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Is x=square root of x^2?
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Updated on: 04 Dec 2012, 02:01
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Is \(x = \sqrt{x^2}\)? (1) x = even (2) 13 < x < 17
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Rahul
Originally posted by ITMRAHUL on 23 Jan 2011, 07:18.
Last edited by Bunuel on 04 Dec 2012, 02:01, edited 1 time in total.
Renamed the topic and edited the question.




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Re: Root. Modulus question
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23 Jan 2011, 07:51




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Re: Root. Modulus question
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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???
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Is x=square root of x^2?
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23 Jan 2011, 09:38
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 cannot 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 nonnegative number. (1) x = even > not sufficient as x can be negative as well as nonnegative even number. (2) 13<x<17 > x is nonnegative. Sufficient. Answer: B.
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Re: Root. Modulus question
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23 Jan 2011, 09:58
thanku very very much i got ur point more clearly nw thx again
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Re: Is x = \sqrt{x^2} if (1) x = even (2) 13 < x < 17
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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
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Re: Root. Modulus question
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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 nonnegative number. (1) x = even > not sufficient as x can be negative as well as a nonnegative even number. (2) 13<x<17 > x is nonnegative. Sufficient. Answer: B. Similar questions about this concept: isrootx323x92204.htmlifx0thenrootxxis81600.htmlissqrtx525x100517.htmlifx0thenrootxxis100303.htmlHope it helps.



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Re: Root. Modulus question
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19 Jun 2013, 20:47
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.
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Re: Root. Modulus question
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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.



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Re: Root. Modulus question
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20 Jun 2013, 09:46



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Re: Root. Modulus question
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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.



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Re: Root. Modulus question
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20 Jun 2013, 10:40
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. Hope it's clear.
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Re: Is x=square root of x^2?
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28 Jun 2013, 11:40
Is x = √(x^2) ?
Is x = (x) OR Is x = (x)
(1) x = even
X could be even but it may be positive or negative. x MUST be positive. INSUFFICIENT
(2) 13 < x < 17
X is positive. SUFFICIENT
(A)



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Re: Is x=square root of x^2?
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20 Nov 2016, 23:30
Great Question Here in order for x=√x^2=> x must be positive as √x^2 is always positive Hence what question is really Asking is that => If x≥0 Statement 1 x is even x can be positive or negative Hence insufficient Remember => Negatives can be even too Statement 2 This tells us that x is always positive hence √x^2=> always equal to x hence Sufficient Hence B
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Re: Is x=square root of x^2?
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