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# Is 2ab > ab ?

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Joined: 06 Jun 2012
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Is 2ab > ab ?  [#permalink]

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Updated on: 14 Apr 2018, 00:41
4
00:00

Difficulty:

75% (hard)

Question Stats:

55% (02:15) correct 45% (02:04) wrong based on 108 sessions

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Is 2ab > ab ?

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

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

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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.
Edited the question.
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Joined: 02 Aug 2009
Posts: 7764
Re: Is 2ab > ab ?  [#permalink]

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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..
insuff

(2) $$(ab)^3<(ab)^4$$.....
$$(ab)^3<(ab)^4..........(ab)^4-(ab)^3>0......(ab)^3(ab-1)>0$$
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
insuff

combined
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
Insuff

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Re: Is 2ab > ab ?  [#permalink]

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05 Aug 2013, 05:54
4
1
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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##### General Discussion
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Re: Is 2ab > ab ?  [#permalink]

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20 Jun 2019, 02:15
Hi experts,

I have a question related to the second equation

(ab)^3 < (ab)^4

We can rewrite this as : (Dividing both sides by ab^3)

1 < (ab)

Now since ab>1 hence ab has to be positive and hence 2ab will always be greater than ab

I am going wrong somewhere???
Re: Is 2ab > ab ?   [#permalink] 20 Jun 2019, 02:15
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