Sq. Root Problem

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gmatassistance: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Jul 26, 2009 3:42 pm; Thanked: 1 times

by gmatassistance » Sun Jul 26, 2009 4:05 pm

For which of the following values of x is
(sq. root of 1 - (sq. root of 2 - (sq. root of x)))
NOT defined as a real number?

A) 1
B) 2
C) 3
D) 4
E) 5[/b]

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Source: Beat The GMAT — Problem Solving | Sun Jul 26, 2009 4:05 pm

shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Sun Jul 26, 2009 4:09 pm

5 because sq root of 5 is biger than 2, and when you subtract it from the sqroot of 2 it will be negtive, hence not a real number

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anabbasi: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Tue Dec 02, 2008 4:12 pm; Thanked: 1 times

Is this question correctly stated

by anabbasi » Sun Jul 26, 2009 10:52 pm

Is it
(sq. root of 1 - (sq. root of 2 - (sq. root of x)))
or
(sq. root of 1 -sq.root of (sq. root of 2 - (sq. root of x)))

I think in second case D option make sense.

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gmatassistance: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Jul 26, 2009 3:42 pm; Thanked: 1 times

by gmatassistance » Mon Jul 27, 2009 3:39 pm

The correct ans. is E) 5 ...

(sq. root of 1 - (sq. root of 2 - (sq. root of x)))

D) 4 is incorrect as it leads to a REAL number unlike E) 5

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krisraam: Master | Next Rank: 500 Posts; Posts: 221; Joined: Wed Jan 21, 2009 10:33 amFollowed by: 1 member; Thanked: 12 times

by krisraam » Mon Jul 27, 2009 5:47 pm

All the choices lead to real numbers.

when x= 1==> sqrt(1) - (Sqrt(2) -Sqrt(1))
==> 2 -Sqrt(2)
Irrational number. But real number.
Similarly for all other choices.

If the number is not a real number it need to be either imaginary number or complex number.

Thanks
Raama

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b2eby: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue May 19, 2009 12:56 pm; Thanked: 1 times

by b2eby » Mon Jul 27, 2009 6:19 pm

All numbers on the GMAT are real numbers. What's the source?

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gmatassistance: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Jul 26, 2009 3:42 pm; Thanked: 1 times

by gmatassistance » Tue Jul 28, 2009 4:30 pm

The problem is from one of the GMAT Prep exams ... per the earlier explanation the answer is 5 because it leads to a square root of a negative which isn't a real number.

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