If |x|

Question

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

(1)  x > 0.5*x^2

(2)  \frac{x}{|x|}=1

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mcmoorthy · Answer

Given -10.5x^2 Let's consider x as negative, say -0.5 (between -1 and 0) Now squaring this will a positive number 0.25 and that into 0.5 will again be positive. For x being negative the expression x>0.5*x^2 will not hold. Therefore x is not between -1 and 0 SUFFICIENT Statement 2: x/|x| = 1 This means x has to be positive because for negative value of x, the expression will be -1. X is not between -1 and 0. SUFFICIENT. ANS: D Posted from my mobile device

GCMEMBER · Answer

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

|x| < 1
-1 < x < 1

(1) x > 0.5x^2
2x/x^2 > 1
2/x > 1
2/x - 1 > 0
(2-x)/x > 0
Or (x-2)/x < 0

0 < x < 2

Sufficient

(2) x/|x| = 1
x = |x|
So, x > 0

Sufficient

Option D

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TarunKumar1234 · Answer

If |x| < 1, so, -1 < x < 1 Stat1: x> 0.5∗x2 or, x^2 - 2*x< 0 or, x*(x-2) < 0 or, 0

rsrighosh · Answer

TarunKumar1234 x*(x-2) < 0 Why aren't we taking 2 cases where Case 1:- The one u took Case 2:- x<0 OR x-2>0 or x>2 x cannot be greater than 2 therefore -1

TarunKumar1234 · Answer

Posted from my mobile device rsrighosh ! Please refer below explanation, both cases are considered. You are right! we have to consider both cases along with given condition.

rsrighosh · Answer

TarunKumar1234 Thanks it is clear now.. I totally forgot to use this method..

If |x| < 1, is x < 0 ? (1) x > 0.5*x^2 (2) x/|x| = 1

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