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05 Feb 2021, 01:15
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D
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Difficulty:
45%
(medium)
Question Stats:
62% (01:39) correct
38%
(02:00)
wrong
based on 117
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If |x| < 1, is x < 0 ?
(1) \(x > 0.5*x^2\)
(2) \(\frac{x}{|x|}=1\)
Are You Up For the Challenge: 700 Level Questions
(1) \(x > 0.5*x^2\)
(2) \(\frac{x}{|x|}=1\)
Are You Up For the Challenge: 700 Level Questions
05 Feb 2021, 02:46
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Given -1<x<1. The question asks whether -1<x<0.
Statement 1
x>0.5x^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
Statement 1
x>0.5x^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
05 Feb 2021, 21:47
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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
Posted from my mobile device
|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
Posted from my mobile device
