Exercise from OFFICIAL GMAT PREP- I could use a little help

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bobdylan: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Wed Nov 30, 2011 3:12 pm

by bobdylan » Mon Apr 09, 2012 5:12 am

1) If X<0, then sq. root of -X . I X I is:

a) - X
b) - 1
c) 1
d) X
e) sq root of X

Thanks in advance!

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Source: Beat The GMAT — Problem Solving | Mon Apr 09, 2012 5:12 am

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

by Anurag@Gurome » Mon Apr 09, 2012 5:22 am

bobdylan wrote:1) If X<0, then sq. root of -X . I X I is:

a) - X
b) - 1
c) 1
d) X
e) sq root of X

Thanks in advance!

Note that âˆš(xÂ²) = |x|, which means that the square root cannot give a negative result.
So, âˆš(xÂ²) â‰¥ 0
Now if x = 5, then âˆš(xÂ²) = âˆš25 = 5 = x = positive.
If x = -5, then âˆš(xÂ²) = âˆš25 = 5 = -x = positive.

So, we can say that âˆš(xÂ²) = x if x â‰¥ 0.
and âˆš(xÂ²) = -x, if x < 0.

âˆš(-x *|x|) = âˆš(-x * -x) = âˆš(xÂ²) = |x| = -x

The correct answer is A.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Apr 09, 2012 5:30 am

bobdylan wrote:1) If X<0, then âˆš( -X*IX| ) is:

a) - X
b) - 1
c) 1
d) X
e) âˆšX

Thanks in advance!

Please note that âˆš means the POSITIVE ROOT ONLY.

Let x=-2.
Then âˆš( -x*Ix| ) = âˆš( -(-2)*I-2| ) = âˆš4 = 2. This is our target.
Now we plug x=-2 into the answers to see which yields our target of 2.
Only answer choice A works:
-x = -(-2) = 2.

The correct answer is A.

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Shalabh's Quants: Master | Next Rank: 500 Posts; Posts: 134; Joined: Fri Apr 06, 2012 3:11 amFollowed by: 5 members; Thanked: 35 times

by Shalabh's Quants » Mon Apr 09, 2012 5:30 am

bobdylan wrote:1) If X<0, then sq. root of -X . I X I is:

a) - X
b) - 1
c) 1
d) X
e) sq root of X

Thanks in advance!

If I understood correctly...

It asks for sqrt [(-x)*|x|];

As X < 0; hence sqrt [(-x)*|x|] = sqrt[(x)*|-x|] = sqrt[(x)*x]= sqrt(x^2) = x. (With sign adjustment)

X is of opposite sign of -X, hence answer should be A.

------------

One approach can be take any random value of X = -4. You will get sqrt [(-x)*|x|] = 4 or -X.

Shalabh Jain,
e-GMAT Instructor

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ranjeet75: Master | Next Rank: 500 Posts; Posts: 242; Joined: Fri Aug 01, 2008 8:49 am; Location: Delhi; Thanked: 6 times

by ranjeet75 » Tue Apr 10, 2012 7:53 am

[quote="GMATGuruNY"][quote="bobdylan"]1) If X<0, then âˆš( -X*IX| ) is:

a) - X
b) - 1
c) 1
d) X
e) âˆšX

Thanks in advance![/quote]

Please note that âˆš means the POSITIVE ROOT ONLY.

Let x=-2.
Then âˆš( -x*Ix| ) = âˆš( -(-2)*I-2| ) = âˆš4 = 2. This is our target.
Now we plug x=-2 into the answers to see which yields our target of 2.
Only answer choice [spoiler]A[/spoiler] works:
-x = -(-2) = 2.

The correct answer is [spoiler]A[/spoiler].[/quote]

If we take x = -2, then the answer is 2, so in the question it is given that x<0 so the answer should be x i.e.,

Option D should be correct.

Please help me where i am missing

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