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

 It is currently 22 May 2013, 11:56

we can't change the inequality when we have LHS -ve nd RHS

Author Message
TAGS:
Senior Manager
Joined: 10 Nov 2010
Posts: 270
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 4

Kudos [?]: 19 [0], given: 22

we can't change the inequality when we have LHS -ve nd RHS [#permalink]  07 Apr 2011, 05:01
00:00

Question Stats:

50% (01:32) correct 50% (01:56) wrong based on 0 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
Joined: 20 Dec 2010
Posts: 2100
Followers: 108

Kudos [?]: 655 [0], given: 376

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink]  07 Apr 2011, 05:39
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
_________________
GMAT Instructor
Joined: 24 Jun 2008
Posts: 973
Location: Toronto
Followers: 167

Kudos [?]: 443 [0], given: 3

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink]  07 Apr 2011, 13:19
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
Affiliations: Chicago Booth
Joined: 03 Feb 2011
Posts: 947
Followers: 10

Kudos [?]: 143 [0], given: 123

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink]  07 Apr 2011, 13:38
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
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]  29 Aug 2011, 19:13
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, 19:13
Similar topics Replies Last post
Similar
Topics:
Usually when we have had an inch or more of rain in a single 14 12 Jun 2004, 21:49
Since, we were all having so much fun with inequalities.. I 7 14 Apr 2005, 16:48
1 what do we do when we take combined case in inequalities? 4 17 Aug 2011, 05:36
From JumboTests.com: The changes that we may have to face 3 16 Feb 2012, 09:58
Job changing with minimal WE 2 28 Nov 2012, 13:07
Display posts from previous: Sort by