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# If x^2 = 2^x, what is the value of x ?

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If x^2 = 2^x, what is the value of x ? [#permalink]

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27 Jul 2017, 07:12
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Question Stats:

59% (01:29) correct 41% (01:48) wrong based on 207 sessions

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If $$x^2 = 2^x$$, what is the value of x ?

(1) $$2x = (\frac{x}{2})^3$$

(2) $$x = 2^{x-2}$$
[Reveal] Spoiler: OA

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Kudos [?]: 9481 [1], given: 1202

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Joined: 02 Aug 2009
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Re: If x^2 = 2^x, what is the value of x ? [#permalink]

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27 Jul 2017, 07:35
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carcass wrote:
If $$x^2 = 2^x$$, what is the value of x ?

(1) $$2x = (\frac{x}{2})^3$$

(2) $$x = 2^x-2$$

Hi..

If $$x^2 = 2^x$$, what is the value of x ?

(1) $$2x = (\frac{x}{2})^3$$
$$x*(\frac{x^2}{8}-2)=0$$
we get x as 0, 4 or -4..
when we substitute value in $$x^2 = 2^x$$, ONLY x = 4 is possible..
sufficient

(2) $$x = 2^x-2$$
or $$x+2=2^x$$...
2^x has to be multiple of 2 and so also x+2 should be in power of 2 that is 2,4,8,16...AND x+2 will fit in only at x+2=4 as 2^2
ONLY when x is 2 both sides are 4.
.
suff

although ans is D, but values of x differ as 4 in statement I and 2 in II
generally not possible in OG..

carcass i believe statement II should be $$x=2^{x-2}$$.. here possible value is 4 SAME as statement I.. pl relook into Q
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6107 [2], given: 121

Board of Directors
Joined: 01 Sep 2010
Posts: 3420

Kudos [?]: 9481 [1], given: 1202

Re: If x^2 = 2^x, what is the value of x ? [#permalink]

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27 Jul 2017, 08:19
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Hi Chetan,

fixed, was a question of formatting rather than a typo.

Thank you so much for pointing out
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Re: If x^2 = 2^x, what is the value of x ? [#permalink]

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07 Aug 2017, 05:45
Statement II can be turned into 4x=2^x which clearly has the only answer x=4, so it is sufficient

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Re: If x^2 = 2^x, what is the value of x ? [#permalink]

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12 Aug 2017, 11:59
My 2 cents:
Attachment:

my 2 cents.png [ 3.04 MiB | Viewed 721 times ]

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Re: If x^2 = 2^x, what is the value of x ?   [#permalink] 12 Aug 2017, 11:59
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