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

It is currently 22 Jul 2014, 16:11

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 of x?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Status: :O
Joined: 11 Jul 2012
Posts: 43
GMAT 1: 670 Q48 V35
Followers: 1

Kudos [?]: 21 [0], given: 27

If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 25 Aug 2012, 00:47
2
This post was
BOOKMARKED
If \frac{4}{x} <\frac{1}{3} , what is the possible range of values of x?

The question is from an MGMAT guide and the solution provided multiplies the inequality by x and flips the sign to arrive at the solution x < 0 or x > 12 . However the way I naturally would solve the given equation is:
\frac{4}{x} - \frac{1}{3} < 0
\frac{(12 - x)}{(3x)} < 0

Two cases:
a) 12 - x < 0 &3x > 0 :: x > 12 & x > 0 therefore x > 12
b) 12 - x > 0 & 3x < 0 :: x < 12 & x < 0 therefore x < 12
Hence my solution: x < 12 or x > 12

Can someone kindly explain where I went wrong here?

_________________

disaster-spelled-in-670-ways-10-not-to-do-s-139230.html
GMAT Demystified: gmat-demystified-great-ebook-to-get-started-with-download-140836.html
Tense Tutorial: uber-awesome-resource-on-tenses-download-140837.html
CR Question Bank (LSAT): critical-reasoning-question-bank-download-140838.html

Manhattan GMAT Discount CodesKaplan GMAT Prep Discount CodesVeritas Prep GMAT Discount Codes
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22200 [1] , given: 2601

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 25 Aug 2012, 01:46
1
This post received
KUDOS
Expert's post
harshvinayak wrote:
If \frac{4}{x} <\frac{1}{3} , what is the possible range of values of x?

The question is from an MGMAT guide and the solution provided multiplies the inequality by x and flips the sign to arrive at the solution x < 0 or x > 12 . However the way I naturally would solve the given equation is:
\frac{4}{x} - \frac{1}{3} < 0
\frac{(12 - x)}{(3x)} < 0

Two cases:
a) 12 - x < 0 &3x > 0 :: x > 12 & x > 0 therefore x > 12
b) 12 - x > 0 & 3x < 0 :: x < 12 & x < 0 therefore x < 12
Hence my solution: x < 12 or x > 12

Can someone kindly explain where I went wrong here?


When we consider the case when 12 - x > 0 and 3x < 0, we have: x<12and x<0, therefore x<0.

Solving inequalities:
inequalities-trick-91482.html (check this one first)
x2-4x-94661.html#p731476
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

2 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 474 [2] , given: 43

GMAT Tests User
Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 25 Aug 2012, 02:50
2
This post received
KUDOS
harshvinayak wrote:
If \frac{4}{x} <\frac{1}{3} , what is the possible range of values of x?

The question is from an MGMAT guide and the solution provided multiplies the inequality by x and flips the sign to arrive at the solution x < 0 or x > 12 . However the way I naturally would solve the given equation is:
\frac{4}{x} - \frac{1}{3} < 0
\frac{(12 - x)}{(3x)} < 0

Two cases:
a) 12 - x < 0 &3x > 0 :: x > 12 & x > 0 therefore x > 12
b) 12 - x > 0 & 3x < 0 :: x < 12 & x < 0 therefore x < 12
Hence my solution: x < 12 or x > 12

Can someone kindly explain where I went wrong here?


Another way to solve this type of inequality:

From \frac{4}{x}<\frac{1}{3} it follows that x\neq0, therefore we can multiply both sides by 3x^2, which is positive.
We obtain 12x<x^2 or x^2-12x>0.
Now, imagine the graph of the quadratic function, y=12x^2-x, which is an upward parabola. See the attached drawing.
This parabola intercepts the X-axis at x=0 and x=12, the two "arms" are above the X-axis, meaning the values of y are positive when x<12 or x>0, and the values of y are negative (graph under the X-axis) when 0<x<12.

Hence the solution x<0 or x>12.

