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

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Director
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What is the value of x? sq root(x^4)=9 sq root(x^2)=-x [#permalink]

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06 Nov 2009, 06:32
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What is the value of x?

sq root(x^4)=9
sq root(x^2)=-x
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Senior Manager
Joined: 31 Aug 2009
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Location: Sydney, Australia
Re: What is the value of x? [#permalink]

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06 Nov 2009, 06:35
tejal777 wrote:
What is the value of x?

sq root(x^4)=9
sq root(x^2)=-x

Statement 1 is insufficient.
sq root(x^4)=9 can be simplified to x^2 = 9
x = + or - 3.

Statement 2 is sufficient.
x can be positive or negative. But since the right side is -x the only posible value of x is 0.

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

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06 Nov 2009, 08:28
B too.

(x^2)^(1/2)=-x =>x=-x; x is 0.

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Director
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Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: What is the value of x? [#permalink]

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06 Nov 2009, 10:40
I get C..

1. x is + or -3.
2. $$\sqrt{x^2} = |x|$$
hence, |x| = -x implies x is 0 or -ve.

Combining, x can only be -3.

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Director
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Kudos [?]: 1129 [0], given: 100

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

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06 Nov 2009, 17:47
Guys but I got the answer as B..can't understand why C is the correct answer..
from B alone we get x=0..so suff.. Sad
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Senior Manager
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Re: What is the value of x? [#permalink]

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06 Nov 2009, 17:53
I am in total agreement with Economist here.
$$\sqrt{x^2} = |x|$$ and not $$x$$.
So the answer should be C.

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

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06 Nov 2009, 18:23
could you please elaborate a bit?
How did the right-hand side change from -x to mod x?
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Senior Manager
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Re: What is the value of x? [#permalink]

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06 Nov 2009, 20:42
tejal777 wrote:
could you please elaborate a bit?
How did the right-hand side change from -x to mod x?

Right hand did not change from -x to mod |x|, rather left hand side itself is equal to |x|.
Okay, consider this: what is the value of $$\sqrt{5^2}$$? It is {-5,5} That means it is |5|.
So $$\sqrt{x^2}=|x|$$.
Now $$|x| = -x$$. So x = 0 or negative. Thus the value of x cannot be determined.
Considering statement 1 and 2 together you can find out that value of x is -3.

One IMPORTANT CLUE to remember: In DS, both statement 1 and statement 2 ALWAYS RETURN THE SAME RESULT. So when in doubt just check the result from other statement.

As statement 1 in this case represents the value of x as either 3 or -3, statement 2 CANNOT return the value of x as ZERO.
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Re: What is the value of x?   [#permalink] 06 Nov 2009, 20:42
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