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 500,000 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:

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

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

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).

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

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

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?

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.

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...