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Is x greater than zero?

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Is x greater than zero?  [#permalink]

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New post Updated on: 11 Jul 2017, 01:33
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Question Stats:

50% (01:37) correct 50% (01:25) wrong based on 41 sessions

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Is x greater than zero?

(1) \(x^6>x^2\)

(2) \(x^5<x^2\)

Originally posted by Tan2017 on 10 Jul 2017, 19:25.
Last edited by Bunuel on 11 Jul 2017, 01:33, edited 1 time in total.
Edited the question.
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Re: Is x greater than zero?  [#permalink]

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New post 11 Jul 2017, 01:41
Is x greater than zero?


(1) \(x^6>x^2\). First of all notice that this implies that \(x \neq 0\). Next, since x^2 is always non-negative (and in this case because \(x \neq 0\), x^2 is positive), we can safely divide the entire inequality by x^2 and we'll get: \(x^4 > 1\). Taking the 4th root from both sides will give us |x| > 1, so x > 1 or x < -1. Not sufficient.


(2) \(x^5<x^2\). By the similar logic after reducing by x^2 we'll get: \(x^3 < 1\), which is the same as \(x < 1\) (\(x \neq 0\)). Not sufficient.


(1)+(2) Intersection of the ranges from the statements is x < -1, so the answer to the question whether x is greater than zero is a definite NO. Sufficient.


Answer: C.

Hope it's clear.
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Re: Is x greater than zero?   [#permalink] 11 Jul 2017, 01:41
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