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555-605 (Medium)|   Roots|      
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skylimit
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What is the value of x? Updated on: 10 Sep 2015, 12:33
Originally posted by skylimit on 10 Sep 2015, 09:09.
Last edited by skylimit on 10 Sep 2015, 12:33, edited 4 times in total.
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25% (medium)

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70% (00:55) correct 30% (00:52) wrong based on 275 sessions

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EDIT - I realized I wrote the question AND solution wrong. Statement 1 should equal 4.
Maybe delete the hole thing!

What is the value of x?

(1) \(\sqrt{(x^2)}\) = 4
(2) \((\sqrt{x})^2\) = 4

Question:
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For statement 1 the solution says x = 4 or -4. But we can't take square root of a negative. So, x = 4. No?
This is a GMAT prep now question.
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ENGRTOMBA2018
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What is the value of x? Updated on: 10 Sep 2015, 13:05
Originally posted by ENGRTOMBA2018 on 10 Sep 2015, 09:16.
Last edited by ENGRTOMBA2018 on 10 Sep 2015, 13:05, edited 2 times in total.
Edited the solution
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skylimit
What is the value of x?
1) \(\sqrt{(x^2)}\) = 2
2) \((\sqrt{x})^2\) = 4

Question: For statement 1 the solution says x = 2 or -2. But we can't take square root of a negative. So, x = 2. No?
This is a GMAT prep now question.
Show more

Please follow posting guidelines, put all your analyses either in the next post or under spoiler.

As for this question,

\(\sqrt{x^2} = 4\), you can see that x = \(\pm\)4 will satisfy this equation and hence x can have 2 different values leading to this statement being not sufficient.

Per statement 2, \((\sqrt{x})^2 = 4\) ---> for GMAT, \(\sqrt{x}\) \(\geq 0\) and thus \(\sqrt{x}\)= +2 ONLY. Thus this statement is sufficient.
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What is the value of x? 10 Sep 2015, 09:30
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skylimit
What is the value of x?
1) \(\sqrt{(x^2)}\) = 2
2) \((\sqrt{x})^2\) = 4

Question: For statement 1 the solution says x = 2 or -2. But we can't take square root of a negative. So, x = 2. No?
This is a GMAT prep now question.

Please follow posting guidelines, put all your analyses either in the next post or under spoiler.

As for this question,

\(\sqrt{x^2} = 2\), you can see that x = \(\pm\)2 will satisfy this equation and hence x can have 2 different values leading to this statement being not sufficient.

Per statement 2, \((\sqrt{x})^2 = 4\) ---> for GMAT, \(\sqrt{x}\) \(\geq 0\) and thus \(\sqrt{x}\)= +2 ONLY. Thus this statement is sufficient.
Show more
Sorry, I didn't know about putting my comments under the spoiler.
But aren't we breaking the rule about finding the square root of a negative number? Isn't it undefined?
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What is the value of x? 10 Sep 2015, 11:46
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skylimit
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skylimit
What is the value of x?
1) \(\sqrt{(x^2)}\) = 2
2) \((\sqrt{x})^2\) = 4

Question: For statement 1 the solution says x = 2 or -2. But we can't take square root of a negative. So, x = 2. No?
This is a GMAT prep now question.

Please follow posting guidelines, put all your analyses either in the next post or under spoiler.

As for this question,

\(\sqrt{x^2} = 2\), you can see that x = \(\pm\)2 will satisfy this equation and hence x can have 2 different values leading to this statement being not sufficient.

Per statement 2, \((\sqrt{x})^2 = 4\) ---> for GMAT, \(\sqrt{x}\) \(\geq 0\) and thus \(\sqrt{x}\)= +2 ONLY. Thus this statement is sufficient.
Sorry, I didn't know about putting my comments under the spoiler.
But aren't we breaking the rule about finding the square root of a negative number? Isn't it undefined?
Show more

No rules are getting broken with x=-2 in statement 1, you are not directly taking square root of (-2), you are squaring it and then applying the square root. When you put x=-2, you get \(\sqrt{(-2)^2} = \sqrt{4} = \sqrt{(+2)^2}\), thus statement 1 is not sufficient.
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What is the value of x? 10 Sep 2015, 11:57
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I see. It's a PEMDAS thing.
Thanks!
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What is the value of x? 10 Sep 2015, 12:40
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skylimit
I see. It's a PEMDAS thing.
Thanks!

Not really. It does not depend on PEMDAS.

\(\sqrt{x} = x^{0.5}\) is the standard representation of any square root.

Thus, \(\sqrt{x^2} = (x^2)^{0.5}\) = \(x^{2*0.5}\) = \(x^1\) = \(x\)

But then you can do the same thing with both statements. But one is sufficient and one is not
Show more

I think I jumped the gun there and assumed that \(\sqrt {x^2} was = 4\) ! My posts above refer to m]\sqrt {x^2} was = 2[/m]

Thanks for editing the question.

Per GMAT, \(\sqrt{x} \geq 0\) and thus \(\sqrt{x} = 2\) should be the ONLY solution.

\(\sqrt{-2}\) is NOT defined in GMAT.
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What is the value of x? 10 Sep 2015, 12:50
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skylimit
I see. It's a PEMDAS thing.
Thanks!

Not really. It does not depend on PEMDAS.

\(\sqrt{x} = x^{0.5}\) is the standard representation of any square root.

Thus, \(\sqrt{x^2} = (x^2)^{0.5}\) = \(x^{2*0.5}\) = \(x^1\) = \(x\)
Show more

So can we not then say that statement 1 = \((x^2)^.5\) = x = 4 which makes it sufficient?
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What is the value of x? 10 Sep 2015, 13:02
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skylimit
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skylimit
I see. It's a PEMDAS thing.
Thanks!

Not really. It does not depend on PEMDAS.

\(\sqrt{x} = x^{0.5}\) is the standard representation of any square root.

Thus, \(\sqrt{x^2} = (x^2)^{0.5}\) = \(x^{2*0.5}\) = \(x^1\) = \(x\)

So can we not then say that statement 1 = \((x^2)^.5\) = x = 4 which makes it sufficient?
Show more


I have updated my solution above.

Yes, it is a PEMDAS thing wherein you need to evaluate the expression inside the parentheses or brackets first befoe anything. Dont know what I was thinking above. Sorry for the confusion.
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What is the value of x? 15 Dec 2025, 04:40
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