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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: When is |x-4| = 4-x? [#permalink]
03 May 2012, 11:04

15

This post received KUDOS

Expert's post

8

This post was BOOKMARKED

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 \(x-4\leq{0}\) --> \(x\leq{4}\).

Re: When is |x-4| = 4-x? [#permalink]
28 Oct 2012, 01:56

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 \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). 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 am trying to understand theese two properties, but how is it possible to have |X|=-X, in order that absolute value has to be always positive? Could you please provide me an explaination in more details? Thanks in advance

Re: When is |x-4| = 4-x? [#permalink]
29 Oct 2012, 01:56

1

This post received KUDOS

Expert's post

mario1987 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 \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). 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 am trying to understand theese two properties, but how is it possible to have |X|=-X, in order that absolute value has to be always positive? Could you please provide me an explaination in more details? Thanks in advance

When \(x\leq{0}\), for example when \(x=-5\), then \(|-5|=5=-(-5)\) so \(|x|=-x\) (|negative |=-(negative)=positive).

Re: When is |x-4| = 4-x? [#permalink]
14 Mar 2013, 12:19

2

This post received KUDOS

Absolute value of any number or expression must be positive. If (x-4) is positive then |x-4| is also positive What if x-4 is negative? Since the absolute value must be positive, |x-4| would be equal to -(x-4)=4-x. Right?

We know that x-4 would have to be negative for the equation in question to be true. This would imply that x would have to be a small positive number smaller than 4 or a negative number. You can take examples to test that. x=-14 (x-4)=-ve x=1, x-4=-3 -ve x=4, implies x-4=0 and 4-x=0. Thus, the equation is satisfied.

Hence, d is the answer.

Coming to your question, if a question deals with equality it also indirectly deals with inequality. If you say the equation is satisfied when x=0,x=4,x=-5 and so on, it also implies that the equation is true for all values of x less than or equal to 4.

An equation exists only at certain points. We have to find those points and if those points range over a large space, the easiest way would be express it as inequality.

Note: An equality question can have answers which might be expressed as inequalities. There is nothing wrong with it.

Hope it helps! Let me know if I can help you any further.

dhlee922 wrote:

how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand

Re: When is |x-4| = 4-x? [#permalink]
14 Mar 2013, 16:34

thanks Kris. that does help. i guess my follow up question would be, is there a way to solve it algebraically rather than plugging in numbers?

Kris01 wrote:

Absolute value of any number or expression must be positive. If (x-4) is positive then |x-4| is also positive What if x-4 is negative? Since the absolute value must be positive, |x-4| would be equal to -(x-4)=4-x. Right?

We know that x-4 would have to be negative for the equation in question to be true. This would imply that x would have to be a small positive number smaller than 4 or a negative number. You can take examples to test that. x=-14 (x-4)=-ve x=1, x-4=-3 -ve x=4, implies x-4=0 and 4-x=0. Thus, the equation is satisfied.

Hence, d is the answer.

Coming to your question, if a question deals with equality it also indirectly deals with inequality. If you say the equation is satisfied when x=0,x=4,x=-5 and so on, it also implies that the equation is true for all values of x less than or equal to 4.

An equation exists only at certain points. We have to find those points and if those points range over a large space, the easiest way would be express it as inequality.

Note: An equality question can have answers which might be expressed as inequalities. There is nothing wrong with it.

Hope it helps! Let me know if I can help you any further.

dhlee922 wrote:

how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand

More:"All I wish someone had told me about GMAT beforehand" There are many things you want to know before doing the GMAT exam (how is exam day, what to expect, how to think, to do's...), and you have them in this blog, in a simple way

Re: When is |x-4| = 4-x? [#permalink]
15 Mar 2013, 10:26

As Johnwesley said, for |x-4|=4-x, s-4 should be negative or equal to 0.

i.e. x-4<=0 Hence, x<=4

[quote="dhlee922"]thanks Kris. that does help. i guess my follow up question would be, is there a way to solve it algebraically rather than plugging in numbers? _________________

Re: When is |x-4| = 4-x? [#permalink]
09 Aug 2013, 21:24

I solved it in this way.

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

Choice A: X=4, it is true but X cannot be always 4 Choice B: X=0, it is also true, but X cannot be always 0 Choice C: X>4, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2 Choice D: X<=4, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is D.

It took only 1min to solve this problem with above method.

: Social ventures, both non-profits and for-profits, seek to better the world in such industries as education, microfinance, workforce development, public health and community development, among others. Organizations that...

Essay B for Stanford GSB will essentially ask you to explain why you’re doing what you’re doing. Namely, the essay wants to know, A) why you’re seeking...

Over the last week my Facebook wall has been flooded with most positive, almost euphoric emotions: “End of a fantastic school year”, “What a life-changing year it’s been”, “My...