GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Aug 2018, 08:20

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.

Close

Request Expert Reply

Confirm Cancel

If |12x−5|>|7−6x|, which of the following CANNOT be the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 120
If |12x−5|>|7−6x|, which of the following CANNOT be the  [#permalink]

Show Tags

New post 11 Jun 2013, 04:17
21
1
71
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

38% (03:23) correct 62% (02:32) wrong based on 1289 sessions

HideShow timer Statistics

If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47918
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 11 Jun 2013, 05:19
24
22
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


Square both sides: \(144x^2-120 x+25>36 x^2-84 x+49\) --> \(9 x^2-3x-2>0\) --> factor: \((x+\frac{1}{3})(x-\frac{2}{3})>0\) (check here: http://www.purplemath.com/modules/factquad.htm). "\(>\)" sign indicates that the solutions lies to the left of the smaller root and to the right of the greater root (check here: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476). Thus \(x<-\frac{1}{3}\) OR \(x>\frac{2}{3}\).

\(x=-4<-\frac{1}{3}\) and \(x=3>\frac{2}{3}\) are possible values of x --> the product = -12;
\(x=-\frac{7}{5}<-\frac{1}{3}\) and \(x=1>\frac{2}{3}\) are possible values of x --> the product = -7/5;
\(x=-\frac{4}{9}<-\frac{1}{3}\) and \(x=-1<-\frac{1}{3}\) are possible values of x --> the product = 4/9;
\(x=-1<-\frac{1}{3}\) and \(x=-17<-\frac{1}{3}\) are possible values of x --> the product = 17.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 13 Aug 2012
Posts: 105
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the  [#permalink]

Show Tags

New post 02 Apr 2014, 09:17
6
3
Another Method
\(|12x-5|>|7-6x|\)
Only 2 cases can arise; the other 2 cases are the same as these ones
Ist Case
\(|12x-5|>|7-6x|\)
\(2x-5>7-6x\)
\(18x>12\)
\(x>2/3\)

IInd Case
\(|12x-5|>|7-6x|\)
\(12x-5<6x-7\)
\(x<-2/6\)
\(x<-1/3\)



Now we know that\(x>2/3\) and \(x<-1/3\)
So from the above we can deduce that the answer has to be negative, thus we can cross out D and E.
From the next 3 options which are all negative, Option A and B both can be formed, but option C is between \(-1/3\) and \(2/3\) which is not in the range of x. Thus C is your answer.
General Discussion
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 430
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 12 Jun 2013, 20:40
Hi.

I thought we cannot square both sides (|12x−5|>|7−6x|) unless we know that they are positive.

Thanks!

Bunuel wrote:
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


Square both sides: \(144x^2-120 x+25>36 x^2-84 x+49\) --> \(9 x^2-3x-2>0\) --> factor: \((x+\frac{1}{3})(x-\frac{2}{3})>0\) (check here: http://www.purplemath.com/modules/factquad.htm). "\(>\)" sign indicates that the solutions lies to the left of the smaller root and to the right of the greater root (check here: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476). Thus \(x<-\frac{1}{3}\) OR \(x>\frac{2}{3}\).

\(x=-4<-\frac{1}{3}\) and \(x=3>\frac{2}{3}\) are possible values of x --> the product = -12;
\(x=-\frac{7}{5}<-\frac{1}{3}\) and \(x=1>\frac{2}{3}\) are possible values of x --> the product = -7/5;
\(x=-\frac{4}{9}<-\frac{1}{3}\) and \(x=-1<-\frac{1}{3}\) are possible values of x --> the product = 4/9;
\(x=-1<-\frac{1}{3}\) and \(x=17>\frac{2}{3}\) are possible values of x --> the product = 17.

Answer: C.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47918
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 12 Jun 2013, 23:08
1
WholeLottaLove wrote:
Hi.

I thought we cannot square both sides (|12x−5|>|7−6x|) unless we know that they are positive.

Thanks!

Bunuel wrote:
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


Square both sides: \(144x^2-120 x+25>36 x^2-84 x+49\) --> \(9 x^2-3x-2>0\) --> factor: \((x+\frac{1}{3})(x-\frac{2}{3})>0\) (check here: http://www.purplemath.com/modules/factquad.htm). "\(>\)" sign indicates that the solutions lies to the left of the smaller root and to the right of the greater root (check here: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476). Thus \(x<-\frac{1}{3}\) OR \(x>\frac{2}{3}\).

