Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Apr 2015, 04:56

Close

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

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 4/x <1/3, what is the possible range of values for x?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 10 Nov 2010
Posts: 268
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 88 [0], given: 22

If 4/x <1/3, what is the possible range of values for x? [#permalink] New post 07 Apr 2011, 04:01
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

50% (01:32) correct 50% (01:56) wrong based on 3 sessions
we can't change the inequality when we have -ve nd RHS +ve in reciprocal

10) If 4/x <1/3, what is the possible range of values for x?

We need to consider 2 cases

Case 1 x is +ve

x>12

Case 2 when we consider x as -ve we will have Left hand side -ve but right hand side +ve so in that case we cnt flip the inequality.
But OA is showing both x>12 nd x<12

Pls comment which condition is wrong.

thanks
_________________

The proof of understanding is the ability to explain it.

Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2035
Followers: 135

Kudos [?]: 1100 [0], given: 376

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink] New post 07 Apr 2011, 04:39
GMATD11 wrote:
we can't change the inequality when we have -ve nd RHS +ve in reciprocal

10) If 4/x <1/3, what is the possible range of values for x?

We need to consider 2 cases

Case 1 x is +ve

x>12

Case 2 when we consider x as -ve we will have Left hand side -ve but right hand side +ve so in that case we cnt flip the inequality.
But OA is showing both x>12 nd x<12

Pls comment which condition is wrong.

thanks


4/x <1/3
12/x-1<0
(12-x)/x < 0

Means either numerator or denominators is -ve:

Case I:
If Denominator is -ve.
x<0 ------1

Numerator must be +ve
12-x > 0
-x > -12
x< 12--------------2

In equation 1 and 2, 1 is more restrictive:
x<0

Case II:
If Denominator is +ve.
x>0 ------3

Numerator must be -ve
12-x < 0
-x < -12
x > 12


In equation 3 and 4, 4 is more restrictive:
x>12

Thus;
complete Range of x:

x<0 or x>12
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 280

Kudos [?]: 794 [0], given: 3

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink] New post 07 Apr 2011, 12:19
GMATD11 wrote:
we can't change the inequality when we have -ve nd RHS +ve in reciprocal


I don't understand what you mean by this?

GMATD11 wrote:
10) If 4/x <1/3, what is the possible range of values for x?

We need to consider 2 cases


You do need to consider 2 cases, but you only need to spend any time on one of them. We know:

4/x < 1/3

This will clearly be true if x is negative, since then the left side is negative, and the right side is positive, and negative numbers are certainly smaller than positive ones. So whenever x < 0, the inequality is true.

Now for the second case: if x > 0, we can multiply both sides by x without needing to worry about reversing the inequality:

4 < x/3
12 < x

So either x < 0, or 12 < x.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 926
Followers: 13

Kudos [?]: 218 [0], given: 123

Reviews Badge
Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink] New post 07 Apr 2011, 12:38
Brilliant !

And when I know the sign of x > 0 then taking the reciprocal of left hand side Vs the right hand side will reverse the direction of the inequality

4/x < 1/3 and x > 0
or x/4 > 3 (reverse the direction)
or x > 12
Intern
Intern
avatar
Joined: 06 May 2011
Posts: 13
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink] New post 29 Aug 2011, 18:13
GMATD11 wrote:
10) If 4/x <1/3, what is the possible range of values for x?


4/x < 1/3 => 12/x < 1
For the fraction 12/x to be <1 ,

Scenario1 : x has to be negative.
Scenario2 : The denominator should be greater than 12

=> x < 0 or x > 12 .

Please correct me if i am wrong.
Re: we can't change the inequality when we have LHS -ve nd RHS   [#permalink] 29 Aug 2011, 18:13
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic What is the value of |x+4|+x? aimtoteach 1 09 Dec 2014, 06:15
Experts publish their posts in the topic What is the value of 4x + 18 ? avohden 2 02 Oct 2013, 09:26
4 Experts publish their posts in the topic If 4/x < 1/3 , what is the possible range of values of x? harshvinayak 12 25 Aug 2012, 00:47
9 Experts publish their posts in the topic 4^x + 4 ^-x = 2 What is the value of X nimc2012 18 07 Feb 2012, 08:56
9 Experts publish their posts in the topic For what range of values of 'x' ? Eden 19 03 Sep 2010, 06:02
Display posts from previous: Sort by

If 4/x <1/3, what is the possible range of values for x?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.