gmat preparation courses

It is currently Sun Jan 21, 2018 11:54 pm

All times are UTC - 5 hours [ DST ]




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: GMAT Algebra (Data Sufficiency)
PostPosted: Thu Feb 03, 2011 10:18 am 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Is x greater than 2?
(1) x² is greater than 4.
(2) x is between -1 and 3.

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) The statement (1) tells us that x² > 4. That means that x < -2 or x > 2. Therefore the statement (1) is not sufficient to answer the question.

The statement (2) tells us that -1 < x < 3. It is not sufficient to answer the question, because x can be 0, which is not greater than 2, or it can be 2.5, which is.

The both statements combined give the following system of the inequalities:
-1 < x < 3
x < -2 or x > 2

The solution to the system is:
2 < x < 3

Therefore x is definitely greater than 2. The correct answer is C.
----------
Could you please explain how combining the two statements yields 2 < x < 3?

1) x > 2 OR x < -2
2) -1< x <3

Thanks.


Top
 Profile  
 
 Post subject: Re: math (test 5, question 8): data sufficiency, inequalitie
PostPosted: Thu Feb 03, 2011 10:59 am 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
In order to solve a system of inequalities, we need to find a set of all the possible values of the variable that satisfy all the original inequalities. Such set is the intersection of the solutions of each inequality.

It's easier to keep in mind the graphical interpretation on a number line:
Image

1. The first inequality, x² > 4, results in:
x > 2 OR x < -2.

Image
The solution is the red crosshatched region.


2. The second inequality, -1 < x < 3, results in:
-1 < x AND x < 3.

Image
The solution to this inequality is the blue crosshatched region.

Therefore the solution of the system is the intersection:
Image
Image

2 < x < 3


Attachments:
number_line_5.gif [2.85 KiB]
Not downloaded yet
number_line_4.gif [3.92 KiB]
Not downloaded yet
number_line_3.gif [2.68 KiB]
Not downloaded yet
number_line_2.gif [3.37 KiB]
Not downloaded yet
number_line_1.gif [1.8 KiB]
Not downloaded yet
Top
 Profile  
 
 Post subject: Re: math (test 5, question 8): data sufficiency, inequalitie
PostPosted: Thu Feb 03, 2011 8:11 pm 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Thanks, Great Explanation!


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC - 5 hours [ DST ]


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