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:

Which of the following represents all the possible values of x that are solutions to the equation \(3x=|x^2 -10|\)?

A. -5, -2, and 0 B. -5, -2, 2, and 5 C. -5 and 2 D. -2 and 5 E. 2 and 5

Could someone explain how to get to the solution? Thanks!

\(3x=|x^2 -10|\).

First of all: as RHS (right hand side) is absolute value, which is never negative (absolute value \(\geq{0}\)), LHS also must be \(\geq{0}\) --> \(3x\geq{0}\) --> \(x\geq{0}\).

\(3x=x^2-10\) --> \(x=-2\) or \(x=5\). First values is not valid as \(x\geq{0}\).

\(3x=-x^2+10\) --> \(x=-5\) or \(x=2\). First values is not valid as \(x\geq{0}\).

So there are only two valid solutions: \(x=5\) and \(x=2\).

But why didn't we check for 3x = -(x^2)-10 ???? Can someone explain???

Please read the solution.

We checked for two cases:

1. \(3x=x^2-10\) --> \(x=-2\) or \(x=5\). First values is not valid as \(x\geq{0}\). and 2. \(3x=-(x^2-10)\) --> \(x=-5\) or \(x=2\). First values is not valid as \(x\geq{0}\).

What case does \(3x = -(x^2)-10\) represent? _________________

Re: Which of the following represents all the possible values of [#permalink]

Show Tags

06 Jul 2013, 12:14

Expert's post

jjack0310 wrote:

I squared both the LHS and RHS. Get totally weird answer. (Roots come out to be -5 and 5/2)

What is wrong with that approach? Clearly something is because those two roots are not options

Probably math:

\((3x)^2=(x^2-10)^2\) --> \(x^4-29 x^2+100 = 0\) --> solve for \(x^2\): \(x^2=4\) or \(x^2=25\) --> \(x=2\) or \(x=5\) (discarding negative roots \(x=-2\) or \(x=-5\), since from 3x=|x^2 -10| it follows that x cannot be negative).

Re: Which of the following represents all the possible values of [#permalink]

Show Tags

06 Jul 2013, 18:19

Bunuel wrote:

jjack0310 wrote:

I squared both the LHS and RHS. Get totally weird answer. (Roots come out to be -5 and 5/2)

What is wrong with that approach? Clearly something is because those two roots are not options

Probably math:

\((3x)^2=(x^2-10)^2\) --> \(x^4-29 x^2+100 = 0\) --> solve for \(x^2\): \(x^2=4\) or \(x^2=25\) --> \(x=2\) or \(x=5\) (discarding negative roots \(x=-2\) or \(x=-5\), since from 3x=|x^2 -10| it follows that x cannot be negative).

Re: Which of the following represents all the possible values of [#permalink]

Show Tags

08 Jul 2013, 20:42

Which of the following represents all the possible values of x that are solutions to the equation 3x=|x^2 -10| ?

x>3.33: Positive: 3x=x^2-10 -x^2+3x+10=0 x^2-3x-10=0 (x-5)*(x+2)=0 x=5, x=-2 x=5 falls in the range of x>3.33. X=2 does not.

x<3.33 Negative: 3x=-(x^2-10) 3x=-x^2+10 x^2+3x-10=0 (x+5)*(x-2)=0 x=-5, x=2 Both -5 and 2 fall within the range of x<3.33

Solutions = -5,2,5

In other words, in a similar problem I would check the results of the positive and negative case and see if they fell within the range I was testing. For example, for x>3.33, we get two solutions (x=5, x=-2) but only x=5 is valid. Why is that? I see that you are using 3x (and therefore, x) as the metric for what values are valid and what ones arent) but it doesn't seem like thats the case in other problems)

Last edited by WholeLottaLove on 09 Jul 2013, 15:52, edited 2 times in total.

Re: Which of the following represents all the possible values of [#permalink]

Show Tags

08 Jul 2013, 21:23

1

This post received KUDOS

I think no need to calculate at all... We are solving for LHS = RHS and we know RHS can not be negative (x^2-10) can be negative but |x^2-10| is always positive. So the RHS should also be positive for equality. RHS>0 3x>0 HENCE...X>0 and only option E satisfies

Re: Which of the following represents all the possible values of [#permalink]

Show Tags

10 Jul 2013, 09:09

2

This post received KUDOS

1

This post was BOOKMARKED

WholeLottaLove wrote:

Which of the following represents all the possible values of x that are solutions to the equation 3x=|x^2 -10| ?

x>3.33: Positive: 3x=x^2-10 -x^2+3x+10=0 x^2-3x-10=0 (x-5)*(x+2)=0 x=5, x=-2 x=5 falls in the range of x>3.33. X=2 does not.

x<3.33 Negative: 3x=-(x^2-10) 3x=-x^2+10 x^2+3x-10=0 (x+5)*(x-2)=0 x=-5, x=2 Both -5 and 2 fall within the range of x<3.33

Solutions = -5,2,5

In other words, in a similar problem I would check the results of the positive and negative case and see if they fell within the range I was testing. For example, for x>3.33, we get two solutions (x=5, x=-2) but only x=5 is valid. Why is that? I see that you are using 3x (and therefore, x) as the metric for what values are valid and what ones arent) but it doesn't seem like thats the case in other problems)

Your intervals are not correct:

\(3x=|x^2 -10|\), \(x^2 -10>0\) if \(x>\sqrt{10}\) and if \(x<-\sqrt{10}\).

