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25 Oct 2023, 09:50
Kudos
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D
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Difficulty:
35%
(medium)
Question Stats:
69% (01:38) correct
31%
(01:40)
wrong
based on 13
sessions
History
Date
Time
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Not Attempted Yet
If x is non-zero number, \(|x| < |x^3|\)?
(1) \(x < -1\)
(2) \(|x^2| < |x^4|\)
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(1) \(x < -1\)
(2) \(|x^2| < |x^4|\)
Posted from my mobile device
25 Oct 2023, 14:21
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Hyeyoung
Question: \(|x| < |x^3|\)?
Inference: On a number line, is the distance of \(x^3\) from 0 is greater than the distance of \(x\) from \(0\)?
Statement 1
(1) \(x < -1\)
If \(x\) is less than -1, \(x^3\) will be less than x. On a number line \(x^3\) lies to the left of x. Hence the distance of \(x^3\) is greater than the distance of \(x\) from \(0\).
---------\( x^3 \)--------------------- \(x\) ------- -1 --------- 0
Hence, the statement alone is sufficient.
Eliminate B, C, and A
Statement 2
(2) \(|x^2| < |x^4|\)
As the distance of \(x^4\) is greater than the distance of\( x^2\) from \(0\), \(x\) is either greater than 1 or less than -1.
If x is greater than 1 ➞ If x > 1, we know that \(x^3\) will lie to the right of x. Hence, the distance of \(x^3\) from 0 is greater than the distance of x from zero.
If x is less than -1 ➞ If x < -1, we know that \(x^3\) will lie to the left of x. Hence, the distance of \(x^3\) from 0 is greater than the distance of x from zero.
Hence, this statement is sufficient to conclude that the distance of \(x^3\) is greater than the distance of \(x \)from zero.
Option D
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