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# If |x| < 1, is x < 0 ?

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Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
If |x| < 1, is x < 0 ?  [#permalink]

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30 Oct 2018, 00:39
2
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:54) correct 40% (01:50) wrong based on 83 sessions

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If |x| < 1, is x < 0 ?

A) $$x > 0.5*x^2$$
B) $$\frac{x}{|x|}=1$$

Kudos for a very clear explanation

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If |x| < 1, is x < 0 ?  [#permalink]

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30 Oct 2018, 02:29
1
AnisMURR wrote:
If |x| < 1, is x < 0 ?

A) $$x > 0.5*x^2$$
B) $$\frac{x}{|x|}=1$$

Kudos for a very clear explanation

Question: If |x| < 1, is x < 0 ?

Question REPHRASED: If -1 < x < 1, is x < 0 ?

Statement 1: $$x > 0.5*x^2$$

But 0.5 is positive as well as x^2 is always non negative
and x is greater than $$0.5*x^2$$
I.E. X MUST BE POSITIVE

SUFFICIENT

Statement 2: $$\frac{x}{|x|}=1$$

The given expression is true ONLY if x is POSITIVE

i.e. x is NOT less than 0 hence

SUFFICIENT

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Re: If |x| < 1, is x < 0 ?  [#permalink]

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30 Oct 2018, 03:13
If |x| < 1, is x < 0 ?

A) x>0.5∗x2x>0.5∗x2
B) x|x|=1

From stmnt 1 we can deduce the following:

=> x>0.5*x^2
=> 1/x>1/2
=> hence X must be +ve

From statement 2 :

x/|x|=1

For statement 2 to be valid value of x must be +ve ; hence x must be +ve..

Option D would be correct...
Re: If |x| < 1, is x < 0 ?   [#permalink] 30 Oct 2018, 03:13
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