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26 Jul 2014, 13:02
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:48) correct
30%
(02:06)
wrong
based on 867
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Date
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Not Attempted Yet
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
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
26 Jul 2014, 13:09
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goodyear2013
\(x^4=300\):
4^4 = 16^2 = 256, hence x is little bit greater than 4.
Answer: C.
06 Jan 2016, 22:12
Kudos
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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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich
