ab > ab ?

(1) \(\frac{a^4}{b^3}<-17\)

(2) \((ab)^3<(ab)^4\)

Q is "is \(2ab>ab........2ab-ab>0.........ab>0\)?"
when will this happen?
when both a and b are of SAME sign.

let's see the statements..

(1) \(\frac{a^4}{b^3}<-17\)
Now \(a^4\) is positive but a could be anything as it has EVEN power..
b is surely negative..
if a is negative ans is YES, if b is 0 or positive, ans is NO..

(2) \((ab)^3<(ab)^4\).....
we can easily see from \((ab)^4-(ab)^3>0\), ab could be positive or negative..
otherwise \((ab)^3(ab-1)>0\) gives two cases..
(i) ab>0, ab-1>0 or ab>1
(ii) ab<0, ab-1<0 or ab<1.....
so ab>1 or ab<0

b is negative but ab>1, then a<0 and ans is YES
b is negative but ab<0, then a is positive and ans is NO


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Combination of similar and dissimilar things :

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Re: Is 2ab > ab ?   [#permalink] 14 Apr 2018, 03:36
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