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# Is x^2 greater than x ?

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Is x^2 greater than x ? [#permalink]

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13 Feb 2013, 16:45
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Question Stats:

63% (01:51) correct 38% (00:43) wrong based on 128 sessions

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Is x^2 greater than x ?

(1) x is less than -1.

(2) x^2 is greater than 1.
[Reveal] Spoiler: OA

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Re: Is x^2 greater than x ? [#permalink]

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13 Feb 2013, 18:14
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1) x < -1 means that x^2 > x , e.g. -2, -1.5 are all positive so x^2 > x, sufficient

2) x^2 > 1 means that |x| > 1, so if x is either say -1.5 or 1.5, then x^2 > x, sufficient.

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Re: Is x^2 greater than x ? [#permalink]

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13 Feb 2013, 21:21
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carcass wrote:
Is $$x^2$$ greater than x ?

(1) $$x$$ is less than -1.

(2) $$x^2$$ is greater than 1.

For 700+ level questions, you should know these properties of numbers very well:

When is x^2 > x?
For all negative values of x (since the square will be positive) or whenever x > 1 (Square will be more than the number).

When is x^2 < x?
When 0 < x < 1

When is x^3 > x?
When x > 1 or -1 < x < 0

When is x^3 < x?
When 0 < x < 1 or x < -1

Draw them on the number line and mark the corresponding regions. Take examples from each region to convince yourself why the squares and cubes behave this way. Then, memorize both the diagrams!

Coming back to this question:
(1) $$x$$ is less than -1.
For negative numbers, x^2 is more than x. So answer is 'Yes'. Sufficient.

(2) $$x^2$$ is greater than 1
implies mod x is greater than 1 or we can say, x is greater than 1 or less than -1. In either case, x^2 is greater than x. So answer is 'Yes'. Sufficient.

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Re: Is x^2 greater than x ? [#permalink]

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14 Feb 2013, 04:54
VeritasPrepKarishma wrote:
carcass wrote:
Is $$x^2$$ greater than x ?

(1) $$x$$ is less than -1.

(2) $$x^2$$ is greater than 1.

For 700+ level questions, you should know these properties of numbers very well:

When is x^2 > x?
For all negative values of x (since the square will be positive) or whenever x > 1 (Square will be more than the number).

When is x^2 < x?
When 0 < x < 1

When is x^3 > x?
When x > 1 or -1 < x < 0

When is x^3 < x?
When 0 < x < 1 or x < -1

Draw them on the number line and mark the corresponding regions. Take examples from each region to convince yourself why the squares and cubes behave this way. Then, memorize both the diagrams!

Coming back to this question:
(1) $$x$$ is less than -1.
For negative numbers, x^2 is more than x. So answer is 'Yes'. Sufficient.

(2) $$x^2$$ is greater than 1
implies mod x is greater than 1 or we can say, x is greater than 1 or less than -1. In either case, x^2 is greater than x. So answer is 'Yes'. Sufficient.

Thanks Karishma I know: I 'm working to memorize these rules and tackle the question with more proficiency.

Infact at the moment I 'm quite comfortable with this question but I'm working on how attack a question from an odd angle i.e. trying different strategy.

This is why I posted here this question. Please see if I did correct

$$x^2 > x$$ or $$x^2 - x > 0$$

This imply that $$x < 0$$ and $$x > 1$$

1) $$x < - 1$$ suff

2) $$x^2 > 1$$ basically says $$x > 1$$ suff

In less than 50 seconds. Is fine or I'm wrong ??

Thanks a lot
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Re: Is x^2 greater than x ? [#permalink]

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14 Feb 2013, 05:11
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Expert's post
carcass wrote:
VeritasPrepKarishma wrote:
carcass wrote:
Is $$x^2$$ greater than x ?

(1) $$x$$ is less than -1.

(2) $$x^2$$ is greater than 1.

For 700+ level questions, you should know these properties of numbers very well:

When is x^2 > x?
For all negative values of x (since the square will be positive) or whenever x > 1 (Square will be more than the number).

When is x^2 < x?
When 0 < x < 1

When is x^3 > x?
When x > 1 or -1 < x < 0

When is x^3 < x?
When 0 < x < 1 or x < -1

Draw them on the number line and mark the corresponding regions. Take examples from each region to convince yourself why the squares and cubes behave this way. Then, memorize both the diagrams!

Coming back to this question:
(1) $$x$$ is less than -1.
For negative numbers, x^2 is more than x. So answer is 'Yes'. Sufficient.

(2) $$x^2$$ is greater than 1
implies mod x is greater than 1 or we can say, x is greater than 1 or less than -1. In either case, x^2 is greater than x. So answer is 'Yes'. Sufficient.

Thanks Karishma I know: I 'm working to memorize these rules and tackle the question with more proficiency.

Infact at the moment I 'm quite comfortable with this question but I'm working on how attack a question from an odd angle i.e. trying different strategy.

This is why I posted here this question. Please see if I did correct

$$x^2 > x$$ or $$x^2 - x > 0$$

This imply that $$x < 0$$ and $$x > 1$$

1) $$x < - 1$$ suff

2) $$x^2 > 1$$ basically says $$x > 1$$ suff

In less than 50 seconds. Is fine or I'm wrong ??

Thanks a lot

Everything is correct except the red part above.

Is x^2 greater than x ?

Is $$x^2 > x$$? --> is $$x(x-1)>0$$? Is $$x<0$$ or $$x>1$$? So, as Karishma correctly noted above $$x^2>x$$ hods true for all negative values of x as well as for values of x which are more than 1.

(1) x is less than -1. If x is negative, then $$x^2=positive>x=negative$$. Sufficient.

(2) x^2 is greater than 1 --> $$x^2>1$$ --> $$|x|>1$$ --> $$x<-1$$ or $$x>1$$ --> for both case $$x^2>x$$. Sufficient.

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Re: Is x^2 greater than x ? [#permalink]

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14 Feb 2013, 06:21
Quote:

Everything is correct except the red part above.

Is x^2 greater than x ?

Is $$x^2 > x$$? --> is $$x(x-1)>0$$? Is $$x<0$$ or $$x>1$$? So, as Karishma correctly noted above $$x^2>x$$, for all negative value of x as well as for values of x which are more than 1.

(1) x is less than -1. If x is negative, then $$x^2=positive>x=negative$$. Sufficient.

(2) x^2 is greater than 1 --> $$x^2>1$$ --> $$|x|>1$$ --> $$x<-1$$ or $$x>1$$ --> for both case $$x^2>x$$. Sufficient.

grrrrrrrrrrrrrrrrrrrrrrr always this silly stupid dumb mistake : I'm not so far from a good score ( $$>=48$$ )

and always if you do not know the sign of x you can't square both sides, simply.

thanks both of you
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Re: Is x^2 greater than x ? [#permalink]

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13 Jul 2014, 10:26
Hello from the GMAT Club BumpBot!

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Re: Is x^2 greater than x ? [#permalink]

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12 Mar 2016, 18:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is x^2 greater than x ?   [#permalink] 12 Mar 2016, 18:39
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