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[-x × |x|]^½ is

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by sanju09 » Fri Mar 18, 2011 2:27 am
If x < 0, then [-x × |x|]^½ is
A. -x
B. -1
C. 1
D. x
E. x^½




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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri Mar 18, 2011 4:42 am
sanju09 wrote:If x < 0, then [-x × |x|]^½ is
A. -x
B. -1
C. 1
D. x
E. x^½

https://www.urch.com/forums/gmat-problem-solving
If x = -3, then [-x × |x|]^½ = [-(-3) * |-3|]^(1/2) = (9)^(1/2) = 3 = -(-3) = -x

The correct answer is A.
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by DarkKnight » Tue Mar 22, 2011 7:43 pm
Anurag@Gurome wrote:
sanju09 wrote:If x < 0, then [-x × |x|]^½ is
A. -x
B. -1
C. 1
D. x
E. x^½

https://www.urch.com/forums/gmat-problem-solving
If x = -3, then [-x × |x|]^½ = [-(-3) * |-3|]^(1/2) = (9)^(1/2) = 3 = -(-3) = -x

The correct answer is A.
Hi Anurag,

In the above calculation, why did you take (9)^(1/2) = 3 ?? It could also be -3. What am I missing?

Thanks for your help.
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by Anurag@Gurome » Tue Mar 22, 2011 7:59 pm
DarkKnight wrote:
Anurag@Gurome wrote:
sanju09 wrote:If x < 0, then [-x × |x|]^½ is
A. -x
B. -1
C. 1
D. x
E. x^½

https://www.urch.com/forums/gmat-problem-solving
If x = -3, then [-x × |x|]^½ = [-(-3) * |-3|]^(1/2) = (9)^(1/2) = 3 = -(-3) = -x

The correct answer is A.
Hi Anurag,

In the above calculation, why did you take (9)^(1/2) = 3 ?? It could also be -3. What am I missing?

Thanks for your help.
(9)^(1/2) means √9, and square root of a number is only its positive square root. In this case it will be 3, and not -3. Had it been x² = 9, then x = +3, -3.
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by manpsingh87 » Tue Mar 22, 2011 9:58 pm
sanju09 wrote:If x < 0, then [-x × |x|]^½ is
A. -x
B. -1
C. 1
D. x
E. x^½




https://www.urch.com/forums/gmat-problem-solving

as x<0; therefore |x|= -x;
so [-x * -x]^1/2;
(x^2)^1/2;
therefore possible values of expression can be either x, -x;
now as x<0; therefore expression yield -x as an answer. hence A
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by sanju09 » Wed Mar 23, 2011 1:01 am
I don't know how I posted this PS in DS bin, moderators please move it to the right bin.
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by ajmoney09 » Wed Mar 23, 2011 5:54 pm
manpsingh87 wrote:
sanju09 wrote:If x < 0, then [-x × |x|]^½ is
A. -x
B. -1
C. 1
D. x
E. x^½




https://www.urch.com/forums/gmat-problem-solving

as x<0; therefore |x|= -x;
so [-x * -x]^1/2;
(x^2)^1/2;
therefore possible values of expression can be either x, -x;
now as x<0; therefore expression yield -x as an answer. hence A
Like this method, much better. Although I understand it is better to substitute numbers, but Anurag's way confused me, not sure how we go form 3 to -(-3) = -x....

Sorry Anurag.
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