NEW HERE? LEARN MORE
closeclose
Last visit was: 04 May 2024, 21:33 It is currently 04 May 2024, 21:33
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
ashiima
Manager
Manager
Joined: 05 Mar 2011
Posts: 78
Own Kudos [?]: 603 [80]
Given Kudos: 3
Send PM
Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   10 Dec 2011, 17:52
4
Kudos
76
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

63% (02:03) correct 37% (02:11) wrong based on 1500 sessions
Hide Show timer Statistics
Is x < 0 ?

(1) x^3(1 - x^2) < 0
(2) x^2 - 1 < 0
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93029
Own Kudos [?]: 621237 [15]
Given Kudos: 81745
Send PM
CAT Tests Forum Quiz Mode
Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   07 Jul 2012, 03:01
8
Kudos
7
Bookmarks
Expert Reply
Is x<0 ?


(1) x^3(1-x^2)<0 --> \(x^3(1-x)(1+x)<0\) --> the roots are -1, 0, and 1 (equate the expressions to zero to get the roots and list them in ascending order), this gives us 4 ranges: \(x<-1\), \(-1<x<0\), \(0<x<1\), and \(x>1\).

Now, test some extreme value: for example if \(x\) is very large number then \(x\) and \(1+x\) are positive, while \(1-x\) is negative, which gives negative product for the whole expression, so when \(x>1\) the expression is negative. Now the trick: as in the 4th range expression is negative then in 3rd it'll be positive, in 2nd it'll be negative again and finally in 1st it'll be positive: + - + -. So, the ranges when the expression is negative are: \(-1<x<0\) and \(x>1\).

So, \(x\) could be negative as well as positive. Not sufficient.

Or:
\(x^3(1-x^2)<0\);
\(x(1-x^2)<0\);
\(x<x^3\);
\(-1<x<0\) or \(x>1\). Not sufficient.


(2) x^2-1<0 --> \(x^2<1\) --> \(-1<x<1\). Not sufficient.


(1)+(2) Intersection of the ranges from (1) and (2) is \(-1<x<0\), hence the answer to the question whether \(x<0\) is YES. Sufficient.

Answer: C.

Solving inequalities:
https://gmatclub.com/forum/x2-4x-94661.html#p731476
https://gmatclub.com/forum/inequalities-trick-91482.html
https://gmatclub.com/forum/everything-is ... me#p868863
https://gmatclub.com/forum/xy-plane-7149 ... ic#p841486

Hope it helps.
User avatar
omerrauf
Manager
Manager
Joined: 17 Nov 2011
Status:Employed
Posts: 67
Own Kudos [?]: 433 [5]
Given Kudos: 10
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE:Business Development (Internet and New Media)
Send PM
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   15 Dec 2011, 04:25
2
Kudos
3
Bookmarks
Lucky2783 wrote:
How does 1) X^3(1-X^2)<0 led to x<0 or x>1
eg: X=-2
-2^3 (1-(-2)^2) = -8*-3 = 24
eg: X=-1 , result 0<0 , not true.
eg:X=0 result 0<0, not true
X=1 , 0<0, not true.

i feel it is only when X>1 , X^3(1-X^2)<0


Actually just re-write with factors:

x^3(1-x^2) < 0
So: (x^3)(1-x)(1+x) < 0

so either all three or negative or any one can be negative for the expression to be true.

If (x^3) is negative, x < 0
If (1-x) is negative, x > 1
If (1+x) is negative, x < -1

When you combine statement 1 and 2, the only overlap is x < -1 so we know for sure that x is negative

Hope this answers your question.
General Discussion
avatar
paragpha
Intern
Intern
Joined: 17 Oct 2011
Posts: 5
Own Kudos [?]: 9 [0]
Given Kudos: 2
Send PM
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   11 Dec 2011, 16:32
IMO it is C.

(1) By itself is not sufficient.
(2) tells us x is a +ve or -ve fraction. Not sufficient.

(Together)
If x is +ve fraction it does not satisfy st. (1) (plug in x = 1/2 for testing)
If x is -ve fraction it satifies (1). so x is a -ve fraction and hence x < 0. SUFFICIENT.
avatar
Bowtie
Intern
Intern
Joined: 08 Sep 2011
Posts: 29
Own Kudos [?]: 23 [1]
Given Kudos: 5
Concentration: Finance, Strategy
Send PM
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   12 Dec 2011, 13:26
1
Bookmarks
agree C

stmt 1: x<0 or x>1
stmt 2: x>-1 x<1

Together:
x>0 and x>-1
User avatar
Lucky2783
Senior Manager
Senior Manager
Joined: 07 Aug 2011
Posts: 425
Own Kudos [?]: 1755 [1]
Given Kudos: 75
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Send PM
GMAT ToolKit User
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   15 Dec 2011, 03:29
1
Bookmarks
How does 1) X^3(1-X^2)<0 led to x<0 or x>1
eg: X=-2
-2^3 (1-(-2)^2) = -8*-3 = 24
eg: X=-1 , result 0<0 , not true.
eg:X=0 result 0<0, not true
X=1 , 0<0, not true.

i feel it is only when X>1 , X^3(1-X^2)<0
User avatar
Lucky2783
Senior Manager
Senior Manager
Joined: 07 Aug 2011
Posts: 425
Own Kudos [?]: 1755 [0]
Given Kudos: 75
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Send PM
GMAT ToolKit User
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   15 Dec 2011, 04:52
i think we need to consider the three cases in parallel eg: if X<0 what will happen to other two expressions

