Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 2008:00 AM PDT
-08:30 AM PDT
What’s in it for you- Live Profile Evaluation Chat Session with Jenifer Turtschanow, CEO, ARINGO. Come with your details prepared and ARINGO will share insights! Pre-MBA Role/Industry, YOE, Exam Score, C/GPA, ECs Post-MBA Role/ Industry & School List.
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
08 Feb 2011, 09:29
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (02:22) correct
44%
(02:27)
wrong
based on 5827
sessions
History
Date
Time
Result
Not Attempted Yet
Which of the following represents the complete range of x over which \(x^3 – 4x^5 < 0\)?
A. \(0 < |x| < \frac{1}{2}\)
B. \(|x| >\frac{1}{2}\)
C. \(–\frac{1}{2} < x < 0\) or \(\frac{1}{2} < x\)
D. \(x < –\frac{1}{2}\) or \(0 < x < \frac{1}{2}\)
E. \(x < –\frac{1}{2}\) or \(x > 0\)
A. \(0 < |x| < \frac{1}{2}\)
B. \(|x| >\frac{1}{2}\)
C. \(–\frac{1}{2} < x < 0\) or \(\frac{1}{2} < x\)
D. \(x < –\frac{1}{2}\) or \(0 < x < \frac{1}{2}\)
E. \(x < –\frac{1}{2}\) or \(x > 0\)
08 Feb 2011, 09:41
Kudos
Bookmarks
Quote:
Basically we are asked to find the range of \(x\) for which \(x^3-4x^5<0\) is true.
\(x^3-4x^5<0\);
\(x^3(1-4x^2)<0\);
\((1+2x)*x^3*(1-2x)<0\):
"Roots" are -1/2, 0, and 1/2: \(-\frac{1}{2}<x<0\) or \(x>\frac{1}{2}\).
Answer: C.
Check this for more: https://gmatclub.com/forum/inequalities-trick-91482.html
10 Feb 2011, 03:28
Kudos
Bookmarks
144144
Check the link in my previous post. There are beautiful explanations by gurpreetsingh and Karishma.
General idea is as follows:
We have: \((1+2x)*x^3*(1-2x)<0\) --> roots are -1/2, 0, and 1/2 (equate the expressions to zero to get the roots and list them in ascending order), this gives us 4 ranges: \(x<-\frac{1}{2}\), \(-\frac{1}{2}<x<0\), \(0<x<\frac{1}{2}\) and \(x>\frac{1}{2}\) --> now, test some extreme value: for example if \(x\) is very large number than first two terms ((1+2x) and x) will be positive but the third term will be negative which gives the negative product, so when \(x>\frac{1}{2}\) 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'l be negative again and finally in 1st it'll be positive: + - + -. So, the ranges when the expression is negative are: \(-\frac{1}{2}<x<0\) (2nd range) or \(x>\frac{1}{2}\) (4th range).
Hope its clear.
