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# What is the value of x ?

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Senior Manager
Joined: 21 Oct 2013
Posts: 446

Kudos [?]: 1916 [2], given: 289

What is the value of x ? [#permalink]

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02 Aug 2014, 05:17
2
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Difficulty:

35% (medium)

Question Stats:

55% (00:35) correct 45% (00:36) wrong based on 362 sessions

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What is the value of x ?

(1) √(x^2) = 19
(2) √(19^2) = x
[Reveal] Spoiler: OA

Kudos [?]: 1916 [2], given: 289

Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139663 [7], given: 12794

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

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02 Aug 2014, 09:01
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Expert's post
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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
_________________

Kudos [?]: 139663 [7], given: 12794

Senior Manager
Status: DONE!
Joined: 05 Sep 2016
Posts: 407

Kudos [?]: 28 [0], given: 283

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

Kudos [?]: 28 [0], given: 283

Non-Human User
Joined: 09 Sep 2013
Posts: 14201

Kudos [?]: 291 [0], given: 0

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

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18 Dec 2017, 12:26
Hello from the GMAT Club BumpBot!

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Kudos [?]: 291 [0], given: 0

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