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What is the value of x ?

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Senior Manager
Joined: 21 Oct 2013
Posts: 419
What is the value of x ?  [#permalink]

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02 Aug 2014, 05:17
2
12
00:00

Difficulty:

35% (medium)

Question Stats:

58% (00:50) correct 42% (00:52) wrong based on 457 sessions

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What is the value of x ?

(1) √(x^2) = 19
(2) √(19^2) = x
Math Expert
Joined: 02 Sep 2009
Posts: 51280
Re: What is the value of x ?  [#permalink]

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02 Aug 2014, 09:01
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What is the value of x ?

(1) √(x^2) = 19. Since $$\sqrt{x^2}=|x|$$, then we have that |x| = 19. Thus x = 19 or -19. Not sufficient.

(2) √(19^2) = x --> x = 19. Sufficient.

Note for (1): $$\sqrt{x^2}=|x|$$, when $$x\leq{0}$$, then $$\sqrt{x^2}=-x=-negative=positive$$ and when $$x\geq{0}$$, then $$\sqrt{x^2}=x=positive$$.

Note for (2): When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{25}=5$$, NOT +5 or -5. In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

For more check here: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html
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Joined: 05 Sep 2016
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Re: What is the value of x ?  [#permalink]

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19 Sep 2016, 07:16
B is correct. Here's why:

(1) √(x^2) = 19 --> we don't know if x is positive or negative; squaring a number covers this up

INSUFFICIENT

(2) √(19^2) = x --> we can find value of x

SUFFICIENT
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Re: What is the value of x ?  [#permalink]

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18 Dec 2017, 12:26
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: What is the value of x ? &nbs [#permalink] 18 Dec 2017, 12:26
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