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# Is x greater than zero?

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Current Student
Joined: 18 Jan 2017
Posts: 81
Location: India
Concentration: Finance, Economics
GMAT 1: 700 Q50 V34
Is x greater than zero?  [#permalink]

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Updated on: 11 Jul 2017, 01:33
1
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:37) correct 48% (01:23) wrong based on 40 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.
Math Expert
Joined: 02 Sep 2009
Posts: 54376
Re: Is x greater than zero?  [#permalink]

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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.

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

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