Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 14 Feb 2016, 09:19

### 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<0 ?

Author Message
TAGS:
Manager
Joined: 05 Mar 2011
Posts: 150
Followers: 0

Kudos [?]: 29 [2] , given: 3

Is x<0 ? [#permalink]  10 Dec 2011, 16:52
2
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

53% (02:32) correct 47% (01:26) wrong based on 141 sessions
Is x<0 ?

(1) x^3(1-x^2)<0
(2) x^2-1<0
[Reveal] Spoiler: OA
Intern
Joined: 17 Oct 2011
Posts: 11
Followers: 1

Kudos [?]: 5 [0], given: 2

Re: OG 11 [#permalink]  11 Dec 2011, 15:32
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.
_________________

We will either find a way, or make one.

Please consider giving kudos if you find my post hepful

Manager
Joined: 08 Sep 2011
Posts: 75
Concentration: Finance, Strategy
Followers: 3

Kudos [?]: 2 [0], given: 5

Re: OG 11 [#permalink]  12 Dec 2011, 12:26
agree C

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

Together:
x>0 and x>-1
Director
Joined: 07 Aug 2011
Posts: 582
GMAT 1: 630 Q49 V27
Followers: 2

Kudos [?]: 289 [0], given: 75

Re: OG 11 [#permalink]  15 Dec 2011, 02:29
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
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 100
Location: Pakistan
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 5

Kudos [?]: 107 [1] , given: 10

Re: OG 11 [#permalink]  15 Dec 2011, 03:25
1
KUDOS
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

_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Director
Joined: 07 Aug 2011
Posts: 582
GMAT 1: 630 Q49 V27
Followers: 2

Kudos [?]: 289 [0], given: 75

Re: OG 11 [#permalink]  15 Dec 2011, 03:52
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.
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Intern
Joined: 14 Sep 2010
Posts: 22
Followers: 0

Kudos [?]: 9 [0], given: 4

Re: OG 11 [#permalink]  15 Dec 2011, 16:45
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
Director
Joined: 07 Aug 2011
Posts: 582
GMAT 1: 630 Q49 V27
Followers: 2

Kudos [?]: 289 [0], given: 75

Re: OG 11 [#permalink]  15 Dec 2011, 18:53
Study1 you sound promising...
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Intern
Joined: 11 Jun 2011
Posts: 13
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: OG 11 [#permalink]  06 Jul 2012, 22:43
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.
_________________

_______________________________________________________________________________________________________________________________
If you like my solution kindly reward me with Kudos.

Math Expert
Joined: 02 Sep 2009
Posts: 31356
Followers: 5367

Kudos [?]: 62601 [0], given: 9457

Re: Is x<0 ? [#permalink]  07 Jul 2012, 02:01
Expert's post
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.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
_________________
Current Student
Joined: 21 Oct 2013
Posts: 194
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Followers: 1

Kudos [?]: 26 [0], given: 19

Re: Is x<0 ? [#permalink]  30 Jan 2014, 05:57

(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.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 8244
Followers: 420

Kudos [?]: 111 [0], given: 0

Re: Is x<0 ? [#permalink]  17 Mar 2015, 10:14
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.
_________________
Re: Is x<0 ?   [#permalink] 17 Mar 2015, 10:14
Similar topics Replies Last post
Similar
Topics:
4 Is 10–6x<0? 3 06 Feb 2015, 06:17
17 If xyz < 0, is x < 0 ? 8 27 Jun 2014, 09:21
4 Is 10 – 6x < 0 ? 15 04 Jun 2014, 05:30
1 Is X < 0 ? 4 01 Jul 2011, 07:06
2 Is x < 0 ? 5 01 Mar 2011, 09:51
Display posts from previous: Sort by