If |12x−5|>|7−6x|, which of the following CANNOT be the : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 20 Jan 2017, 20:57

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 120
Followers: 1

Kudos [?]: 849 [6] , given: 17

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

### Show Tags

11 Jun 2013, 03:17
6
KUDOS
56
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

35% (04:10) correct 65% (02:36) wrong based on 1044 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
[Reveal] Spoiler: OA

_________________

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

Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93289 [12] , given: 10555

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

11 Jun 2013, 04:19
12
KUDOS
Expert's post
19
This post was
BOOKMARKED
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.

_________________
Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 160 [0], given: 134

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

12 Jun 2013, 19:40
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.

Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93289 [1] , given: 10555

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

12 Jun 2013, 22:08
1
KUDOS
Expert's post
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.

We CAN square an inequality if we know that the sides are non-negative, which is the case here.
_________________
Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 160 [0], given: 134

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

13 Jun 2013, 06:57
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
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93289 [0], given: 10555

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

13 Jun 2013, 07:03
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

Hope it helps.
_________________
Intern
Joined: 22 May 2013
Posts: 49
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 16 [1] , given: 10

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

13 Jun 2013, 07:54
1
KUDOS
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.

Hi Bunuel,
Please correct me if i am wrong here, but dont you mean
$$x=-1<-\frac{1}{3}$$ and $$x=-17<\frac{-1}{3}$$ are possible values of x --> the product = 17.
For the last point??

Since -1 * 17 would be -17??
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93289 [0], given: 10555

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

13 Jun 2013, 08:10
Expert's post
1
This post was
BOOKMARKED
kpali 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 $$x=17>\frac{2}{3}$$ are possible values of x --> the product = 17.

Hi Bunuel,
Please correct me if i am wrong here, but dont you mean
$$x=-1<-\frac{1}{3}$$ and $$x=-17<\frac{-1}{3}$$ are possible values of x --> the product = 17.
For the last point??

Since -1 * 17 would be -17??

Sure. Typo edited. Thank you.
_________________
Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 160 [0], given: 134

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

10 Jul 2013, 09:26
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
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 160 [3] , given: 134

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

15 Jul 2013, 14:16
3
KUDOS
3
This post was
BOOKMARKED
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
Joined: 03 Aug 2012
Posts: 916
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 23

Kudos [?]: 692 [0], given: 322

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

23 Jul 2013, 21:08
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 !!!

Regards,
TGC !
Attachments

query.JPG [ 13.53 KiB | Viewed 12278 times ]

_________________

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

Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93289 [1] , given: 10555

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

23 Jul 2013, 21:42
1
KUDOS
Expert's post
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 !!!

Regards,
TGC !

The graphs drawn are not correct. The proper drawing is below:
Attachment:

MSP2441f260916666dabe40000498a5d50ib182823.gif [ 9.23 KiB | Viewed 12765 times ]
Hope it helps.
_________________
Director
Joined: 03 Aug 2012
Posts: 916
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 23

Kudos [?]: 692 [0], given: 322

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

23 Jul 2013, 23:20
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 !!!

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)

Rgds,
TGC !

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

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

Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93289 [0], given: 10555

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

24 Jul 2013, 00:52
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 !!!

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)

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:

x<-1/3 and x>2/3.
_________________
Director
Joined: 03 Aug 2012
Posts: 916
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 23

Kudos [?]: 692 [0], given: 322

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

24 Jul 2013, 00:59
Bunuel wrote:
I don't understand your question... As I said the graph of |12x−5|>|7−6x| is:

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
_____________________________________________________________________________

Manager
Joined: 09 Nov 2013
Posts: 92
Followers: 1

Kudos [?]: 10 [0], given: 30

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

27 Mar 2014, 11:33
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.

Dear Bunuel

Pl enlighten us in what all cases we can square the modulus

Thanks
sid
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2137

Kudos [?]: 13673 [2] , given: 222

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the [#permalink]

### Show Tags

27 Mar 2014, 21:15
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
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
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Joined: 13 Aug 2012
Posts: 118
Followers: 0

Kudos [?]: 57 [3] , given: 118

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the [#permalink]

### Show Tags

02 Apr 2014, 08:17
3
KUDOS
2
This post was
BOOKMARKED
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.
Manager
Joined: 10 Mar 2014
Posts: 236
Followers: 1

Kudos [?]: 81 [0], given: 13

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the prod [#permalink]

### Show Tags

23 Apr 2014, 09:02
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.

Hi Bunnel,

I have a doubt. how you are getting 7/5, 4/9, 1/3 etc ion above post.

Thanks
Manager
Joined: 17 Nov 2013
Posts: 97
Concentration: Strategy, Healthcare
GMAT 1: 710 Q49 V38
GPA: 3.34
Followers: 5

Kudos [?]: 35 [0], given: 47

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the [#permalink]

### Show Tags

23 Apr 2014, 09:10
thanks Mahendru. the other explanations are all so weird! No offence*
_________________

Re: If |12x−5|>|7−6x|, which of the following CANNOT be the   [#permalink] 23 Apr 2014, 09:10

Go to page    1   2    Next  [ 27 posts ]

Similar topics Replies Last post
Similar
Topics:
4 Which of the following cannot be the square of an integer 3 05 Sep 2014, 20:47
36 If x is a positive integer, which of the following CANNOT be 14 11 Feb 2013, 10:09
5 If x and y are prime numbers, which of the following CANNOT 8 06 Feb 2012, 03:14
35 Which of the following CANNOT be the greatest common divisor 15 08 Feb 2011, 00:43
2 If n is an integer, which of the following CANNOT be 4 19 Jun 2010, 01:31
Display posts from previous: Sort by