It is currently 13 Dec 2017, 16:51

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is x^2 greater than x ?

Author Message
TAGS:

### Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3422

Kudos [?]: 9494 [0], given: 1203

Is x^2 greater than x ? [#permalink]

### Show Tags

13 Feb 2013, 15:45
3
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

64% (00:53) correct 36% (00:38) wrong based on 181 sessions

### HideShow timer Statistics

Is x^2 greater than x ?

(1) x is less than -1.

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

_________________

Kudos [?]: 9494 [0], given: 1203

TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1586

Kudos [?]: 607 [1], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Re: Is x^2 greater than x ? [#permalink]

### Show Tags

13 Feb 2013, 17:14
1
KUDOS
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.

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 607 [1], given: 40

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7792

Kudos [?]: 18119 [2], given: 236

Location: Pune, India
Re: Is x^2 greater than x ? [#permalink]

### Show Tags

13 Feb 2013, 20:21
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18119 [2], given: 236

Board of Directors
Joined: 01 Sep 2010
Posts: 3422

Kudos [?]: 9494 [0], given: 1203

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

### Show Tags

14 Feb 2013, 03:54
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
_________________

Kudos [?]: 9494 [0], given: 1203

Math Expert
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135543 [1], given: 12697

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

### Show Tags

14 Feb 2013, 04:11
1
KUDOS
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.

_________________

Kudos [?]: 135543 [1], given: 12697

Board of Directors
Joined: 01 Sep 2010
Posts: 3422

Kudos [?]: 9494 [0], given: 1203

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

### Show Tags

14 Feb 2013, 05:21
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
_________________

Kudos [?]: 9494 [0], given: 1203

Board of Directors
Joined: 17 Jul 2014
Posts: 2697

Kudos [?]: 449 [0], given: 207

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

### Show Tags

01 Jun 2017, 14:48
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.

Kudos [?]: 449 [0], given: 207

Is x^2 greater than x ?   [#permalink] 01 Jun 2017, 14:48
Display posts from previous: Sort by