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Is (|x|)^x > x|x|^3?

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amgelcer
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Is (|x|)^x > x|x|^3? [#permalink] New post   28 Sep 2013, 08:54
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Is \((|x|)^x > x|x|^3\)?


(1) \(x^2 + 4x + 4 = 0\)

(2) \(x < 0\)
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D
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TirthankarP
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Re: Is (|x|)^x > x|x|^3? [#permalink] New post   28 Sep 2013, 10:45
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Is \((|x|)^x\) > \(x(|x|)^3\)?

(1) \(x^2\) + 4x + 4 = 0
(2) x < 0

Statement 1: \(x^2\) + 4x + 4 = 0
So, x = -2

Putting -2 in original equation we get:
LHS = \((|-2|)^(^-^2^)\) = \(2^(^-^2^)\) = \(\frac{1}{4}\)
RHS = \(-2*(|-2|)^3\) = \(-2*2^3\) = -16
\(\frac{1}{4}\) < -16 ... SUFFICIENT

Statement 2: x < 0
\((|x|)^x\) is between 0 and 1 as explained with x = -2.
|x| is always positive. So \((|x|)^3\) is positive. And as x < 0 so \(x(|x|)^3\) < 0.
Hence SUFFICIENT

Answer D
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Re: Is (|x|)^x > x|x|^3? [#permalink] New post   29 Sep 2013, 12:21
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Is (|x|)^x > x|x|^3?

(1) x^2 + 4x + 4 = 0 --> \((x+2)^2=0\) --> \(x=-2\). We can substitute and answer the question. Sufficient.

(2) x < 0. \(LHS=(|x|)^x=positive\) and \(RHS=x|x|^3=negative*positive^3=negative\) --> LHS>RHS. Sufficient.

Answer: D.
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Re: Is (|x|)^x > x|x|^3? [#permalink] New post   31 May 2016, 06:10
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Bunuel wrote:
Is (|x|)^x > x|x|^3?

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


Hi,

\((|x|)^x > x|x|^3\)... will be true when x is <0 as RHS will be negative and LHS will be +ive always

(1) \(x^2 + 4x + 4 = 0..............(x+2)^2=0\)
x=-2.... so YES
suff

(2) \(x < 0\)
all negative values will make RHS as -ive, whereas LHS will always be +
Suff

D
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fantaisie
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Re: Is (|x|)^x > x|x|^3? [#permalink] New post   31 May 2016, 14:19
1) \(x^2\) + 4x + 4 = 0
\(b^2\) - 4ac = 0
\(4^2\) - 4 x 1 x 4 = 0 ---> one solution x = -2
Having x we can evaluate the equation

SUFFICIENT

2) x < 0 test for a few options
x = -1, then 1 < -1 (NO)
x = -2, then \(\frac{1}{2^2}\) < 2^3 x (-2)
\(\frac{1}{4}\) < -16 (NO)

SUFFICIENT

Answer: D
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Re: Is (|x|)^x > x|x|^3? [#permalink] New post   06 Nov 2022, 02:23
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Re: Is (|x|)^x > x|x|^3? [#permalink]
06 Nov 2022, 02:23
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