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

It is currently 19 Sep 2014, 01:48

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

Is x/3 + 3/x > 2

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Manager
Manager
User avatar
Joined: 12 Mar 2009
Posts: 192
Followers: 1

Kudos [?]: 87 [3] , given: 60

GMAT Tests User
Is x/3 + 3/x > 2 [#permalink] New post 15 Jul 2010, 23:06
3
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

39% (02:03) correct 61% (01:05) wrong based on 173 sessions
Is \frac{x}{3} + \frac{3}{x} > 2?

(1) x < 3
(2) x > 1
[Reveal] Spoiler: OA

Last edited by DenisSh on 16 Jul 2010, 02:15, edited 1 time in total.
3 KUDOS received
Intern
Intern
avatar
Status: fighting hard..
Joined: 12 Jul 2010
Posts: 29
Schools: ISB, Hass, Ross, NYU Stern
Followers: 0

Kudos [?]: 5 [3] , given: 24

Re: Tricky inequality problem [#permalink] New post 16 Jul 2010, 01:28
3
This post received
KUDOS
on rearranging the terms we get,
((x^2 + 9)/3x) - 2 > 0
(x^2 + 9 -6x)/3x > 0
((x - 3)^2)/3x > 0

(x-3)^2 is positive.
amongst options (1) and (2), we can draw a clear cut conclusion only using (2).

Therefore ans is B.
:)
2 KUDOS received
Manager
Manager
User avatar
Joined: 12 Mar 2009
Posts: 192
Followers: 1

Kudos [?]: 87 [2] , given: 60

GMAT Tests User
Re: Tricky inequality problem [#permalink] New post 16 Jul 2010, 02:13
2
This post received
KUDOS
naish wrote:
(x-3)^2 is positive.
amongst options (1) and (2), we can draw a clear cut conclusion only using (2).

Therefore ans is B.
:)


No. As I think, you should get 2 inequalities:
1) (x-3)^2>0 and 2) (x-3)^2<0 (it depends on what the sign does x have).

After that, (2) indicates that x has a positive sign. Thus, we should consider only 1) inequality.
There is one option when (x-3)^2=0 - if x=3.

Since (1) indicates that x \neq 3, the OA is (C).

Correct me if I'm wrong.
2 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 178

Kudos [?]: 948 [2] , given: 235

GMAT Tests User Reviews Badge
Re: Tricky inequality problem [#permalink] New post 16 Jul 2010, 04:06
2
This post received
KUDOS
naish wrote:
on rearranging the terms we get,
((x^2 + 9)/3x) - 2 > 0
(x^2 + 9 -6x)/3x > 0
((x - 3)^2)/3x > 0

(x-3)^2 is positive.
amongst options (1) and (2), we can draw a clear cut conclusion only using (2).

Therefore ans is B.
:)


Ans is C,
For all the +ve values of x the answer to the question is yes, except for x=3 for which its value is 0 thus the answer is no.

1st statement eliminates the x=3 option thus it is required.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23480
Followers: 3500

Kudos [?]: 26409 [2] , given: 2710

Re: Tricky inequality problem [#permalink] New post 16 Jul 2010, 06:42
2
This post received
KUDOS
Expert's post
DenisSh wrote:
Is \frac{x}{3} + \frac{3}{x} > 2?

(1) x < 3

(2) x > 1

Please outline your approach! :)


gurpreetsingh's solution is correct.

Is \frac{x}{3}+\frac{3}{x}>2? --> is \frac{(x-3)^2}{x}>0? Now, nominator is non-negative, thus the fraction to be positive nominator must not be zero (thus it'll be positive) and denominator mut be positive --> x\neq{3} and x>0.

Statement (1) satisfies the first requirement and statement (2) satisfies the second requirement, so taken together they are sufficient.

Answer: C.
_________________

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
User avatar
Joined: 12 Mar 2009
Posts: 192
Followers: 1

Kudos [?]: 87 [0], given: 60

GMAT Tests User
Re: Tricky inequality problem [#permalink] New post 17 Jul 2010, 01:09
Bunuel wrote:
gurpreetsingh's solution is correct.

Is \frac{x}{3}+\frac{3}{x}>2? --> is \frac{(x-3)^2}{x}>0?
Answer: C.


How did you get \frac{(x-3)^2}{x}>0?

Step 1:
\frac{x}{3}+\frac{3}{x}>2?
Step 2 (multiply by 3x):
x^2+9>6x
Step 3 (move 6x to the left side):
x^2-6x+9>0
Step 4 (convert to the compact form):
(x-3)^2>0

Please explain...
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23480
Followers: 3500

Kudos [?]: 26409 [5] , given: 2710

Re: Tricky inequality problem [#permalink] New post 17 Jul 2010, 03:36
5
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
DenisSh wrote:
Bunuel wrote:
gurpreetsingh's solution is correct.

Is \frac{x}{3}+\frac{3}{x}>2? --> is \frac{(x-3)^2}{x}>0?
Answer: C.


How did you get \frac{(x-3)^2}{x}>0?

Step 1:
\frac{x}{3}+\frac{3}{x}>2?
Step 2 (multiply by 3x):
x^2+9>6x
Step 3 (move 6x to the left side):
x^2-6x+9>0
Step 4 (convert to the compact form):
(x-3)^2>0

Please explain...


This is the most common error when solve inequalities. I keep writing this over and over again:

Never multiply or reduce inequality by an unknown (a variable) unless you are sure of its sign.

So you CANNOT multiply \frac{x}{3}+\frac{3}{x}>2 by 3x since you don't know the sign of x.

What you CAN DO is: \frac{x}{3}+\frac{3}{x}>2 --> \frac{x}{3}+\frac{3}{x}-2> --> common denominator is 3x --> \frac{x^2+9-6x}{3x}>0 --> multiply be 3 --> \frac{x^2+9-6x}{x}>0 --> \frac{(x-3)^2}{x}>0.

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

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 178

Kudos [?]: 948 [0], given: 235

GMAT Tests User Reviews Badge
Re: Tricky inequality problem [#permalink] New post 17 Jul 2010, 06:59
Another way :

Arithmatic mean >= geometric mean ( the numbers should be +ve )

=> \frac{x}{3} + \frac{3}{x} >=2 ; equality holds when x/3 = 3/x => x^2 = 9 => x = + 3

1st statement removes the possibility of x=3 but we do not know whether x>0 or not.

2nd statement removes the possibility of x<0 but x can be equal to 3

Thus both statements taken together states x is not equal to 3 and x is +ve

Thus C is the answer.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Intern
avatar
Joined: 19 Dec 2009
Posts: 37
Followers: 0

Kudos [?]: 10 [0], given: 8

Re: Tricky inequality problem [#permalink] New post 18 Jul 2010, 09:55
The way I solved it.

1. x < 3 : LT3 - Insuf because with x = -1 the inequality is false and with x = 2 it is true.
2. x > 1 : GT1 - Insuf because with x = 2 the inequality is true and with x = 3 it is false


Combining the two options yeilds 1 < x < 3 which clearly shows that the original expression is > 2.

So the correct answer is C. 1 and 2 together are sufficient.
Manager
Manager
avatar
Joined: 03 Jun 2010
Posts: 184
Location: United States (MI)
Concentration: Marketing, General Management
WE: Business Development (Consumer Products)
Followers: 4

Kudos [?]: 22 [0], given: 40

GMAT ToolKit User GMAT Tests User
Re: Tricky inequality problem [#permalink] New post 19 Jul 2010, 02:20
(x-3)^2/x >0

(x-3)^2 is always >0, therefore we just need x to be >0.
The correct answer is (0;3) and (3;+inf)
It's (B), because if we consider (C), we will loose answers. Try 10, 11, 12 and so on. It fits.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23480
Followers: 3500

Kudos [?]: 26409 [1] , given: 2710

Re: Tricky inequality problem [#permalink] New post 19 Jul 2010, 08:18
1
This post received
KUDOS
Expert's post
ulm wrote:
(x-3)^2/x >0

(x-3)^2 is always >0, therefore we just need x to be >0.
The correct answer is (0;3) and (3;+inf)
It's (B), because if we consider (C), we will loose answers. Try 10, 11, 12 and so on. It fits.


