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# If √x = x, then which of the following must be true?

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Joined: 09 Feb 2013
Posts: 111
If √x = x, then which of the following must be true?  [#permalink]

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Updated on: 22 Mar 2013, 02:54
11
00:00

Difficulty:

35% (medium)

Question Stats:

58% (00:56) correct 42% (00:58) wrong based on 274 sessions

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If $$\sqrt{x}$$ = x, then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above

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Originally posted by emmak on 22 Mar 2013, 00:56.
Last edited by Bunuel on 22 Mar 2013, 02:54, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If √x=x , then which of the following must be true? x is  [#permalink]

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22 Mar 2013, 01:34
emmak wrote:
If $$\sqrt{x}$$=x , then which of the following must be true?
a) x is positive
b) x=1
c) $$x^2$$>x
d) x is non-negative
e) none of the above

Square both the sides we get
x = x^2
x^2 - x= 0
x(x-1)=0
either x=0 or x=1
So, asnwer will be D

hope it helps!
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Re: If √x = x, then which of the following must be true?  [#permalink]

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22 Mar 2013, 03:03
If $$\sqrt{x}= x$$ , then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above

We have that x is equal to the square root of some number ($$\sqrt{x}$$). Now, we know that the square root function cannot give negative result ($$\sqrt{{some \ expression}}\geq{0}$$), thus LHS ($$\sqrt{x}$$) is more than or equal to zero, which implies tha RHS (x) is also more than or equal to zero. Hence we have that $$x\geq{0}$$.

Or simply be solving: $$\sqrt{x}= x$$ --> $$x=x^2$$ --> $$x(x-1)=0$$ --> $$x=0$$ or $$x=1$$.

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Re: If √x = x, then which of the following must be true?  [#permalink]

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17 Feb 2018, 03:39
Square it on both sides
x^2=x
x^2-x=0
x(x-1)=0
x=0,1
So D should be the answer because this is a "must be true" question
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Re: If √x = x, then which of the following must be true?  [#permalink]

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19 Feb 2019, 16:27
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).

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Re: If √x = x, then which of the following must be true?   [#permalink] 19 Feb 2019, 16:27
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