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Roots - GMAT Prep Problem - Please help

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rjanardhanan Just gettin' started! Default Avatar
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Roots - GMAT Prep Problem - Please help Post Thu Feb 16, 2012 8:27 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    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

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    Post Thu Feb 16, 2012 8:49 pm

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    Post Thu Feb 16, 2012 9:54 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 m > 4

    The correct answer is E.

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