If (x^3) is negative, x < 0
say X is -0.5, X^3 is -ive , 1-X is +ive and 1+X too is positive. expression holds.
Now say X=-2, X^3 is -ive , 1-X is +ive but 1+X is -ive . expression doesnt hold .
so we cannot say that if X<0 , X^3 (1-X) (1+X) < 0

1+X will be -ive only when X <-1 , in that case 1-X will be +ive and X^3 will be -ive , over all expression will be +ive
so this set of values of X also ruled out.

now
1-X will be -ive for all values of X greater than 1 and the other two X^3 and 1+X will be positive in this case.
we can safely say that for all X>1 the expression will hold.


may be i am wrong though in my thought process , pls advise.
avatar
Study1
Intern
Intern
Joined: 14 Sep 2010
Posts: 8
Own Kudos [?]: 51 [1]
Given Kudos: 4
Send PM
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   15 Dec 2011, 17:45
1
Kudos
Is X<0 ?

1) X^3(1-X^2)<0
2) X^2-1<0

C

From 1)

-1 < x < 0 and 1 < x

From 2)

-1 < x < 1

Combining,

-1 < x < 0
User avatar
Lucky2783
Senior Manager
Senior Manager
Joined: 07 Aug 2011
Posts: 425
Own Kudos [?]: 1755 [0]
Given Kudos: 75
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Send PM
GMAT ToolKit User
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   15 Dec 2011, 19:53
Study1 you sound promising...
avatar
riteshgupta
Intern
Intern
Joined: 11 Jun 2011
Posts: 4
Own Kudos [?]: 7 [0]
Given Kudos: 6
Send PM
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   06 Jul 2012, 23:43
ashiima wrote:
Is X<0 ?

1) X^3(1-X^2)<0
2) X^2-1<0


Question asks if X is negative

Statement-1
If X is -ve: x^3 will be -ve, then (1-x^2) has to be positive, can't say
If X is +ve: x^3 will be +ve then (1-x^2) has to be negative, can't say
Insufficient

Statement-2
X^2-1<0, this is possible only when x is fraction. But fraction can be negative or positive, Insufficient

Both statements together

we get
when x is -ve, x^3 is negative, and 1-x^2 is positive ( as x is a fraction now eg. 1/2)
when x is +ve, not valid
Hence x is -ve, when both statements combined together.

Hence C

Hope I am clear.
avatar
unceldolan
Manager
Manager
Joined: 21 Oct 2013
Posts: 154
Own Kudos [?]: 214 [2]
Given Kudos: 19
Location: Germany
Schools: Owen '17 (A$) Sauder '17 (A$) Schulich '17 (WD) Anderson FEMBA '17 (S) McDonough '17 (A) Desautels '17 (S)
GMAT 1: 660 Q45 V36
GPA: 3.51
Send PM
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   30 Jan 2014, 06:57
2
Kudos
Answer is C.

(1): x³(1-x²) < 0 --> x³ < 0 or 1-x² < 0. If x³ < 0 then x < 0, BUT x² < 1 x could be both. IS.

(2): Clearly IS. x² < 1, x could be < or > 0.

Together: From 1 we know EITHER x³ <0 OR 1-x² < 0. From 2 we know that 1-x² < 0 hence x³ is > 0, thus x is > 0.
avatar
B
sidchandan
Intern
Intern
Joined: 24 Oct 2016
Posts: 12
Own Kudos [?]: 11 [0]
Given Kudos: 32
Send PM
Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   13 Jul 2021, 09:36
Bunuel can you help me with what is wrong in my approach?

1. X^3(1-X^2)<0

--> X^3-X^5<0
--> X^3<X^5 : Thus, X!=1,0,-1

positive integer value can have X^3<X^5 eg. 8<32
But if x<0, -8/<-32. Thus X>0 ----------- 1 Sufficient

x^2-1<0
X^2<1
|X|<1 i.e. x <1 or -x<1=> x>-1. Thus -------------2 Not Sufficient.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93029
Own Kudos [?]: 621237 [2]
Given Kudos: 81745
Send PM
CAT Tests Forum Quiz Mode
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   13 Jul 2021, 10:11
2
Kudos
Expert Reply
sidchandan wrote:
Bunuel can you help me with what is wrong in my approach?

1. X^3(1-X^2)<0

--> X^3-X^5<0
--> X^3<X^5 : Thus, X!=1,0,-1

positive integer value can have X^3<X^5 eg. 8<32
But if x<0, -8/<-32. Thus X>0 ----------- 1 Sufficient

x^2-1<0
X^2<1
|X|<1 i.e. x <1 or -x<1=> x>-1. Thus -------------2 Not Sufficient.


What if -1 < x < 0 ? For example, if x = -1/2, then \((x^3 = -\frac{1}{8}) < (x = -\frac{1}{32})\). So, as you can see, from (1) x can be negative as well as positive.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32799
Own Kudos [?]: 826 [0]
Given Kudos: 0
Send PM
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink] New post   19 Sep 2023, 20:16
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Is x < 0 ? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0 [#permalink]
19 Sep 2023, 20:16
Moderator:
Bunuel
Math Expert
93029 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions