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# GMATPrep - Number properties - PS

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GMATPrep - Number properties - PS [#permalink]  22 Jul 2006, 16:44
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Interesting question - thought I should post it
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Manager
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[#permalink]  22 Jul 2006, 17:55
since sqrt x^2 can be either +/- x

I think the answe is E
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[#permalink]  22 Jul 2006, 22:26
Please correct me if I am wrong. This is what I observed for GMAT Q's

if x^2 = 9
then x is + or - 9.
But if x = sqrt of 9 then x = 3

According to OG11 - Every positive number has two square roots, one positive and one negative but Sqrt n denotes a positive no. whose square is n. (pg.114)

So the answer should be 1.

Thanks
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[#permalink]  23 Jul 2006, 00:07
The answer is in fact E and I chose C for the same reason that you just mentioned. However in this question x could potetially by any value as long as it is not equal to 0 .. so E is the right choice.
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[#permalink]  26 Jul 2006, 04:24
E.

Sqr(x^2) = -x when x<0
= x when x>0

Hence sqr(x^2) can be written as |x|
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[#permalink]  27 Jul 2006, 12:30
Answer is 1. Option C

SQRT (x^2) means --- x (power 2 * power 1/2) = x power 1 = x

x/x = 1

We don't need to substitute any value to find it.

Ofcourse if it is 0 the value would not be there.
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[#permalink]  27 Jul 2006, 13:42
Clear E.

if x<0
sqrt(x^2)/x = -1
if x>0
sqrt(x^2)/x = 1

Thus, sqrt(x^2)/x = |x|/x
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[#permalink]  27 Jul 2006, 20:48
ghantark,
Your reference to OG

According to OG11 - Every positive number has two square roots, one positive and one negative but Sqrt n denotes a positive no. whose square is n. (pg.114)

does not contradict to the solution provided here (which is, btw, E). In fact, it helps. Just try plugging -1 and 1 as X and you will see
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[#permalink]  30 Jul 2006, 20:57
I am confused
How can there be a square root of a negative?
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[#permalink]  31 Jul 2006, 05:45
jamesrwright3 wrote:
I am confused
How can there be a square root of a negative?

Negative numbers do have square roots.

You just have to use imaginary numbers in order to solve them.

E.G.
Sqrt (-9) = -1 * sqrt (9)

Hope this helps.
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[#permalink] 31 Jul 2006, 05:45
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# GMATPrep - Number properties - PS

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