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

It is currently 01 May 2016, 17:13
GMAT Club Tests

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

When is |x-4| = 4-x?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 42

Kudos [?]: 456 [0], given: 355

GMAT ToolKit User
Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 19 Dec 2013, 06:54
Silly me, thats correct
Thanks
Cheers
J:)

Posted from my mobile device Image
Intern
Intern
avatar
Joined: 19 Jan 2014
Posts: 31
Followers: 0

Kudos [?]: 13 [0], given: 51

GMAT ToolKit User
Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 22 Jan 2014, 00:30
Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how do i prove this using algebra?


Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) to be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.


This might sound silly but i just started preparing for GMAT, and I have a question. Why is it then in some cases we take x<0 or x>0 and in this problem we have x<=0 and x>=0

Thank you.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5639

Kudos [?]: 68391 [0], given: 9797

Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 23 Jan 2014, 03:50
Expert's post
bytatia wrote:
Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how do i prove this using algebra?


Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) to be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.


This might sound silly but i just started preparing for GMAT, and I have a question. Why is it then in some cases we take x<0 or x>0 and in this problem we have x<=0 and x>=0

Thank you.


Well, it all depends on the problem at hand. For this problem, we need = sign because x=4 also satisfies |x-4| = 4-x.

Below posts might help to brush up fundamentals on modulus:
Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
avatar
Joined: 04 Oct 2013
Posts: 162
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Followers: 3

Kudos [?]: 90 [0], given: 54

GMAT ToolKit User Premium Member Reviews Badge
Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 24 Jan 2014, 01:03
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0


\(|x-4| = 4-x\)

Or, \(\frac{|x-4|}{x-4}=-1\)

=> \((x-4) < 0\) or \(x = 0\)

Or, \(x <= 4\)

Answer: (D)
1 KUDOS received
Director
Director
User avatar
Joined: 23 Jan 2013
Posts: 506
Schools: Cambridge'16
Followers: 2

Kudos [?]: 49 [1] , given: 37

Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 29 Nov 2014, 00:23
1
This post received
KUDOS
Question asks when distance between x and 4 expressed as |x-4| is equal to 4-x

until x is left to 4 or equal to 4 we get the equation right so |x-4|=4-x

Number line is

----------x--------------------4------------->


if x goes righter we get

-----------4-------------x------------------>

|x-4| will continue to be positive, but 4-x will be negative


Algebraically:

x-4=4-x
2x=8,
x=4

-(x-4)=4-x
-x+4=4-x
0=0, so infinitely many solutions when x<4


x<=4


D
Manager
Manager
avatar
Joined: 13 Dec 2013
Posts: 58
GPA: 2.71
Followers: 0

Kudos [?]: 3 [0], given: 21

GMAT ToolKit User
When is |x-4| = 4-x? [#permalink]

Show Tags

New post 10 Dec 2014, 00:29
Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how do i prove this using algebra?


Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) to be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.


I am still new to modulus so please do bare with me if I sound stupid.

This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read.
So according to the book, I need to take into account when the modulus is positive and negative when solving

\(x-4>0, x>4\)

x-4=4-x
x=4
(not sure if this value has to be rejected or not. Please help)

and when \(x+4<0, x<=4\)
-(x+4)=4-x
-x-4=4-x
Just lost here.

My question is why do we chose X<=4 why do we chose one condition over the other.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5639

Kudos [?]: 68391 [0], given: 9797

When is |x-4| = 4-x? [#permalink]

Show Tags

New post 10 Dec 2014, 04:34
Expert's post
saadis87 wrote:
Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how do i prove this using algebra?


Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) to be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.


I am still new to modulus so please do bare with me if I sound stupid.

This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read.
So according to the book, I need to take into account when the modulus is positive and negative when solving

\(x-4>0, x>4\)

x-4=4-x
x=4
(not sure if this value has to be rejected or not. Please help)

and when \(x+4<0, x<=4\)
-(x+4)=4-x
-x-4=4-x
Just lost here.

My question is why do we chose X<=4 why do we chose one condition over the other.


For the second case, when x - 4 < 0 (x < 4), |x - 4| becomes -(x - 4), so we'd have -(x - 4) = 4 - x, which gives 4 = 4. Since 4 = 4 is true, then it means that for x < -4, |x-4| = 4-x holds true.

Combining x = 4 from the first case and x < 4 from the second, we'll have x <= 4.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
avatar
Joined: 13 Dec 2013
Posts: 58
GPA: 2.71
Followers: 0

Kudos [?]: 3 [0], given: 21

GMAT ToolKit User
Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 10 Dec 2014, 05:28
Bunuel wrote:
saadis87 wrote:

I am still new to modulus so please do bare with me if I sound stupid.