\(x=-4<-\frac{1}{3}\) and \(x=3>\frac{2}{3}\) are possible values of x --> the product = -12;
\(x=-\frac{7}{5}<-\frac{1}{3}\) and \(x=1>\frac{2}{3}\) are possible values of x --> the product = -7/5;
\(x=-\frac{4}{9}<-\frac{1}{3}\) and \(x=-1<-\frac{1}{3}\) are possible values of x --> the product = 4/9;
\(x=-1<-\frac{1}{3}\) and \(x=17>\frac{2}{3}\) are possible values of x --> the product = 17.

Answer: C.


We CAN square an inequality if we know that the sides are non-negative, which is the case here.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 430
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 13 Jun 2013, 07:57
Thanks for the clarification.

When I factored this problem out, I got 12(9x^2-3x-2)>0 That factored out to:

12(3x+1)(3x-2)>0

So I have two questions:

1.) What happens with the factored out 12?

2.) upon simplifying for the inequalities in the equations, I got:


I.) (3x+1)>0 3x>-1 x>-1/3
II.) (3x-2)>0 3x>2 x>2/3


So my question is, how did you flip the inequality signs to get x<-\frac{1}{3} OR x>\frac{2}{3}. whereas I have x>-1/3 and x>2/3

Thanks!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47918
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 13 Jun 2013, 08:03
WholeLottaLove wrote:
Thanks for the clarification.

When I factored this problem out, I got 12(9x^2-3x-2)>0 That factored out to:

12(3x+1)(3x-2)>0

So I have two questions:

1.) What happens with the factored out 12?

2.) upon simplifying for the inequalities in the equations, I got:


I.) (3x+1)>0 3x>-1 x>-1/3
II.) (3x-2)>0 3x>2 x>2/3


So my question is, how did you flip the inequality signs to get x<-\frac{1}{3} OR x>\frac{2}{3}. whereas I have x>-1/3 and x>2/3

Thanks!


1. 12 is reduced (divide by 12 both sides).
2. Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#p841486

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 430
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 10 Jul 2013, 10:26
1
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

Find two checkpoints:

|12x−5|>|7−6x|

x=5/12, x=7/6

x<5/12, 5/12<x<7/6, x>7/6

x<5/12
|12x−5|>|7−6x|
-(12x-5) > (7-6x)
-12x+5 > 7-6x
-6x > 2
x<-1/3 Valid

5/12<x<7/6
|12x−5|>|7−6x|
(12x-5) > (7-6x)
18x > 12
x > 2/3
2/3<x<7/6

x>7/6
|12x−5|>|7−6x|
(12x-5) > -(7-6x)
12x - 5 > -7 + 6x
6x > -2
x > -1/3
(if the range being tested is >7/6 and x > -1/3 is that valid or invalid?)

I think I am approaching finding x the right way, but I am not sure how I can figure out what CANNOT be the product of two possible values of x. Can anyone help? Thanks!
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 430
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 15 Jul 2013, 15:16
4
3
Another way to solve...

If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

|12x−5|>|7−6x|
(12x-5)>(7-6x)
12x-5>7-6x
18x>12
x>2/3 Valid as a number greater than 2/3 will make |12x−5|>|7−6x| true

|12x−5|>|7−6x|
12x-5>-(7-6x)
12x-5>-7+6x
6x>-2
x>-1/3 Invalid as a number greater than -1/3 may or may not make |12x−5|>|7−6x| true

|12x−5|>|7−6x|
-(12x-5)>-(7-6x)
-12x+5>-7+6x
-18x>-12
x<2/3 Invalid as a number less than 2/3 may or may not make |12x−5|>|7−6x| true

|12x−5|>|7−6x|
-(12x-5)>(7-6x)
-12x+5>7-6x
-6x>2
x<-1/3 Valid as every number less than -1/3 will make |12x−5|>|7−6x| true

The two invalid values of x are -1/3 and 2/3. (-1/3)*(2/3) = (-2/9)

(C)
Director
Director
avatar
Joined: 03 Aug 2012
Posts: 822
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Premium Member
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 23 Jul 2013, 22:08
Hi Folks,

I have a query on this and see the attachment for the same.Please ignore the untidy drawing of mine, couldn't help due to time constraint and poor word knowledge.