Note: Just remember the shape of the parabola, then you can easily deduce the sign of the quadratic function y=x^2+bx+c. If the quadratic equation x^2+bx+c=0 has two roots x_1<x_2 then y<0 (negative) between the two roots and y>0 (positive) outside the roots.
Or succinctly, y>0 if x_1<x<x_2 and y>0 if x<x_1 or x>x_2.

Attachments

ParabolaUp.jpg
ParabolaUp.jpg [ 8.97 KiB | Viewed 1652 times ]


_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Status: :O
Joined: 11 Jul 2012
Posts: 43
GMAT 1: 670 Q48 V35
Followers: 1

Kudos [?]: 21 [0], given: 27

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 25 Aug 2012, 03:06
Ah! :shock: thanks for the clarification Bunuel. I guess staying up all night took its toll. I had to reread and reread and reread and...

finally what I did was (per the first link you suggested) ::

dumping the two cases,
\frac{(12-x)}{(3x)} < 0
\frac{(x-12)}{(3x)} > 0 :idea:
roots: 12 and 0
and then I could ride the waves of + - + ...... weeeeeeeeeee.... weeeeeeeeeee... and weeeeeeeeeeee :-D

Thanks again for helping out Bunuel .. :)

_________________

disaster-spelled-in-670-ways-10-not-to-do-s-139230.html
GMAT Demystified: gmat-demystified-great-ebook-to-get-started-with-download-140836.html
Tense Tutorial: uber-awesome-resource-on-tenses-download-140837.html
CR Question Bank (LSAT): critical-reasoning-question-bank-download-140838.html

Intern
Intern
avatar
Status: :O
Joined: 11 Jul 2012
Posts: 43
GMAT 1: 670 Q48 V35
Followers: 1

Kudos [?]: 21 [0], given: 27

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 25 Aug 2012, 03:15
Thanks EvaJager :) you guys are awesome \m/

PS: I have just started out with my prep and have a lot to learn (and ask :lol: ) in little less than 3 weeks.

_________________

disaster-spelled-in-670-ways-10-not-to-do-s-139230.html
GMAT Demystified: gmat-demystified-great-ebook-to-get-started-with-download-140836.html
Tense Tutorial: uber-awesome-resource-on-tenses-download-140837.html
CR Question Bank (LSAT): critical-reasoning-question-bank-download-140838.html

Manager
Manager
avatar
Joined: 05 Jul 2012
Posts: 83
Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)
Followers: 4

Kudos [?]: 18 [0], given: 8

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 26 Aug 2012, 10:24
harshvinayak wrote:
Thanks EvaJager :) you guys are awesome \m/

PS: I have just started out with my prep and have a lot to learn (and ask :lol: ) in little less than 3 weeks.




One way to understand this is that Sign of \frac{x-a}{x-b} is same as the sign of (x-a)(x-b)
and for (x-a)(x-b) always remember that it will be negative between a & b and positive outside a & b
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4558
Location: Pune, India
Followers: 1028

Kudos [?]: 4449 [1] , given: 162

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 28 Aug 2012, 20:58
1
This post received
KUDOS
Expert's post
harshvinayak wrote:
If \frac{4}{x} <\frac{1}{3} , what is the possible range of values of x?

The question is from an MGMAT guide and the solution provided multiplies the inequality by x and flips the sign to arrive at the solution x < 0 or x > 12 . However the way I naturally would solve the given equation is:
\frac{4}{x} - \frac{1}{3} < 0
\frac{(12 - x)}{(3x)} < 0

Two cases:
a) 12 - x < 0 &3x > 0 :: x > 12 & x > 0 therefore x > 12
b) 12 - x > 0 & 3x < 0 :: x < 12 & x < 0 therefore x < 12
Hence my solution: x < 12 or x > 12

Can someone kindly explain where I went wrong here?