Generally, unknown (or expression with unknown) in even power is NOT always positive, it's non-negative. Not knowing this is the cause of many mistakes on GMAT.

So, (x-3)^2\geq{0}, because if x=3, then (x-3)^2=0 and \frac{(x-3)^2}{x} also equals to zero (and not more than zero). We need statement (1) to exclude the possibility of x being 3 by saying that x<3. That's why the answer to this question is C, not B.

Hope it's clear.
_________________

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: 03 Jun 2010
Posts: 184
Location: United States (MI)
Concentration: Marketing, General Management
WE: Business Development (Consumer Products)
Followers: 4

Kudos [?]: 22 [0], given: 40

GMAT ToolKit User GMAT Tests User
Re: Tricky inequality problem [#permalink] New post 19 Jul 2010, 08:32
I'm completely agree that x not equal 3 (as i wrote earlier;)

But we miss all positive x's that a > 3, don't we?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23480
Followers: 3500

Kudos [?]: 26409 [0], given: 2710

Re: Tricky inequality problem [#permalink] New post 19 Jul 2010, 08:48
Expert's post
ulm wrote:
(x-3)^2/x >0

(x-3)^2 is always >0, therefore we just need x to be >0.
The correct answer is (0;3) and (3;+inf)
It's (B), because if we consider (C), we will loose answers. Try 10, 11, 12 and so on. It fits.



ulm wrote:
I'm completely agree that x not equal 3 (as i wrote earlier;)

But we miss all positive x's that a > 3, don't we?


I'm not sure exactly what you're asking here. You said that the answer to this question should be B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (2) is: x>1 --> denominator is positive, nominator is also positive EXCEPT for one value of x: when x=3>1, then \frac{(x-3)^2}{x}=0 (not more than zero). Hence we have TWO different answers to the question "is \frac{(x-3)^2}{x}>0": one is NO for x=3>1 and another is YES for all other values of x>1. Two different answers = not sufficient.

Hope it's clear.
_________________

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

Senior Manager
Senior Manager
User avatar
Status: Current Student
Joined: 14 Oct 2009
Posts: 370
Schools: Chicago Booth 2013, Ross, Duke , Kellogg , Stanford, Haas
Followers: 13

Kudos [?]: 98 [0], given: 53

GMAT Tests User Reviews Badge
Re: Tricky inequality problem [#permalink] New post 21 Jul 2010, 08:41
Not sure if I took the long way to do this problem and I just got lucky that it worked out quickly for me, but I took a different approach and started plugging in numbers in case this explanation helps anyone...

1) x<3, so I plugged in 2 for x and got 5/6 which is less than 2; I then plugged in 1 for x trying to find an instance where the opposite was true and got 10/3, which is greater than 2, so statement 1 is insufficient

2) x>1; I already had the result when 2 is plugged in which is 5/6 and less than 2; so I tried plugging in 6, since I knew this would give me a higher result and got 2.5 which is greater than 2, so statement 2 insufficient

When combined, you know x has to be 2 which results in 5/6 and is less than 2, so together they are sufficient. C
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23480
Followers: 3500

Kudos [?]: 26409 [0], given: 2710

Re: Tricky inequality problem [#permalink] New post 21 Jul 2010, 09:10
Expert's post
Michmax3 wrote:
Not sure if I took the long way to do this problem and I just got lucky that it worked out quickly for me, but I took a different approach and started plugging in numbers in case this explanation helps anyone...

1) x<3, so I plugged in 2 for x and got 5/6 which is less than 2; I then plugged in 1 for x trying to find an instance where the opposite was true and got 10/3, which is greater than 2, so statement 1 is insufficient

2) x>1; I already had the result when 2 is plugged in which is 5/6 and less than 2; so I tried plugging in 6, since I knew this would give me a higher result and got 2.5 which is greater than 2, so statement 2 insufficient

When combined, you know x has to be 2 which results in 5/6 and is less than 2, so together they are sufficient. C


Unfortunately your approach is not correct.

