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What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x

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What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x  [#permalink]

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New post 13 Aug 2018, 03:03
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

54% (00:48) correct 46% (01:02) wrong based on 90 sessions

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Director
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Joined: 01 Oct 2017
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WE: Supply Chain Management (Energy and Utilities)
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What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x  [#permalink]

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New post 13 Aug 2018, 04:02
Bunuel wrote:
What is the value of x?


(1) \(\sqrt{x^4} = 9\)

(2) \(\sqrt{x^2} = -x\)


St1:- \(\sqrt{x^4} = 9\)

Squaring both sides,
\((\sqrt{x^4})^2 = 9^2\)
Or, \(((x^4(^{\frac{1}{2}}))^2=9^2\)
Or, \(x^(4*\frac{1}{2}*2)=9^2\)
Or, \(x^4=81\)
Or, x=3 ,-3
Insufficient.

St2:- \(\sqrt{x^2} = -x\)
Since square root is always positive, hence 'x' in RHS must be less than 0.
Squaring both sides,
\((\sqrt{x^2})^2 = (-x)^2\)
Or, \(x^2=x^2\)
Or, \(x\le \:0\)
Insufficient.

Combined, We have x=-3
Sufficient.

Ans. (C)
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PKN

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Re: What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x  [#permalink]

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New post 24 Aug 2018, 07:56
1
askhere wrote:
IMO B.

Statement 1 - insufficient - sqrt (x^4) = 9
-> (x^4)^1/2 = 9
-> X^2 = 9
->X = +3 or -3.

Statement 2 - sqrt(X^2) = -X
-> (X^2)^1/2 = -X
->X= -X
-> 2X=0
-> X = 0 Sufficient. What am I missing here? Please help!


Hi askhere,
You have to always handle roots operations carefully.
You know , In GMAT even root operation always yield +value.
For example, \(\sqrt{4}\)= +2 NOT -2 since \(\sqrt{-2}\) is imaginary and GMAT stays in real world. Only real values are accepted.
However, \(x^2=4\) has two solutions x=+2 or -2.

Now, as per above concepts, \(\sqrt{x^2}\) is always positive.
But RHS is negative of x. Negative of x will be positive when x<0 (or x is negative).--------------(1)

1) For example if x=-4, then \(LHS= \sqrt{x^2}=\sqrt{(-4)^2}=\sqrt{16}= +4\)
\(RHS=-x=-(-4)=4\)
So LHS=RHS when\(x<0\)

2) LHS will be equal to RHS when x=0

So, x can never be +ve.

From (1) and (2), \(x\leq{0}\) (More than one value of x, so insufficient)

Your method:- The moment we simplified the statement, we lost the essence of the statement ,i.e, what GMAT wanted to test us. Simplify when it is necessary or when the original statement has no worth significance. if the original statement conveys various possibilities, then we mustn't simplify.

Hope it helps.

P.S:- Never simplify root operations , first think of the logic behind the root operation, then do the needful.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

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What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x  [#permalink]

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New post 25 Aug 2018, 10:05
Bunuel wrote:
What is the value of x?


(1) \(\sqrt{x^4} = 9\)

(2) \(\sqrt{x^2} = -x\)



(1) \(\sqrt{x^4} = 9\)

\(\sqrt{x^2}\) = |x| = +x , -x
so \(\sqrt{x^4}\) = +3,-3
insufficient

(2) \(\sqrt{x^2} = -x\)
X is -ve

insufficient

using both x= -3
C
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What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x &nbs [#permalink] 25 Aug 2018, 10:05
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