GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 00:33

### 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

# If x^3 < x^2, is x < 0 ?

Author Message
TAGS:

### Hide Tags

Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
If x^3 < x^2, is x < 0 ?  [#permalink]

### Show Tags

31 Oct 2018, 01:45
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:42) correct 43% (01:45) wrong based on 44 sessions

### HideShow timer Statistics

If $$x^3 < x^2$$, is $$x < 0$$ ?

A) $$|x| > x^2$$
B) $$x > x^2$$

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
If x^3 < x^2, is x < 0 ?  [#permalink]

### Show Tags

31 Oct 2018, 08:03
1
AnisMURR wrote:
If $$x^3 < x^2$$, is $$x < 0$$ ?

A) $$|x| > x^2$$
B) $$x > x^2$$

Given: $$x^3 < x^2$$
i.e. $$x^3 - x^2 < 0$$
i.e. $$x^2(x - 1) < 0$$
But $$x^2$$ can NOT be negative as being square of a number
i.e. $$x-1 < 0$$
i.e. $$x < 1$$

Question: is $$x < 0$$ ?

Statement 1: $$|x| > x^2$$
i.e. $$-1 < x < 1$$
NOT SUFFICIENT

Statement 2: $$x > x^2$$

i.e. $$0 < x < 1$$

SUFFICIENT

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like $$x^3 < x^2$$ given in this question
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 19 Aug 2018
Posts: 31
Re: If x^3 < x^2, is x < 0 ?  [#permalink]

### Show Tags

31 Oct 2018, 10:07
GMATinsight wrote:
AnisMURR wrote:
If $$x^3 < x^2$$, is $$x < 0$$ ?

A) $$|x| > x^2$$
B) $$x > x^2$$

Given: $$x^3 < x^2$$
i.e. $$x^3 - x^2 < 0$$
i.e. $$x^2(x - 1) < 0$$
But $$x^2$$ can NOT be negative as being square of a number
i.e. $$x-1 < 0$$
i.e. $$x < 1$$

Question: is $$x < 0$$ ?

Statement 1: $$|x| > x^2$$
i.e. $$-1 < x < 1$$
NOT SUFFICIENT

Statement 2: $$x > x^2$$

i.e. $$0 < x < 1$$

SUFFICIENT

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like $$x^3 < x^2$$ given in this question

Excuse me, how do you solve the first equation?
$$|x| > x^2$$
Thank you.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If x^3 < x^2, is x < 0 ?  [#permalink]

### Show Tags

31 Oct 2018, 20:24
jorgetomas9 wrote:
GMATinsight wrote:
AnisMURR wrote:
If $$x^3 < x^2$$, is $$x < 0$$ ?

A) $$|x| > x^2$$
B) $$x > x^2$$

Given: $$x^3 < x^2$$
i.e. $$x^3 - x^2 < 0$$
i.e. $$x^2(x - 1) < 0$$
But $$x^2$$ can NOT be negative as being square of a number
i.e. $$x-1 < 0$$
i.e. $$x < 1$$

Question: is $$x < 0$$ ?

Statement 1: $$|x| > x^2$$
i.e. $$-1 < x < 1$$
NOT SUFFICIENT

Statement 2: $$x > x^2$$

i.e. $$0 < x < 1$$

SUFFICIENT

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like $$x^3 < x^2$$ given in this question

Excuse me, how do you solve the first equation?
$$|x| > x^2$$
Thank you.

jorgetomas9

I prefer to avoid mathematically solving such expressions.

There are 4 critical ranges which are
0 to 1
greater than 1
0 to -1 and
Less than -1

I always prefer to test the given expression in these ranges to test the validity.

Here I see that $$|x| > x^2$$

so point to be noted is $$|x|$$ as well as $$x^2$$ will always be positive for all values of x except zero.
also the absolute value of the number should become a smaller number when squared which happened in range 0 to 1

i.e. the expression will be valid in ranges 0 to 1 and 0 to -1

I HOPE THIS HELPS!!!
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Re: If x^3 < x^2, is x < 0 ?   [#permalink] 31 Oct 2018, 20:24
Display posts from previous: Sort by