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:

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.

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???
_________________

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]

Show Tags

03 Jan 2012, 11:31

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

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.

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.
_________________

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.

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.

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.

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.

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.
_________________

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Term 1 has begun. If you're confused, wondering what my post on the last 2 official weeks was, that was pre-term. What that means is that the school...