So if \(x>\sqrt{10}\) or \(x<-\sqrt{10}\) => positive \(3x=x^2-10\) that has two solutions: \(x=5\) (possible) and \(x=-2\) not possible because it's outside the range we are considering.

If \(-\sqrt{10}<x<\sqrt{10}\) => negative \(3x=-x^2+10\) that has two solutions: \(x=2\) (possible) and \(x=-5\) not possible because it's outside the range we are considering.

So overall x can be 2 or 5.

"Why is that? " you anlyze parts of the function each time, so you have to pay attention to which ranges you are considering. If a given solution falls within that range, then it's solution, but it it falls out, it's not valid.

Hope it clarifies _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Which of the following represents all the possible values of [#permalink]

Show Tags

10 Jul 2013, 09:25

Ahhh...I wasn't considering that for x^2, the range might be greater than x or less than negative x. I am used to solving for, say, |x-3| which is a bit more straightforward. Thanks a lot for the explanation it cleared everything up!

Zarrolou wrote:

WholeLottaLove wrote:

Which of the following represents all the possible values of x that are solutions to the equation 3x=|x^2 -10| ?

x>3.33: Positive: 3x=x^2-10 -x^2+3x+10=0 x^2-3x-10=0 (x-5)*(x+2)=0 x=5, x=-2 x=5 falls in the range of x>3.33. X=2 does not.

x<3.33 Negative: 3x=-(x^2-10) 3x=-x^2+10 x^2+3x-10=0 (x+5)*(x-2)=0 x=-5, x=2 Both -5 and 2 fall within the range of x<3.33

Solutions = -5,2,5

In other words, in a similar problem I would check the results of the positive and negative case and see if they fell within the range I was testing. For example, for x>3.33, we get two solutions (x=5, x=-2) but only x=5 is valid. Why is that? I see that you are using 3x (and therefore, x) as the metric for what values are valid and what ones arent) but it doesn't seem like thats the case in other problems)

Your intervals are not correct:

\(3x=|x^2 -10|\), \(x^2 -10>0\) if \(x>\sqrt{10}\) and if \(x<-\sqrt{10}\).

So if \(x>\sqrt{10}\) or \(x<-\sqrt{10}\) => positive \(3x=x^2-10\) that has two solutions: \(x=5\) (possible) and \(x=-2\) not possible because it's outside the range we are considering.

If \(-\sqrt{10}<x<\sqrt{10}\) => negative \(3x=-x^2+10\) that has two solutions: \(x=2\) (possible) and \(x=-5\) not possible because it's outside the range we are considering.

So overall x can be 2 or 5.

"Why is that? " you anlyze parts of the function each time, so you have to pay attention to which ranges you are considering. If a given solution falls within that range, then it's solution, but it it falls out, it's not valid.

Re: Which of the following represents all the possible values of [#permalink]

Show Tags

19 Jun 2014, 02:43

1

This post received KUDOS

Bunuel wrote:

perseverant wrote:

Which of the following represents all the possible values of x that are solutions to the equation \(3x=|x^2 -10|\)?

A. -5, -2, and 0 B. -5, -2, 2, and 5 C. -5 and 2 D. -2 and 5 E. 2 and 5

Could someone explain how to get to the solution? Thanks!

\(3x=|x^2 -10|\).

First of all: as RHS (right hand side) is absolute value, which is never negative (absolute value \(\geq{0}\)), LHS also must be \(\geq{0}\) --> \(3x\geq{0}\) --> \(x\geq{0}\).

\(3x=x^2-10\) --> \(x=-2\) or \(x=5\). First values is not valid as \(x\geq{0}\).

\(3x=-x^2+10\) --> \(x=-5\) or \(x=2\). First values is not valid as \(x\geq{0}\).

So there are only two valid solutions: \(x=5\) and \(x=2\).

Answer: E.

RHS = an absolute value then 3x>=0 => x>=0 => Only E is appropriate

Re: Which of the following represents all the possible values of [#permalink]

Show Tags

18 Jul 2015, 02:46

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. _________________

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

They say you get better at doing something by doing it. then doing it again ... and again ... and again, and you keep doing it until one day you look...

I barely remember taking decent rest in the last 60 hours. It’s been relentless with submissions, birthday celebration, exams, vacating the flat, meeting people before leaving and of...