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

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Manager
Joined: 19 Nov 2017
Posts: 183
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Is |a| > a? (1) a^2 > a (2) a/2 > 2/a  [#permalink]

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09 Aug 2018, 06:28
1
00:00

Difficulty:

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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Regards,

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC
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Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: Is |a| > a? (1) a^2 > a (2) a/2 > 2/a  [#permalink]

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09 Aug 2018, 07:06
2
1
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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PKN

Rise above the storm, you will find the sunshine
Re: Is |a| > a? (1) a^2 > a (2) a/2 > 2/a   [#permalink] 09 Aug 2018, 07:06
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