I have drawn graphs for |12x+5| and |7-6x| and compared where the first modulus is greater than the second modulus. However, against the above solutions , I got only x> 2/3 solution which doesn't satisfies above solution.

The line in red is the graph for |7-6x| and the line in black is for |12x-5|. The pink line shows intersection point of the lines and has (2/3) as x - coordinate.So by the graph we can see that |12x-5| > |7-6x| only after x= 2/3.

Please tell where I am going wrong !!!

Plz Advise !!

Regards,
TGC !
Attachments

query.JPG
query.JPG [ 13.53 KiB | Viewed 16952 times ]


_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47918
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 23 Jul 2013, 22:42
1
targetgmatchotu wrote:
Hi Folks,

I have a query on this and see the attachment for the same.Please ignore the untidy drawing of mine, couldn't help due to time constraint and poor word knowledge.

I have drawn graphs for |12x+5| and |7-6x| and compared where the first modulus is greater than the second modulus. However, against the above solutions , I got only x> 2/3 solution which doesn't satisfies above solution.

The line in red is the graph for |7-6x| and the line in black is for |12x-5|. The pink line shows intersection point of the lines and has (2/3) as x - coordinate.So by the graph we can see that |12x-5| > |7-6x| only after x= 2/3.

Please tell where I am going wrong !!!

Plz Advise !!

Regards,
TGC !


The graphs drawn are not correct. The proper drawing is below:
Attachment:
MSP2441f260916666dabe40000498a5d50ib182823.gif
MSP2441f260916666dabe40000498a5d50ib182823.gif [ 9.23 KiB | Viewed 17984 times ]
Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
avatar
Joined: 03 Aug 2012
Posts: 822
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Premium Member
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 24 Jul 2013, 00:20
Bunuel wrote:
targetgmatchotu wrote:
Hi Folks,

I have a query on this and see the attachment for the same.Please ignore the untidy drawing of mine, couldn't help due to time constraint and poor word knowledge.

I have drawn graphs for |12x+5| and |7-6x| and compared where the first modulus is greater than the second modulus. However, against the above solutions , I got only x> 2/3 solution which doesn't satisfies above solution.

The line in red is the graph for |7-6x| and the line in black is for |12x-5|. The pink line shows intersection point of the lines and has (2/3) as x - coordinate.So by the graph we can see that |12x-5| > |7-6x| only after x= 2/3.

Please tell where I am going wrong !!!

Plz Advise !!

Regards,
TGC !


The graphs drawn are not correct. The proper drawing is below:
Attachment:
MSP2441f260916666dabe40000498a5d50ib182823.gif
Hope it helps.


12x -5 , the graph touches y axis where x=0 => y = -5 taking modulus => y=5

7-6x, x=0 => y =7 .

Further, touches x axis where y=0 hence x=5/12 and x=7/6 (7/6 > 5/12)

Please correct me !!

Rgds,
TGC !

So by any chance the graph cross??????
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47918
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 24 Jul 2013, 01:52
targetgmatchotu wrote:
Bunuel wrote:
targetgmatchotu wrote:
Hi Folks,

I have a query on this and see the attachment for the same.Please ignore the untidy drawing of mine, couldn't help due to time constraint and poor word knowledge.

I have drawn graphs for |12x+5| and |7-6x| and compared where the first modulus is greater than the second modulus. However, against the above solutions , I got only x> 2/3 solution which doesn't satisfies above solution.

The line in red is the graph for |7-6x| and the line in black is for |12x-5|. The pink line shows intersection point of the lines and has (2/3) as x - coordinate.So by the graph we can see that |12x-5| > |7-6x| only after x= 2/3.

Please tell where I am going wrong !!!

Plz Advise !!

Regards,
TGC !


The graphs drawn are not correct. The proper drawing is below:
Attachment:
MSP2441f260916666dabe40000498a5d50ib182823.gif
Hope it helps.


12x -5 , the graph touches y axis where x=0 => y = -5 taking modulus => y=5

7-6x, x=0 => y =7 .

Further, touches x axis where y=0 hence x=5/12 and x=7/6 (7/6 > 5/12)

Please correct me !!

Rgds,
TGC !

So by any chance the graph cross??????


