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Real numbers!!!

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by Anurag@Gurome » Tue Feb 19, 2013 5:31 am
rajatvmittal wrote:Is x a real number?

√x is not positive
x^2 is not positive
Statement 1: By definition, if x is a nonnegative real number then √x is always nonnegative. As √x is not positive, then we can only conclude that x is not a positive real number. But x can be either equal to zero or a negative real number or not real at all.

Not sufficient

Statement 2: As square of any real number is always nonnegative, x is either equal to zero or not real at all.

Not sufficient

1 & 2 Together: x is either equal to zero or not real at all.

Not sufficient

The correct answer is E.
Last edited by Anurag@Gurome on Tue Feb 19, 2013 8:52 am, edited 1 time in total.
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by GMATGuruNY » Tue Feb 19, 2013 5:35 am
Ignore this problem.
Imaginary numbers are beyond the scope of the GMAT.
An actual GMAT problem will never ask whether a value is real (versus imaginary).
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by Ian Stewart » Tue Feb 19, 2013 8:44 am
Anurag@Gurome wrote:
Statement 2: As square of any real number is always positive, x is not a real number.
No, that's not the case. If x = 0, then x^2 is not positive.

But as Mitch says, every number on the GMAT is a real number. So if this were a GMAT question, you wouldn't need any Statements at all to answer this question - the answer must be 'yes' no matter what the Statements say.

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For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by Anurag@Gurome » Tue Feb 19, 2013 8:58 am
Ian Stewart wrote:... No, that's not the case. If x = 0, then x^2 is not positive.
Thanks for pointing it out, Ian.
I completely missed the x = 0 scenario.
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