Check out these posts. They discuss how to solve inequalities efficiently (using the wave) and how to handle various complications that can arise in a question.

http://www.veritasprep.com/blog/2012/06 ... e-factors/
http://www.veritasprep.com/blog/2012/07 ... ns-part-i/
http://www.veritasprep.com/blog/2012/07 ... s-part-ii/
http://www.veritasprep.com/blog/2012/07 ... qualities/

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Intern
avatar
Status: :O
Joined: 11 Jul 2012
Posts: 43
GMAT 1: 670 Q48 V35
Followers: 1

Kudos [?]: 21 [0], given: 27

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 28 Aug 2012, 21:16
WOW ! :shock:
Thanks Karishma, thats one awesome collection of inequalities stuff. A kudos alone wouldnt have cut it :-D

_________________

disaster-spelled-in-670-ways-10-not-to-do-s-139230.html
GMAT Demystified: gmat-demystified-great-ebook-to-get-started-with-download-140836.html
Tense Tutorial: uber-awesome-resource-on-tenses-download-140837.html
CR Question Bank (LSAT): critical-reasoning-question-bank-download-140838.html

Manager
Manager
avatar
Joined: 12 Feb 2012
Posts: 106
Followers: 1

Kudos [?]: 9 [0], given: 28

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 12 Jul 2013, 13:15
Sorry to bring back this old post. I know how to solve this problems using the methods mentioned above. But I tried solving it another way and that method gave me a weird solution. Let say you wanted to solve the problem this way:

\frac{4}{x} <\frac{1}{3}

Since x cannot be 0. Lets look at the positive/negative scenarios

If x>0, then 12 <x
if x<0, then 12 >x but x cannot be both negative and greater than 12. So this is a contradiction.

Hence the range is 12 <x.

But this is incomplete. The range of x for this inquality is x<0 OR 12 <x. So what am I doing wrong?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22200 [0], given: 2601

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 12 Jul 2013, 13:57
Expert's post
alphabeta1234 wrote:
Sorry to bring back this old post. I know how to solve this problems using the methods mentioned above. But I tried solving it another way and that method gave me a weird solution. Let say you wanted to solve the problem this way:

\frac{4}{x} <\frac{1}{3}

Since x cannot be 0. Lets look at the positive/negative scenarios

If x>0, then 12 <x
if x<0, then 12 >x but x cannot be both negative and greater than 12. So this is a contradiction.

Hence the range is 12 <x.

But this is incomplete. The range of x for this inquality is x<0 OR 12 <x. So what am I doing wrong?


This is a correct approach but you made a mistake in the second case.

If x<0, then 12>x (x is less than 12) --> intersection is x<0.

So, the inequality holds true for x>12 (from the first case) and x<0 (from the second case).

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 11 Jan 2011
Posts: 71
GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40
Followers: 0

Kudos [?]: 2 [0], given: 3

GMAT ToolKit User
Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 24 Oct 2013, 17:15
Gotta bump this back up because I'm stuck on what should be a very simple inequalities problem.

Given: \frac{4}{x} < -\frac{1}{3}, I simplified the equation to: 12 < -x by cross-multiplying

Now, we have 2 scenarios:

1. x > 0 : no sign changes in 12 < -x, so x < -12. However, since we know x > 0, this scenario is impossible.

2. x < 0 : 12 < -x should become 12 < -(-x) so wouldn't this just be 12 < x? However, given x < 0, this scenario doesn't appear possible either.

Can someone please point out the obvious? It's driving me crazy...
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4558
Location: Pune, India
Followers: 1028

Kudos [?]: 4449 [0], given: 162

Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 24 Oct 2013, 19:38
Expert's post
NvrEvrGvUp wrote:
Gotta bump this back up because I'm stuck on what should be a very simple inequalities problem.

Given: \frac{4}{x} < -\frac{1}{3}, I simplified the equation to: 12 < -x by cross-multiplying

Now, we have 2 scenarios:

1. x > 0 : no sign changes in 12 < -x, so x < -12. However, since we know x > 0, this scenario is impossible.

2. x < 0 : 12 < -x should become 12 < -(-x) so wouldn't this just be 12 < x? However, given x < 0, this scenario doesn't appear possible either.

