Is x=square root of x^2?

Question

Is  x = \sqrt{x^2} ?

(1) x = even
(2) 13 < x < 17

Bunuel · Accepted Answer

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 is non-negative. Sufficient. Answer: B. Similar questions about this concept: is-root-x-3-2-3-x-92204.html if-x-0-then-root-x-x-is-81600.html is-sqrt-x-5-2-5-x-100517.html if-x-0-then-root-x-x-is-100303.html Hope it helps.

ITMRAHUL · Answer

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???

Bunuel · Answer

Even roots (such as square root) from negative numbers are undefined on the GMAT: \sqrt {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 non-negative number. (1) x = even --> not sufficient as x can be negative as well as non-negative even number. (2) 13 x is non-negative. Sufficient. Answer: B.

ITMRAHUL · Answer

thanku very very much i got ur point more clearly nw
thx again

shinbhu · Answer

1. Insufficient since x can be negative
2. Sufficient, since here x is positive - irrespective of even or odd.

+1 for B

WholeLottaLove · Answer

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?

KarishmaB · Answer

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.

WholeLottaLove · Answer

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?

Bunuel · Answer

Have you read Karishma's response?

WholeLottaLove · Answer

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 · Answer

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.

WholeLottaLove · Answer

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)

stonecold · Answer

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

CEdward · Answer

Is x=√x^2? We're being asked if x = | x |? i.e. is x > 0? (1) x = even Insufficient. x = 2, -2 (2) 13 < x < 17 Sufficient as x >0 Answer is B.

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Is x=square root of x^2?

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