• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 4 posts ] 
Author Message
 Post subject: GMAT Algebra (Data Sufficiency)
PostPosted: Sat Aug 25, 2012 12:17 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 480
Is x + x² + x³ > 0?
(1) x + x² > 0
(2) x² + x³ > 0

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.


(C) Statement (1) tells us that x + x² > 0. We can transform it into x(1 + x) > 0. The product is positive if the both factors have the same sign. So the solution is x > 0, x < -1. If x is positive then statement (1) holds and the desired inequality is true. But what if x < -1? For example, if x = -10 the desired inequality does NOT hold, -10 + 100 – 1000 = -910, which is negative. Therefore statement (1) by itself is NOT sufficient.

Statement (2) tells us that x² + x³ > 0. We can transform it into x²(1 + x) > 0. Since x² is a non-negative number, then the equality is true when (1 + x) > 0. Besides x is NOT 0. Therefore the solution of the inequality (2) is x > 0, 0 > x > -1.
If x is positive then statement (1) holds and the desired inequality is true. But what if 0 > x > -1? Let’s try a value, x = -1/2. The left side of the desired inequality becomes -1/2 + 1/4 – 1/8, which is negative. Therefore statement (2) by itself is NOT sufficient.

The both statements combined give us the solution, which must be true for the both. It is x > 0. The desired inequality is definitely true when x is positive. Therefore statements (1) and (2) taken together are sufficient to answer the question. The correct answer is C.
----------

I am not sure of the solution provided here.
From the first statement we get x > 0 and 1 + x > 0, which gives us x > -1 (if they both are positive), unlike stated here - "x < -1" in the explanation. This will only be possible if both the terms are less than 0.

Seems like, with this, I am still not able to come to C as a solution.


Top
 Profile  
 
 Post subject: Re: GMAT Algebra (Data Sufficiency)
PostPosted: Sat Aug 25, 2012 12:55 am 
Offline

Joined: Thu Jul 05, 2012 11:55 am
Posts: 64
(1) x + x² > 0 , which transforms into
(1) x(1 + x) > 0
Quote:
From the first statement we get x > 0 and 1 + x > 0, …
x(1 + x) > 0 holds true if the factors x and (x + 1) are:
- both positive;
- both negative.

So we have two possible situations: positive and negative, not just positive
Quote:
…, which gives us x > -1 (if they both are positive)
Plug in x = -1/2 or x = 0 to see that x > -1 is NOT the solution of statement (1).

For the both factors to be positive:
x must be positive (x > 0)
Image
x + 1 must be positive (x > -1)
Image

The both factors must be positive at the same time. So we choose the intersection as the solution for the positive factors:
Image
x > 0
Quote:
…, unlike stated here - "x < -1" in the explanation. This will only be possible if both the terms are less than 0.
Statement (1) yields such situation of the both terms being negative. So x < -1 fits statement (1).

The complete solution of Statement (1) consists of two intervals: x < -1 and x > 0
Image
Top
 Profile  
 
 Post subject: Re: GMAT Algebra (Data Sufficiency)
PostPosted: Sun Oct 21, 2012 12:07 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 480
Can you please explain it to me better.
The solution is not clear as to how 1 and 2 combined answer the question. I understand that these separately cannot answer the question.
Thank you.


Top
 Profile  
 
 Post subject: Re: GMAT Algebra (Data Sufficiency)
PostPosted: Sun Oct 21, 2012 11:52 am 
Offline

Joined: Thu Jul 05, 2012 11:55 am
Posts: 64
questioner wrote:
The solution is not clear as to how 1 and 2 combined answer the question.
The solution of the inequality in Statement (1) is
Image

The solution of the inequality in Statement (2) is
Image

Thus the combined solution (the overlapping) is
Image

We already know that x > 0 answers the main question definitely "YES". So the both statements combined are sufficient to answer the question.
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 4 posts ] 

All times are UTC - 7 hours


Who is online

Users browsing this forum: No registered users and 2 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.