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:
Re: Root. Modulus question [#permalink]
23 Jan 2011, 07:51
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Is \(x = \sqrt{x^2}\)?
Note that: \(\sqrt{x^2}=|x|\), so the question basically asks whether \(x=|x|\) or, which is the same, whether \(x\geq{0}\) or whether \(x\) is non-negative number.
(1) x = even --> not sufficient as x can be negative as well as a non-negative even number. (2) 13<x<17 --> x is non-negative. Sufficient.
Re: Root. Modulus question [#permalink]
23 Jan 2011, 09:21
what i understand abt properties of sqr. root that Sqrt(-ve) is not defined i.e sqrt(x) => x has to be positive stmt 2 says x is positive Am i correct??? _________________
Re: Root. Modulus question [#permalink]
23 Jan 2011, 09:38
Expert's post
ITMRAHUL wrote:
what i understand abt properties of sqr. root that Sqrt(-ve) is not defined i.e sqrt(x) => x has to be positive stmt 2 says x is positive Am i correct???
Even roots (such as square root) from negative numbers are undefined on the GMAT: \(\sqrt[{even}]{negative}=undefined\), for example \(\sqrt{-25}=undefined\) (as GMAT is dealing only with Real Numbers);
Also square root function can not give negative result: \(\sqrt{some \ expression}\geq{0}\);
But in our original question we don't have \(\sqrt{x}\) we have \(\sqrt{x^2}\) and you should know that \(\sqrt{x^2}=|x|\), so the question basically asks whether \(x=|x|\) or, which is the same, whether \(x\geq{0}\) or whether \(x\) is non-negative number.
(1) x = even --> not sufficient as x can be negative as well as non-negative even number. (2) 13<x<17 --> x is non-negative. Sufficient.
Re: Is x = \sqrt{x^2} if (1) x = even (2) 13 < x < 17 [#permalink]
03 Jan 2012, 10:31
1. Insufficient since x can be negative 2. Sufficient, since here x is positive - irrespective of even or odd.
+1 for B _________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min
Re: Root. Modulus question [#permalink]
19 Jun 2013, 10:35
x = \sqrt{x^2}
So basically, what this says is the following:
x = |x|
So, x = x or x = -x
Firstly, this means that, for example:
x=5 or x=-5
Correct?
I guess where I get tripped up is here:
Let's say x=14 and x=|x| so x=x or x=-x
so
x=14 OR x=-14
With #2 we are told that x is positive and the stem tells us that x=|x|. But isn't that unnecessary? doesn't x=|x| imply that x is positive anyways? Or, if this makes any sense, if x=x or x=-x then couldn't 14=-x?
Bunuel wrote:
Is \(x = \sqrt{x^2}\)?
Note that: \(\sqrt{x^2}=|x|\), so the question basically asks whether \(x=|x|\) or, which is the same, whether \(x\geq{0}\) or whether \(x\) is non-negative number.
(1) x = even --> not sufficient as x can be negative as well as a non-negative even number. (2) 13<x<17 --> x is non-negative. Sufficient.
Re: Root. Modulus question [#permalink]
19 Jun 2013, 20:47
1
This post received KUDOS
Expert's post
WholeLottaLove wrote:
x = \sqrt{x^2}
So basically, what this says is the following:
x = |x|
So, x = x or x = -x
Firstly, this means that, for example:
x=5 or x=-5
Correct?
I guess where I get tripped up is here:
Let's say x=14 and x=|x| so x=x or x=-x
so
x=14 OR x=-14
With #2 we are told that x is positive and the stem tells us that x=|x|. But isn't that unnecessary? doesn't x=|x| imply that x is positive anyways? Or, if this makes any sense, if x=x or x=-x then couldn't 14=-x?
I think you tripped up on what is given and what is to be found.
You are asked: Is \(x = \sqrt{x^2}\)? You are asked: Is x equal to |x|? The question doesn't tell us this. It wants us to answer whether it is true.
When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone. _________________
Re: Root. Modulus question [#permalink]
20 Jun 2013, 07:16
If x=|x| then don't we already know that x is positive? If that's the case then isn't #1) x=even irrelevant? Doesn't x HAVE to be positive?
VeritasPrepKarishma wrote:
WholeLottaLove wrote:
x = \sqrt{x^2}
So basically, what this says is the following:
x = |x|
So, x = x or x = -x
Firstly, this means that, for example:
x=5 or x=-5
Correct?
I guess where I get tripped up is here:
Let's say x=14 and x=|x| so x=x or x=-x
so
x=14 OR x=-14
With #2 we are told that x is positive and the stem tells us that x=|x|. But isn't that unnecessary? doesn't x=|x| imply that x is positive anyways? Or, if this makes any sense, if x=x or x=-x then couldn't 14=-x?
I think you tripped up on what is given and what is to be found.
You are asked: Is \(x = \sqrt{x^2}\)? You are asked: Is x equal to |x|? The question doesn't tell us this. It wants us to answer whether it is true.
When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.
Re: Root. Modulus question [#permalink]
20 Jun 2013, 09:46
Expert's post
WholeLottaLove wrote:
If x=|x| then don't we already know that x is positive? If that's the case then isn't #1) x=even irrelevant? Doesn't x HAVE to be positive?
Have you read Karishma's response?
VeritasPrepKarishma wrote:
I think you tripped up on what is given and what is to be found.
You are asked: Is \(x = \sqrt{x^2}\)? You are asked: Is x equal to |x|? The question doesn't tell us this. It wants us to answer whether it is true.
When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.
Re: Root. Modulus question [#permalink]
20 Jun 2013, 10:04
Haha! Yes I did read it.
I understand that the question is asking IS x=√x^2 (i.e. x=|x|) but x HAS to be positive because x=|x|. That's what I don't get. I can't help but think both 1+2 are irrelevant because x HAS to be positive.
x=|x| x=positive int.
Sorry for my mental stubbornness!
Bunuel wrote:
WholeLottaLove wrote:
If x=|x| then don't we already know that x is positive? If that's the case then isn't #1) x=even irrelevant? Doesn't x HAVE to be positive?
Have you read Karishma's response?
VeritasPrepKarishma wrote:
I think you tripped up on what is given and what is to be found.
You are asked: Is \(x = \sqrt{x^2}\)? You are asked: Is x equal to |x|? The question doesn't tell us this. It wants us to answer whether it is true.
When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.
Re: Root. Modulus question [#permalink]
20 Jun 2013, 10:40
Expert's post
WholeLottaLove wrote:
Haha! Yes I did read it.
I understand that the question is asking IS x=√x^2 (i.e. x=|x|) but x HAS to be positive because x=|x|. That's what I don't get. I can't help but think both 1+2 are irrelevant because x HAS to be positive.
x=|x| x=positive int.
Sorry for my mental stubbornness!
The question asks: is \(x\geq{0}\)? So, the question asks whether x is more than or equal to zero.
(1) says that x IS even. Can we answer the question based on this statement? NO, because x is even does not imply that it's more than or equal to zero. For example, if x=-2, then the answer to the question is NO but if x=2, then the answer to the question is YES. We have two different answers, which means that this statement is NOT sufficient.
(2) says that 13 < x < 17, so x is some number from 13 to 17, not inclusive. Can we answer the question based on this statement? YES, because this statement implies that x IS indeed positive. Sufficient.
Therefore, the answer is B: statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Re: Is x=square root of x^2? [#permalink]
09 Sep 2015, 10:58
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. _________________
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...