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Board of Directors D
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Is x^2 greater than x ?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 66% (01:16) correct 34% (01:03) wrong based on 166 sessions

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Is x^2 greater than x ?

(1) x is less than -1.

(2) x^2 is greater than 1.

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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
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Re: Is x^2 greater than x ?  [#permalink]

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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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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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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 _________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58335
Re: Is x^2 greater than x ?  [#permalink]

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1
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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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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Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Is x^2 greater than x ?  [#permalink]

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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.

to answer this question, we need to know whether:
x<0
or x>1.
if 0<x<1, x^2 will be less than x.

1. sufficient.
2. it means that |x|>1, sufficient.
the answer is D.
Manager  B
Joined: 03 Sep 2018
Posts: 164
Is x^2 greater than x ?  [#permalink]

Show Tags

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.

Is it not the case that
$$x<x^3 \implies$$ $$-1<x<0$$ OR $$1<x$$ ?

And is it not also the case that

$$x^3<x \implies x<-1$$ OR $$0<x<1$$?
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Please consider giving Kudos if my post contained a helpful reply or question. Is x^2 greater than x ?   [#permalink] 05 Feb 2019, 02:44
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