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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x  [#permalink]

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10 00:00

Difficulty:   45% (medium)

Question Stats: 55% (01:02) correct 45% (01:09) wrong based on 114 sessions

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What is the value of x?

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

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

_________________
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x  [#permalink]

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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

Rise above the storm, you will find the sunshine
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
Re: What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x  [#permalink]

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1
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!

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
Director  G
Joined: 20 Feb 2015
Posts: 762
Concentration: Strategy, General Management
What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x  [#permalink]

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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 What is the value of x? (1) √x^4 = 9 (2) √x^2 = -x   [#permalink] 25 Aug 2018, 11:05
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