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Is |a| > a? (1) a^2 > a (2) a/2 > 2/a

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Joined: 19 Nov 2017
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Is |a| > a? (1) a^2 > a (2) a/2 > 2/a  [#permalink]

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New post 09 Aug 2018, 06:28
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A
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  55% (hard)

Question Stats:

55% (01:40) correct 45% (01:46) wrong based on 27 sessions

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Is \(|a| > a\)?


(1) \(a^2 < a\)

(2) \((\frac{a}{2})>(\frac{2}{a})\)

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Vaibhav



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Re: Is |a| > a? (1) a^2 > a (2) a/2 > 2/a  [#permalink]

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New post 09 Aug 2018, 07:06
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vaibhav1221 wrote:
Is \(|a| > a\)?

1. \(a^2 < a\)

2. \((\frac{a}{2})>(\frac{2}{a})\)


Re-phrasing question stem:-
\(|a| > a\)
Or, \(|a|-a>0\)
Or, a<0

So question stem:- Is a<0

St1:- \(a^2 < a\)
Or, \(a^2-a<0\)
Or, \(a(a-1)<0\)
Or, \(0<a<1\)
Sufficient.

St2:- \((\frac{a}{2})>(\frac{2}{a})\)
Subtracting \(\frac{2}{a}\)from both the sides,
\(\frac{a}{2}-\frac{2}{a}>\frac{2}{a}-\frac{2}{a}\)
Or, \(\frac{a}{2}-\frac{2}{a}>0\)
Or, \(\frac{a^2-4}{2a}>0\)
Or, \(\frac{\left(a+2\right)\left(a-2\right)}{2a}>0\)
Or, \(-2<a<0\) or, \(a>2\)

Insufficient.

Ans. (A)
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Re: Is |a| > a? (1) a^2 > a (2) a/2 > 2/a   [#permalink] 09 Aug 2018, 07:06
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