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

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Math Expert
Joined: 02 Sep 2009
Posts: 49915

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31 May 2016, 05:51
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45% (medium)

Question Stats:

72% (01:59) correct 28% (01:55) wrong based on 167 sessions

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

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

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Joined: 02 Aug 2009
Posts: 6956
Re: Is (|x|)^x > x|x|^3?  [#permalink]

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31 May 2016, 06:10
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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Re: Is (|x|)^x > x|x|^3?  [#permalink]

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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

D
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Re: Is (|x|)^x > x|x|^3?  [#permalink]

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17 Apr 2018, 02:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is (|x|)^x > x|x|^3? &nbs [#permalink] 17 Apr 2018, 02:30
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