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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

(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

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 !!

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. _________________

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

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 !!

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.

(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.

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. _________________

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

They say you get better at doing something by doing it. then doing it again ... and again ... and again, and you keep doing it until one day you look...