Real numbers!!!

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Tue Feb 19, 2013 5:31 am

rajatvmittal wrote:Is x a real number?

âˆšx is not positive
x^2 is not positive

Statement 1: By definition, if x is a nonnegative real number then âˆšx is always nonnegative. As âˆšx 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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

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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Ian Stewart: GMAT Instructor; Posts: 2621; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

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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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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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