I don't understand your question... As I said the graph of |12x−5|>|7−6x| is:
Image
x<-1/3 and x>2/3.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
avatar
Joined: 03 Aug 2012
Posts: 822
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Premium Member
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod  [#permalink]

Show Tags

New post 24 Jul 2013, 01:59
Bunuel wrote:
I don't understand your question... As I said the graph of |12x−5|>|7−6x| is:
Image
x<-1/3 and x>2/3.


Got it,

there was a mistake in drawing the graph !!

Thanks,
TGC !
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8184
Location: Pune, India
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the  [#permalink]

Show Tags

New post 27 Mar 2014, 22:15
2
4
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


You can also use the number line method of mods to solve this question:

|12x−5|>|7−6x|

12|x - 5/12| > 6|x - 7/6|

2|x - 5/12| > |x - 14/12|

Twice of the distance from 5/12 should be more than distance from 14/12.

___________0_______5/12_________________14/12__________

We find the points where the two distances are equal.
The distance between 5/12 and 14/12 is 9/12 which gets divided into 1:2 i.e. the point where the distances will be equal will be 3/12 away from 5/12 i.e. at 8/12 = 2/3. At any point to the right of 2/3, twice the distance from 5/12 will be more than the distance from 14/12.

Another point will be 9/12 to the left of 5/12 i.e. at -4/12 = -1/3. At any left to the left of -1/3, twice the distance from 5/12 will be more than the distance from 14/12.

x < -1/3 OR x > 2/3

Then proceed as given above.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
Joined: 27 Mar 2014
Posts: 24
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the  [#permalink]

Show Tags

New post 21 Jun 2014, 03:30
VeritasPrepKarishma wrote:
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


You can also use the number line method of mods to solve this question:

|12x−5|>|7−6x|

12|x - 5/12| > 6|x - 7/6|

2|x - 5/12| > |x - 14/12|

Twice of the distance from 5/12 should be more than distance from 14/12.

___________0_______5/12_________________14/12__________

We find the points where the two distances are equal.
The distance between 5/12 and 14/12 is 9/12 which gets divided into 1:2 i.e. the point where the distances will be equal will be 3/12 away from 5/12 i.e. at 8/12 = 2/3. At any point to the right of 2/3, twice the distance from 5/12 will be more than the distance from 14/12.

Another point will be 9/12 to the left of 5/12 i.e. at -4/12 = -1/3. At any left to the left of -1/3, twice the distance from 5/12 will be more than the distance from 14/12.

x < -1/3 OR x > 2/3

Then proceed as given above.


I apply this distance inference. But in a different way,

The nearest the number to 5/12 must be the answer, as it yields the shortest distance to 5/12. Then answer is C.
Senior Manager
Senior Manager
avatar
G
Joined: 21 Aug 2016
Posts: 281
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the  [#permalink]

Show Tags

New post 08 Dec 2016, 22:21
1
happyface101 wrote:
Bunuel wrote:
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


Square both sides: \(144x^2-120 x+25>36 x^2-84 x+49\) --> \(9 x^2-3x-2>0\) --> factor: \((x+\frac{1}{3})(x-\frac{2}{3})>0\) (check here: http://www.purplemath.com/modules/factquad.htm). "\(>\)" sign indicates that the solutions lies to the left of the smaller root and to the right of the greater root (check here: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476). Thus \(x<-\frac{1}{3}\) OR \(x>\frac{2}{3}\).

\(x=-4<-\frac{1}{3}\) and \(x=3>\frac{2}{3}\) are possible values of x --> the product = -12;
\(x=-\frac{7}{5}<-\frac{1}{3}\) and \(x=1>\frac{2}{3}\) are possible values of x --> the product = -7/5;
\(x=-\frac{4}{9}<-\frac{1}{3}\) and \(x=-1<-\frac{1}{3}\) are possible values of x --> the product = 4/9;
\(x=-1<-\frac{1}{3}\) and \(x=-17<-\frac{1}{3}\) are possible values of x --> the product = 17.

Answer: C.


Bunuel - this is really helpful, thank you! Can you let us know if a question like this is possible on the GMAT? How is it possible to interpret the question and do all this math / testing in 2mins or 2.5mins max?



