If 4/x <1/3, what is the possible range of values for x? : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 Feb 2017, 14:05

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 10 Nov 2010
Posts: 267
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 313 [0], given: 22

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

Show Tags

07 Apr 2011, 04:01
00:00

Difficulty:

(N/A)

Question Stats:

50% (01:32) correct 50% (01:56) wrong based on 4 sessions

HideShow timer Statistics

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: 2021
Followers: 162

Kudos [?]: 1741 [0], given: 376

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink]

Show Tags

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
_________________
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 423

Kudos [?]: 1531 [0], given: 4

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink]

Show Tags

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.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 346 [0], given: 123

Re: we can't change the inequality when we have LHS -ve nd RHS [#permalink]

Show Tags

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
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]

Show Tags

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 Replies Last post
Similar
Topics:
If x = –2, what is the value of 4x^3? 1 12 Aug 2016, 08:05
If x^2 – 4x = 5, then one possible value of x – 4 = 2 28 Mar 2016, 07:54
26 If 4^4x = 1600, what is the value of (4^x–1)^2? 13 18 Oct 2013, 09:52
13 4^x + 4 ^-x = 2 What is the value of X 19 07 Feb 2012, 08:56
16 If 4^(4x) = 1600, what is the value of [4^(x–1)]^2? 12 23 Nov 2007, 07:56
Display posts from previous: Sort by