First of all if x=2--> \frac{x}{3} + \frac{3}{x}=\frac{13}{6} > 2, so you made an error in calculations (\frac{2}{3} + \frac{3}{2}=\frac{13}{6}\neq{\frac{5}{6}}). Again \frac{x}{3} + \frac{3}{x}>2 is true for ANY value of x but 3, for which \frac{x}{3} + \frac{3}{x}=2.

Next: you say that "When combined, you know x has to be 2". Not so, as we are not told that x is an integer, hence x<3 and x>1 does not mean that x=2, it can be 2.5 or 1.777, basically ANY number from 1 to 3, not inclusive.

Hope it's clear.
_________________

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

Senior Manager
Senior Manager
User avatar
Status: Current Student
Joined: 14 Oct 2009
Posts: 370
Schools: Chicago Booth 2013, Ross, Duke , Kellogg , Stanford, Haas
Followers: 13

Kudos [?]: 98 [0], given: 53

GMAT Tests User Reviews Badge
Re: Tricky inequality problem [#permalink] New post 21 Jul 2010, 09:30
Bunuel wrote:
Michmax3 wrote:
Not sure if I took the long way to do this problem and I just got lucky that it worked out quickly for me, but I took a different approach and started plugging in numbers in case this explanation helps anyone...

1) x<3, so I plugged in 2 for x and got 5/6 which is less than 2; I then plugged in 1 for x trying to find an instance where the opposite was true and got 10/3, which is greater than 2, so statement 1 is insufficient

2) x>1; I already had the result when 2 is plugged in which is 5/6 and less than 2; so I tried plugging in 6, since I knew this would give me a higher result and got 2.5 which is greater than 2, so statement 2 insufficient

When combined, you know x has to be 2 which results in 5/6 and is less than 2, so together they are sufficient. C



Unfortunately your approach is not correct.

First of all if x=2--> \frac{x}{3} + \frac{3}{x}=\frac{13}{6} > 2, so made you an error in calculations (\frac{2}{3} + \frac{3}{2}=\frac{13}{6}\neq{\frac{5}{6}}). Again \frac{x}{3} + \frac{3}{x}>2 is true for ANY value of x but 3, for which \frac{x}{3} + \frac{3}{x}=2.

Next: you say that "When combined, you know x has to be 2". Not so, as we are not told that x is an integer, hence x<3 and x>1 does not mean that x=2, it can be 2.5 or 1.777, basically ANY number from 1 to 3, not inclusive.

Hope it's clear.


Yes, then I guess I got lucky and need a lot more practice with these. Thanks for clarifying
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Retired Moderator
avatar
Joined: 03 Aug 2010
Posts: 248
Followers: 2

Kudos [?]: 30 [0], given: 41

GMAT Tests User
Re: Tricky inequality problem [#permalink] New post 05 Oct 2010, 21:25
Bunuel wrote:
DenisSh wrote:
Bunuel wrote:
gurpreetsingh's solution is correct.

Is \frac{x}{3}+\frac{3}{x}>2? --> is \frac{(x-3)^2}{x}>0?
Answer: C.


How did you get \frac{(x-3)^2}{x}>0?

Step 1:
\frac{x}{3}+\frac{3}{x}>2?
Step 2 (multiply by 3x):
x^2+9>6x
Step 3 (move 6x to the left side):
x^2-6x+9>0
Step 4 (convert to the compact form):
(x-3)^2>0

Please explain...


This is the most common error when solve inequalities. I keep writing this over and over again:

Never multiply or reduce inequality by an unknown (a variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality.

So you CAN NOT multiply \frac{x}{3}+\frac{3}{x}>2 by 3x since you don't know the sign of x.

Wheat you CAN DO is: \frac{x}{3}+\frac{3}{x}>2 --> \frac{x}{3}+\frac{3}{x}-2> --> common denominator is 3x --> \frac{x^2+9-6x}{3x}>0 --> multiply be 3 --> \frac{x^2+9-6x}{x}>0 --> \frac{(x-3)^2}{x}>0.

