Range of Values

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krishna kumar: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Fri Jun 11, 2010 10:02 pmFollowed by: 1 member

by krishna kumar » Fri Jun 25, 2010 5:36 am

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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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Source: Beat The GMAT — Problem Solving | Fri Jun 25, 2010 5:36 am

Rich@VeritasPrep: GMAT Instructor; Posts: 147; Joined: Tue Aug 25, 2009 7:57 pmFollowed by: 17 members; Location: New York City; Thanked: 76 times; GMAT Score:770

by Rich@VeritasPrep » 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)

Rich Zwelling
GMAT Instructor, Veritas Prep

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by [email protected] » Sat Apr 07, 2018 2:08 pm

Hi All,

We're told that X^2 - 2 < 0. We're asked which of the following specifies ALL of the possible values of X. If you recognize the patterns involved in this question, then you don't actually have to do much math to answer it.

To start, we should look at a simpler example that's based on the same logic:

X^2 - 4 < 0
X^2 < 4

With this inequality, we're dealing with a perfect square (4), so it's not tricky to see that X can get really close to 2 and really close to -2 (and X can be everything else 'in between.' Now, take that SAME idea and apply it to this question.

X^2 - 2 < 0
X^2 < 2

X can get really close to root(2) and really close to -root(2).... (and X can be everything else 'in between.'

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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