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) \(p^3(1-p^2)<0\), or which is the same \(p(1-p^2)<0\) --> \(p<p^3\) --> either \(p\) is more than 1, \(p>1\) OR \(p\) is negative fraction \(-1<p<0\).

So we have two ranges for \(p\): \(p>1\) or \(-1<p<0\). Not sufficient.

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

(1)+(2) Intersection of the ranges from (1) and (2) is the range \(-1<p<0\), so the answer to the question "is \(p<0\)" is YES. Sufficient.

The fastest way to solve this problem is to plot a graph. I would love to help but I lack right now the resources to post a picture. I believe that Bunuel will soon show up and help us.

I will try to explain anyway:

(1) Consider three parallel number lines (p) , one for \(p^3\), one for \(1-p^2\) and a third one to represent the product of the these two functions. The "+" and "-" represents the sign (Y) of the functions.

A: \(p^3\):-------(-1)---0+++(+1)++++ B: \(1-p^2\):----(-1)+++0+++(+1)----- A*B:++++++++(-1)---0+++(+1)----- --> So p can be either positive or negative = Insuff.

(2) \(p^2 - 1\) ++++(-1)---(0)---(+1)++++++ Same as in (1), p can be either positive or negative = Insuff.

(1) and (2) together shows a clear intersection when p < 0, so Suff.

in the above solution we considered "p" in the range -1<p<0

Question: is \(p\) negative? Is \(p<0\)?

When we considered statements together we've got that \(-1<p<0\): every \(p\) from this range is negative (every \(p\) from this range is \(<0\)). Hence taken together statements are sufficient.

in the above solution we considered "p" in the range -1<p<0

Question: is \(p\) negative? Is \(p<0\)?

When we considered statements together we've got that \(-1<p<0\): every \(p\) from this range is negative (every \(p\) from this range is \(<0\)). Hence taken together statements are sufficient.

Answer: C.

Hope it's clear.

This is fine..but the original poster has put it as "Is p a negative number"? Do they both mean the same??

in the above solution we considered "p" in the range -1<p<0

Question: is \(p\) negative? Is \(p<0\)?

When we considered statements together we've got that \(-1<p<0\): every \(p\) from this range is negative (every \(p\) from this range is \(<0\)). Hence taken together statements are sufficient.

Answer: C.

Hope it's clear.

This is fine..but the original poster has put it as "Is p a negative number"? Do they both mean the same??

The questions "is \(p\) negative" and "is \(p\) a negative number" are the same. Maybe you confused "number" with "integer"?
_________________

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.
_________________

1) the inequality holds true for +ve numbers as well as -1<p<0 so insufficient.

2) the inequality holds true for 0<p<1 & -1<p<0 or -1<p<1 so insufficient.

(1)+(2) (2) says p^2 - 1 < 0 or (1-p^2) > 0 plugging that in 1, we get p^3(positive quantity) < 0 or p^3 < 0 which means p < 0 hence 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.
_________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...