Hope it helps.



thanks for your explanation... can you explain the below mentioned rule with an example and its reasoning.

Never multiply or reduce inequality by an unknown (a variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequalit
_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 807
Location: London
Followers: 76

Kudos [?]: 481 [0], given: 25

GMAT ToolKit User GMAT Tests User Reviews Badge
Re: Tricky inequality problem [#permalink] New post 05 Oct 2010, 23:23
hirendhanak wrote:
thanks for your explanation... can you explain the below mentioned rule with an example and its reasoning.

Never multiply or reduce inequality by an unknown (a variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequalit


Consider the inequality \frac{x^2-12}{x}>-1

Lets say I multiply both sides by 7x without considering the signs of the variable, what happens ?

x^2-12>-x
x^2+x-12>0
(x+4)(x-3)>0

Which is true whenever x>3 (both terms positive) or when x<-4 (both terms negative)

But since we haven't kept the Sign of x in mind when we multiplied in step 1, the solution is wrong.

For eg. Take x=-1 which according to us is not a solution. It is easy to see ((-1)^2-12)/(-1)=11>-1. So it should be a solution
Similarly take x=-6 which according to us is a solution, but ((-6)^2-12)/-6=-4<-1. So it should not be a solution
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23480
Followers: 3500

Kudos [?]: 26409 [0], given: 2710

Re: Tricky inequality problem [#permalink] New post 06 Oct 2010, 03:09
Expert's post
hirendhanak wrote:
thanks for your explanation... can you explain the below mentioned rule with an example and its reasoning.

Never multiply or reduce inequality by an unknown (a variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequalit


Consider a simple inequality 4>3 and some variable x.

Now, you can't multiply (or divide) both parts of this inequality by x and write: 4x>3x, because if x=1>0 then yes 4*1>3*1 but if x=-1 then 4*(-1)=-4<3*(-1)=-3. Similarly, you can not divide an inequality by x not knowing its sign.

Hope it's clear.
_________________

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

Director
Director
User avatar
Status: GMAT Learner
Joined: 14 Jul 2010
Posts: 652
Followers: 34

Kudos [?]: 231 [0], given: 32

GMAT Tests User
is (x/3+3/x) > 2? (1) x < 3 (2) x > 1 This ds has [#permalink] New post 08 Jun 2011, 02:52
is (x/3+3/x) > 2?
(1) x < 3
(2) x > 1

This ds has been discussed thoroughly at http://gmatclub.com/forum/tricky-inequality-problem-97331.html. It inequality simplified there as [(x - 3)^2]/3 > 0.
if i do not simplify then i can i solved it as:
(1) if x = 2 then the (x/3+3/x) > 2 but if x = negative the (x/3+3/x) > 2 is not true. so Insufficient.
(2) if x = 2 then (x/3+3/x) > 2 but if x = 1 then (x/3+3/x) > 2 is true. so insufficient.

for C x =2 and (x/3+3/x) > 2.

so why i will simplify as i am getting direct answer?
_________________

I am student of everyone-baten
Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

is (x/3+3/x) > 2? (1) x < 3 (2) x > 1 This ds has   [#permalink] 08 Jun 2011, 02:52
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Is (x - 4)(x - 3)(x + 2)(x + 1) > 0 HKHR 3 27 Sep 2013, 07:01
3 Experts publish their posts in the topic Is x/3 + 3/x > 2 sher676 19 04 Aug 2009, 15:33
Is sqrt[(x-3)^2] = (3-x)^2 ? (1) x ≠ 3 (2) – x | x | > 0 goalsnr 8 16 May 2008, 16:43
Is sqrt.(x-3)^2 = 3-x? (1) x != 3 (2) -x|x| > 0 Looking nupurgupt 3 28 Jul 2007, 11:09
Is sqrt((x-3)^2) = 3-x? (1) x ? 3 (2) x | x | > 0 as13 3 08 Nov 2005, 18:20
Display posts from previous: Sort by

Is x/3 + 3/x > 2

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 30 posts ] 



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®.