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# If, x = 300^(1/4) then which of the following is true?

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Senior Manager
Joined: 21 Oct 2013
Posts: 418
If, x = 300^(1/4) then which of the following is true?  [#permalink]

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26 Jul 2014, 12:02
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Difficulty:

45% (medium)

Question Stats:

65% (01:46) correct 35% (02:01) wrong based on 251 sessions

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If $$x = \sqrt[4]{300}$$ then which of the following is true?

A. 3 < x < 3.5
B. 3.5 < x < 4
C. 4 < x < 4.5
D. 4.5 < x < 5
E. 5 < x < 5.5
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Joined: 02 Sep 2009
Posts: 53067
Re: If, x = 300^(1/4) then which of the following is true?  [#permalink]

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26 Jul 2014, 12:09
2
goodyear2013 wrote:
If $$x = \sqrt[4]{300}$$ then which of the following is true?

A. 3 < x < 3.5
B. 3.5 < x < 4
C. 4 < x < 4.5
D. 4.5 < x < 5
E. 5 < x < 5.5

$$x^4=300$$:

4^4 = 16^2 = 256, hence x is little bit greater than 4.

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Re: If, x = 300^(1/4) then which of the following is true?  [#permalink]

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13 Aug 2014, 11:02
or maybe
x^4=300:
X ^2= 10 √3 ±17
Therefore X =√17= 4 something

hope it helps
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Re: If, x = 300^(1/4) then which of the following is true?  [#permalink]

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06 Jan 2016, 21:12
1
Hi All,

The prior explanations show how X would have to be greater than 4, but if you're not perfectly clear on whether X is greater than 4.5 or not, then here's how to mathematically prove it without doing too much extra work...

4.5 = 9/2

(9/2)^4 =
(9)(9)(9)(9)/(2)(2)(2)(2) =
(9)(9)(9)(9)/16 =
(81)(81)/16

81/16 = about 5 (it's actually a little more than 5, but I'm going to round down to 5).

So the above fraction is essentially just....

(81)(5) = 405 (actually a little bigger than that). This is far GREATER than 300, so 4.5 is TOO BIG. This confirms the range/correct answer.

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Re: If, x = 300^(1/4) then which of the following is true?  [#permalink]

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10 Mar 2016, 10:28
Here the exact value of x can be determined using approximating the root method => x= 4+44/369 = 4.1 approx
hence C
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Re: If, x = 300^(1/4) then which of the following is true?  [#permalink]

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15 Oct 2018, 02:49
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: If, x = 300^(1/4) then which of the following is true?   [#permalink] 15 Oct 2018, 02:49
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