This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read.
So according to the book, I need to take into account when the modulus is positive and negative when solving

\(x-4>0, x>4\)

x-4=4-x
x=4
(not sure if this value has to be rejected or not. Please help)

and when \(x+4<0, x<=4\)
-(x+4)=4-x
-x-4=4-x
Just lost here.

My question is why do we chose X<=4 why do we chose one condition over the other.


For the second case, when x + 4 < 0 (x < -4), |x - 4| becomes -(x - 4), so we'd have -(x - 4) = 4 - x, which gives 4 = 4. Since 4 = 4 is true, then it means that for x < -4, |x-4| = 4-x holds true.

Combining x = 4 from the first case and x < -4 from the second, we'll have x <= -4.

Hope it's clear.



Makes a lot more sense, Thankyou :)
Intern
Intern
avatar
Joined: 27 Jan 2015
Posts: 7
Followers: 0

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

Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 24 Mar 2015, 04:12
The equation holds true for every x value < 0. IMO answer choice E satisfies the equation as well. How can we cross out E?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5639

Kudos [?]: 68391 [0], given: 9797

Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 24 Mar 2015, 04:18
Expert's post
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9248
Followers: 454

Kudos [?]: 115 [0], given: 0

Premium Member
Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 28 Mar 2016, 05:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 02 Aug 2009
Posts: 3175
Followers: 171

Kudos [?]: 1666 [0], given: 75

Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 15 Apr 2016, 20:59
Expert's post
Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how do i prove this using algebra?


Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) to be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.


Hi Bunuel,
I feel the way Q is asked, even x= 4, x=0 or x<0 may fit in..

the Q asks " When is |x-4| = 4-x?
ofcourse when x=4, ans is yes..
when x= 0... ans is yes..
yes x<=4 gives the entire range, BUT the Q does not ask that..


Had the Q been.
when all is |x-4| = 4-x?
for which all values is |x-4| = 4-x? OR
What is the range of x for |x-4| = 4-x?


Would in ACTUAL GMAT, the wordings of this kind MEAN what we are inferring here?
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5639

Kudos [?]: 68391 [0], given: 9797

Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 16 Apr 2016, 10:14
Expert's post
chetan2u wrote:
Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how do i prove this using algebra?


Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) to be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.


Hi Bunuel,
I feel the way Q is asked, even x= 4, x=0 or x<0 may fit in..

the Q asks " When is |x-4| = 4-x?
ofcourse when x=4, ans is yes..
when x= 0... ans is yes..
yes x<=4 gives the entire range, BUT the Q does not ask that..


Had the Q been.
when all is |x-4| = 4-x?
for which all values is |x-4| = 4-x? OR
What is the range of x for |x-4| = 4-x?


Would in ACTUAL GMAT, the wordings of this kind MEAN what we are inferring here?


You are right the wording of the question is poor.
_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
avatar
Joined: 10 Apr 2016
Posts: 50
Concentration: Strategy, Entrepreneurship
GMAT 1: 520 Q26 V53
GPA: 3.01
Followers: 0

Kudos [?]: 1 [0], given: 7

Re: When is |x-4| = 4-x? [#permalink]

Show Tags

New post 17 Apr 2016, 04:54
For those struggling to understand how this works with the equal / lesser signs

X=4
|x-4|=4-x --> 4-4=4-4
X=3
|x-4|=4-x --> |-1|=1
X=2
|2-4|=4-2 --> |-2|=2
X=1
X=0
And so on :).
_________________

Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day.

Re: When is |x-4| = 4-x?   [#permalink] 17 Apr 2016, 04:54

Go to page   Previous    1   2   [ 34 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If 4^x + 4^(-x) = 2, which of the following is the value of x? Bunuel 2 20 Mar 2016, 23:30
11 Experts publish their posts in the topic 4^x + 4 ^-x = 2 What is the value of X nimc2012 18 07 Feb 2012, 09:56
14 Experts publish their posts in the topic If the 4 x 4 grid in the attached picture is filled with the enigma123 7 31 Jan 2012, 19:25
when is absolute(x-4) equal to 4-x ? sher676 3 26 Apr 2010, 05:45
21 What is the maximum number of 4x4x4 cubes that can fit in a uvs_mba 20 03 Nov 2006, 23:01
Display posts from previous: Sort by

When is |x-4| = 4-x?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.