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absolute value of x to power x

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Source: — Data Sufficiency |
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by [email protected] » Sun May 19, 2013 1:09 am
faraz_jeddah wrote:Is (|x|)^x > x(|x|)^3?

(1) x2 + 4x + 4 = 0
(2) x < 0

OA is d

I know 1 is suff but how is 2 suff?
Plugging numbers is quiet fast here..
Statement 2: -1, -2,-3 and so on
When X=-1
1^-1>-1 * 1^3 ie 1/1> -1 (yes)
When x=-2
2^-2> -2* 2^3 ie 1/4> -16 ie positive> negative same as in x=-1...(Yes)

this is the trend. thus statement 2 is sufficient.
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by Atekihcan » Sun May 19, 2013 4:43 am
For statement 2, x is negative.
Now, |x| is always positive.
So, any power of |x| will be also positive.
So, |x|ˣ and |x|³ both are positive.

Now, the left-hand side of the inequality is x*|x|³ = (negative)*(positive) = negative
So, |x|ˣ must be greater than x*|x|³.

So, statement 2 is sufficient.
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