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For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?

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by neelgandham » Tue Apr 03, 2012 6:36 am
ashfu2002 wrote:Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?
A. x
B. x - 1
C. x + 1
D. - x
E. - x + 1
OA D
{-(x + 1) |x-1| + 1}^1/2
= {(-(x + 1) *-(x-1)) + 1}^1/2 - Since, x<0, x-1<0, |x-1| = -(x-1)
={((x+1)*(x-1))+1}^1/2
= {((x^2) -1)+1}^1/2
= {x^2}^1/2
= -x, since square root(Any number) > 0
Answer D
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by neelgandham » Tue Apr 03, 2012 6:48 am
ashfu2002 wrote:Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?
A. x
B. x - 1
C. x + 1
D. - x
E. - x + 1
Now the GMAT way

x < 0 , let x = -2, then
{-(x + 1) |x-1| + 1}^1/2 = {-(-2 + 1)*|-2-1| + 1}^1/2
= {-(-1)*|-3| + 1}^1/2
= {-(-1)*(3) + 1}^1/2
= {(1*3) + 1}^1/2
= {4}^1/2
= 2
If x = -2, then {-(x + 1) |x-1| + 1}^1/2 = 2 = -x Option D
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by killer1387 » Tue Apr 03, 2012 8:42 am
{-(x + 1) |x-1| + 1}^1/2
=> {(x+1)(x-1)+1}^0.5
=> {x^2}^0.5
=> -x as x<0 but sq. rt of a>0
Hence D
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by GMATGuruNY » Tue Apr 03, 2012 11:12 am
ashfu2002 wrote:Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?

A. x

B. x - 1

C. x + 1

D. - x

E. - x + 1

OA D
To simplify the arithmetic, let x=-1, so that -(x+1) = -(-1+1) = 0.

Plugging x=-1 into √(-(x + 1) |x-1| + 1), we get:
= √(0+1)
= 1. This is our target.

Now we plug x=-1 into the answers to see which yields our target of 1.
Only D works:
-x = -(-1) = 1.

The correct answer is D.
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