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

 It is currently 19 Jun 2018, 20:52

### 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 ?

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
VP
Joined: 30 Jun 2008
Posts: 1008
How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 07:34
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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

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

Current Student
Joined: 28 Dec 2004
Posts: 3292
Location: New York City
Schools: Wharton'11 HBS'12
Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 08:09
1
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
VP
Joined: 30 Jun 2008
Posts: 1008
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

VP
Joined: 17 Jun 2008
Posts: 1479
Re: How to do this ? [#permalink]

### Show Tags

03 Nov 2008, 11:32
1
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.
VP
Joined: 30 Jun 2008
Posts: 1008
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

Manager
Joined: 15 Oct 2008
Posts: 102
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?
Manager
Joined: 05 Aug 2008
Posts: 88
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?
Manager
Joined: 15 Oct 2008
Posts: 102
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.
Manager
Joined: 05 Aug 2008
Posts: 88
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.
Manager
Joined: 15 Oct 2008
Posts: 102
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?
VP
Joined: 30 Jun 2008
Posts: 1008
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 ...

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

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

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

# How to do this ?

 post reply Question banks Downloads My Bookmarks Reviews Important topics

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®.