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]
21 Jan 2014, 23:30

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

Re: When is |x-4| = 4-x? [#permalink]
23 Jan 2014, 02:50

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:

When is |x-4| = 4-x? [#permalink]
09 Dec 2014, 23:29

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.

When is |x-4| = 4-x? [#permalink]
10 Dec 2014, 03:34

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.

Re: When is |x-4| = 4-x? [#permalink]
10 Dec 2014, 04:28

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.

My last interview took place at the Johnson School of Management at Cornell University. Since it was my final interview, I had my answers to the general interview questions...