Can someone please point out the obvious? It's driving me crazy...


First of all, the actual question is \frac{4}{x} < \frac{1}{3} (there is no negative with 1/3)

Also, you know what you have to do but you probably do not understand why you have to do it. That is why you are facing problem in this question.

Given: \frac{4}{x} < -\frac{1}{3}, I simplified the equation to: 12 < -x by cross-multiplying

There is a problem here. You don't cross multiply and then take cases. You take cases and then cross multiply. Why? Because you CANNOT cross multiply till you know (or assume) the sign of x. The result of the cross multiplication depends on whether x is positive or negative. So you need to take cases and then cross multiply.

Case 1: x > 0
12 < x

Case 2: x < 0
12 > x (note that the sign has flipped here because you are multiplying by a negative number)
x should be less than 12 AND less than 0 so the range in x < 0.

Hence, two cases: x > 12 or x < 0.

Also because x is negative, you cannot just multiply it by -1 to make -x = x. That is certainly not correct. -x is positive and x is negative. They are not equal if x is not 0.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
avatar
Joined: 11 Jan 2011
Posts: 71
GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40
Followers: 0

Kudos [?]: 2 [0], given: 3

GMAT ToolKit User
Re: If 4/x < 1/3 , what is the possible range of values of x? [#permalink] New post 25 Oct 2013, 10:44
VeritasPrepKarishma wrote:
NvrEvrGvUp wrote:
Gotta bump this back up because I'm stuck on what should be a very simple inequalities problem.

Given: \frac{4}{x} < -\frac{1}{3}, I simplified the equation to: 12 < -x by cross-multiplying

Now, we have 2 scenarios:

1. x > 0 : no sign changes in 12 < -x, so x < -12. However, since we know x > 0, this scenario is impossible.

2. x < 0 : 12 < -x should become 12 < -(-x) so wouldn't this just be 12 < x? However, given x < 0, this scenario doesn't appear possible either.

Can someone please point out the obvious? It's driving me crazy...


First of all, the actual question is \frac{4}{x} < \frac{1}{3} (there is no negative with 1/3)

Also, you know what you have to do but you probably do not understand why you have to do it. That is why you are facing problem in this question.

Given: \frac{4}{x} < -\frac{1}{3}, I simplified the equation to: 12 < -x by cross-multiplying

There is a problem here. You don't cross multiply and then take cases. You take cases and then cross multiply. Why? Because you CANNOT cross multiply till you know (or assume) the sign of x. The result of the cross multiplication depends on whether x is positive or negative. So you need to take cases and then cross multiply.

Case 1: x > 0
12 < x

Case 2: x < 0
12 > x (note that the sign has flipped here because you are multiplying by a negative number)
x should be less than 12 AND less than 0 so the range in x < 0.

Hence, two cases: x > 12 or x < 0.

Also because x is negative, you cannot just multiply it by -1 to make -x = x. That is certainly not correct. -x is positive and x is negative. They are not equal if x is not 0.


Hi Karishma,

That was my mistake. There is a problem with a negative -1/3 and one without - I didn't realize this one was referencing the one with the positive 1/3.

I'll search for the -1/3 problem and explanation.

Thanks.
Re: If 4/x < 1/3 , what is the possible range of values of x?   [#permalink] 25 Oct 2013, 10:44
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic What is the value of 4x + 18 ? avohden 2 02 Oct 2013, 09:26
Experts publish their posts in the topic What is the value of (4x-y)*1/(3y)? macjas 1 27 May 2012, 08:13
6 Experts publish their posts in the topic 4^x + 4 ^-x = 2 What is the value of X nimc2012 15 07 Feb 2012, 08:56
If 4/x <1/3, what is the possible range of values for x? GMATD11 4 07 Apr 2011, 04:01
9 Experts publish their posts in the topic For what range of values of 'x' ? Eden 18 03 Sep 2010, 06:02
Display posts from previous: Sort by

If 4/x < 1/3 , what is the possible range of values of 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®.