To solve the question faster, we don't have to look at all the choices.
Once we know that x>2/3 and x<−1/3, we can say that x can neither be 2/3 nor -1/3 (x!=2/3 && x!=-1/3)

so the product of two possible values of x can never be 2/3*(-1/3)=-2/9, Hence the correct answer is C.

+1 kudos if it helped you
Senior Manager
Senior Manager
avatar
G
Joined: 21 Aug 2016
Posts: 281
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the  [#permalink]

Show Tags

New post 10 Dec 2016, 07:58
VeritasPrepKarishma wrote:
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


You can also use the number line method of mods to solve this question:

|12x−5|>|7−6x|

12|x - 5/12| > 6|x - 7/6|

2|x - 5/12| > |x - 14/12|

Twice of the distance from 5/12 should be more than distance from 14/12.

___________0_______5/12_________________14/12__________

We find the points where the two distances are equal.
The distance between 5/12 and 14/12 is 9/12 which gets divided into 1:2 i.e. the point where the distances will be equal will be 3/12 away from 5/12 i.e. at 8/12 = 2/3. At any point to the right of 2/3, twice the distance from 5/12 will be more than the distance from 14/12.

Another point will be 9/12 to the left of 5/12 i.e. at -4/12 = -1/3. At any left to the left of -1/3, twice the distance from 5/12 will be more than the distance from 14/12.

x < -1/3 OR x > 2/3

Then proceed as given above.



Hi VeritasPrepKarishma,

I could not understand how did you solve it. I could not comprehend the line
"Twice of the distance from 5/12 should be more than distance from 14/12." Please help !
Manager
Manager
User avatar
S
Joined: 28 Nov 2017
Posts: 145
Location: Uzbekistan
Premium Member
Re: If |12x−5|>|7−6x|, which of the following CANNOT be the  [#permalink]

Show Tags

New post 14 Dec 2017, 23:31
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


We have x<−1/3 OR x>2/3.
Therefore, x cannot be -1/3 and 2/3.
(-1/3)*(2/3)=-2/9. Thus, answer is C.
_________________

Kindest Regards!
Tulkin.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47918
If |12x−5|>|7−6x|, which of the following CANNOT be the  [#permalink]

Show Tags

New post 31 Dec 2017, 14:02
emmak wrote:
If |12x−5|>|7−6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17


VERITAS PREP OFFICIAL SOLUTION:

Solution: C. Algebraically, the inequalities give you four different possibilities:

12x – 5 > 7 – 6x (which works out cleanly to 18x > 12, meaning x > 2/3)
12x – 5 < -(7 – 6x)
-(12x – 5) < 7 – 6x
-(12x -5) > -(7 – 6x)

With the last three all involving negatives and inequalities, it can be helpful to simply find the inequality point and then test values on either side to determine whether it's greater than or less than:

12x – 5 < -(7 – 6x) works out to:

12x - 5 < 6x - 7

6x < -2

x < −1/3, but try a value like -1 (less than −1/3) and like 0 (greater than −1/3) to ensure the - vs. + of a tricky inequality with absolute values. -1 fits with the given information and 0 does not, so it should be clear that x < −1/3.

-(12x – 5) < 7 – 6x works out to 5 - 12x < 7 - 6x, which gives you -2 < 6x, and x > −1/3. This is why testing negative/positive is so important...the four "original" inequalities allow for really all sets of possible values other than −1/3 and 2/3, so some quick trial and error can help you determine which side of the inequalities are valid and which are not. Again, it should be clear from a quick plug-in of 0 and -1 that x < −1/3.

-(12x -5) > -(7 – 6x) works out to 5 - 12x > 6x - 7, which leads you to 12 > 18x, and x < 2/3. This confirms the "break point" of 2/3, so again a quick plug in of easy numbers on either side (0 and 1) will help you determine that x must be greater than 2/3.

So you know that x is either greater than 2/3 or less than −1/3. Certain answer choices, then, are easy to pick off: -12 could be -1*12. 17 could be 1*17. 4/9 could be -1*(-4/9) and -7/5 could be -1*7/5. But -2/9 cannot be done.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

If |12x−5|>|7−6x|, which of the following CANNOT be the &nbs [#permalink] 31 Dec 2017, 14:02

Go to page    1   2    Next  [ 23 posts ] 

Display posts from previous: Sort by

If |12x−5|>|7−6x|, which of the following CANNOT be the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.