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

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Director
Joined: 25 Oct 2008
Posts: 599
Location: Kolkata,India
What is the value of x? (1) root(x^4)= 9 (2) root(x^2)= -x [#permalink]

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27 Sep 2009, 22:33
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100% (02:10) correct 0% (00:00) wrong based on 5 sessions

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What is the value of x?

(1) root(x^4)= 9

(2) root(x^2)= -x

How is the ans
[Reveal] Spoiler:
C

1:we get two values.Insuff.B C E
2: x= -x.This is only poss. when x=0.Suff. IMO:B

What am i missing?
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Manager
Joined: 11 Sep 2009
Posts: 129

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27 Sep 2009, 23:50
Statement 1: Root(x^4) = 9

$$x= 3 or x = -3$$

Statement 1 is insufficent.

Statement 2: root(x^2)= -x

x <= 0 (Think about it: if X = -3, x^2 = 9. The root of 9 is 3. -x = -(-3) = 3.)

Statements Analyzed Together

One value: $$-3$$

Last edited by AKProdigy87 on 28 Sep 2009, 00:37, edited 2 times in total.
Senior Manager
Joined: 08 Jan 2009
Posts: 326

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28 Sep 2009, 00:15
Will go with C.

stmt 2 :

root(x^2)= -x can be written as |x| + x = 0 so solution for this is x<=0

stmt 1 :

same ways can be written as | x^2 | = 9

so x can be + 3 or -3

combining :

yes X = -3 so Ans is C.
Director
Joined: 25 Oct 2008
Posts: 599
Location: Kolkata,India

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28 Sep 2009, 02:51
I am sorry its still not clear:
Stmt 2:
Root(x^2)=-x
x=-x
2x=0
x=0 Hence B
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Joined: 20 Aug 2009
Posts: 306
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)

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28 Sep 2009, 04:52
1
KUDOS
tejal777 wrote:
I am sorry its still not clear:
Stmt 2:
Root(x^2)=-x
x=-x
2x=0
x=0 Hence B

general rule is that

$$\sqrt{x^2}=|x|$$

|x| = x, if x>=0

|x| = -x, if x<0

http://en.wikipedia.org/wiki/Square_root

so from the Statement 2 it becomes clear, that x is negative
Senior Manager
Joined: 31 Aug 2009
Posts: 417
Location: Sydney, Australia

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28 Sep 2009, 05:04
Thanks for the info and link Shalva.
Re: value of x?   [#permalink] 28 Sep 2009, 05:04
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