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Re: Root. Modulus question [#permalink]
23 Jan 2011, 07:51

Expert's post

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.

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