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Roots - GMAT Prep Problem - Please help

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by GMATGuruNY » Thu Feb 16, 2012 7:49 pm
I posted a solution here:

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by Anurag@Gurome » Thu Feb 16, 2012 8:54 pm
rjanardhanan wrote:If M = (4)^1/2 + (4)^1/3 + (4)^1/4 , then the value of M is,

Less than 3
Equal to 3
Between 3 and 4
Equal to 4
Greater than 4
m = √4 + (4)^(1/3) + (4)^(1/4)
m = 2 + (4)^(1/4) + (4)^(1/3)
m = 2 + (2²)^(1/4) + (4)^(1/3)
m = 2 + √2 + (4)^(1/3)
m = 2 + 1.4 + (4)^(1/3)
m = 3.4 + (4)^(1/3)

To find (4)^(1/3), we know that (4)^(1/4) is 1.4 approx, so (4)^(1/3) should lie between 1.4 and 2

Therefore, m > 4.8 and hence [spoiler]m > 4[/spoiler]

The correct answer is E.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
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