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gmatusa2010
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m^n<n^m ==> m^n-n^m < 0 --(I)gmatusa2010 wrote:If m and n are positive integers, is m^n < n^m?
(1) m = root(n)
(2) n > 5
Statement 1: m = root(n) ==> n = m^2 -- (II)
From (I) and (II), m^(m^2) - m^2m < 0 -- (III)
Since m is positive, if m = 1, then (III) =0
if m = 2, then (III) = 0
if m > 2, then (III) > 0 -- (IV)
Hence, Statement 1 alone is not sufficient.
Statement 2: n > 5. Since we dont have any information about m, nor its relation with n, Statement 2 alone is not sufficient.
However, Statement I and Statement II together is sufficient, since based on (IV), the equation is always > 0 for all m > 2==> n > 4.
Hence, answer is C.
