It is currently 17 Nov 2017, 18:26

### 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

# How to do this ?

Author Message
VP
Joined: 30 Jun 2008
Posts: 1032

Kudos [?]: 727 [0], given: 1

How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 07:34
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

how do we solve for x in this expression $$|\frac{2}{(x-4)}| > 1$$

Please note the expression $$\frac{2}{(x-4)}$$ is fully in modulus
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Kudos [?]: 727 [0], given: 1

Current Student
Joined: 28 Dec 2004
Posts: 3345

Kudos [?]: 322 [1], given: 2

Location: New York City
Schools: Wharton'11 HBS'12
Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 08:09
1
KUDOS
amitdgr wrote:
how do we solve for x in this expression $$|\frac{2}{(x-4)}| > 1$$

Please note the expression $$\frac{2}{(x-4)}$$ is fully in modulus

so if x>4 then
2/(x-4)>1

2>(x-4)
6>x..or 4<X<6

if x<4

-2/(x-4)>1
2<-(x-4)
2<-x+4
-2<-x or 2>x

so you have the range 2<x<6

Kudos [?]: 322 [1], given: 2

VP
Joined: 30 Jun 2008
Posts: 1032

Kudos [?]: 727 [0], given: 1

Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 08:23
fresinha12 wrote:
amitdgr wrote:
how do we solve for x in this expression $$|\frac{2}{(x-4)}| > 1$$

Please note the expression $$\frac{2}{(x-4)}$$ is fully in modulus

so if x>4 then
2/(x-4)>1

2>(x-4)
6>x..or 4<X<6

if x<4

-2/(x-4)>1
2<-(x-4)
2<-x+4
-2<-x or 2>x

so you have the range 2<x<6

I get it now ... so $$|\frac{2}{(x-4)}|$$ means we consider the cases for $$|x-4|$$

Thanks....

So if the equation was something like $$|\frac{(x+2)}{(x-4)}| > 1$$

then we have to consider scenarios for both nr and dr ... right ?
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Kudos [?]: 727 [0], given: 1

SVP
Joined: 17 Jun 2008
Posts: 1534

Kudos [?]: 280 [1], given: 0

Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 11:32
1
KUDOS
amitdgr wrote:
So if the equation was something like $$|\frac{(x+2)}{(x-4)}| > 1$$

then we have to consider scenarios for both nr and dr ... right ?

In this case there are two points of consideration, x = -2 and x = 4.

Hence, the expression should be evaluated for
case 1: x<-2
case 2: -2<=x<4
Case 3: 4<=x.

Kudos [?]: 280 [1], given: 0

VP
Joined: 30 Jun 2008
Posts: 1032

Kudos [?]: 727 [0], given: 1

Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 11:39
scthakur wrote:
amitdgr wrote:
So if the equation was something like $$|\frac{(x+2)}{(x-4)}| > 1$$

then we have to consider scenarios for both nr and dr ... right ?

In this case there are two points of consideration, x = -2 and x = 4.

Hence, the expression should be evaluated for
case 1: x<-2
case 2: -2<=x<4
Case 3: 4<=x.

Thanks scthakur and fresinha +1 for you both
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Kudos [?]: 727 [0], given: 1

Manager
Joined: 15 Oct 2008
Posts: 103

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

Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 14:40
fresinha12 wrote:
amitdgr wrote:
how do we solve for x in this expression $$|\frac{2}{(x-4)}| > 1$$

Please note the expression $$\frac{2}{(x-4)}$$ is fully in modulus

so if x>4 then
2/(x-4)>1

2>(x-4)
6>x..or 4<X<6

if x<4

-2/(x-4)>1
2<-(x-4)
2<-x+4
-2<-x or 2>x

so you have the range 2<x<6

How can you come up with the range 2<x<6?
From (1), you have 4<x<6, right?
From (2), you have x<2
If you combine, how can you have the range of 2<x<6?

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

Manager
Joined: 05 Aug 2008
Posts: 91

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

Schools: McCombs Class of 2012
Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 15:27
I agree, shouldn't it be 4<x<6, if it's 2<x<6 then when we plug in 3 we get -2 which is not greater than 1, thus fails.

Am I missing something?

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

Manager
Joined: 15 Oct 2008
Posts: 103

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

Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 15:38
smarinov wrote:
I agree, shouldn't it be 4<x<6, if it's 2<x<6 then when we plug in 3 we get -2 which is not greater than 1, thus fails.

Am I missing something?

Actually, when you plug 3 in, you will get the result of 2, not -2 becuase of the sign of the absolute value.

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

Manager
Joined: 05 Aug 2008
Posts: 91

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

Schools: McCombs Class of 2012
Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 15:41
ah that's right, that makes sense now then 2 < x < 6.

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

Manager
Joined: 15 Oct 2008
Posts: 103

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

Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 15:53
fresinha12 wrote:
amitdgr wrote:
how do we solve for x in this expression $$|\frac{2}{(x-4)}| > 1$$

Please note the expression $$\frac{2}{(x-4)}$$ is fully in modulus

so if x>4 then
2/(x-4)>1

2>(x-4)
6>x..or 4<X<6

if x<4

-2/(x-4)>1
2<-(x-4)
2<-x+4
-2<-x or 2>x

so you have the range 2<x<6

Fresinha12,
I went over and over to your explanation and here is what i figured out.

1. I agree with your conclusion of 4<x<6.
2. when x<4, then:
2/(-x+4)>1
2>-x+4
x>2
so from (2), we have 2<x<4

Combine (1) and (2), we have 2<x<6 and x is not equal 4.
Am I right?

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

VP
Joined: 30 Jun 2008
Posts: 1032

Kudos [?]: 727 [0], given: 1

Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 20:21
I agree with nganle08, we ought to have x is not equal to 4 in the solution set, because at x=4 the expression becomes indefinite ...
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Kudos [?]: 727 [0], given: 1

Re: How to do this ?   [#permalink] 03 Nov 2008, 20:21
Display posts from previous: Sort by

# How to do this ?

Moderator: chetan2u

 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®.