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Range of Values

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krishna kumar Junior | Next Rank: 30 Posts Default Avatar
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Range of Values

Post Fri Jun 25, 2010 5:36 am
Hi,

This one stumped me.

If x^2 - 2 < 0, which of the following specifies all the possible values of x ?

A. 0 < x < 2
B. 0 < x < root(2)
C. -root(2) < x < root(2)
D. -2 < x < 0
E. -2 < x < 2

The OA is C

I've come to the point where x < root(2) and x < -root(2).

Thanks

krishna kumar

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Rich@VeritasPrep GMAT Instructor
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Post Fri Jun 25, 2010 5:40 am
Hey Krishna,

You're very close. It's actually:

x < root(2) and x > -root(2).

When you have a variable raised to an even exponent, and the expression (in this case x^2) is less than a certain value, the resulting range is always a single bounded region.

You can rewrite the expression in the prompt as x^2 < 2. The resulting breakdown is x > -root(2) and x < root(2). That in turn can be written as a single bounded region: -root(2) < x < root(2)

If the problem instead specified x^2 > 2, then the result would be two unbounded regions, namely:

x < -root(2) and x > root(2)

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Rich Zwelling
GMAT Instructor, Veritas Prep

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