If a and n are integers and n > 1, is n odd?
(1) a^(n-1) > a^n
(2) a^n > a^(3n)
Since n>1, each statement indicates the following:
(integer a)^(smaller positive power) > (integer a)^(bigger positive power).
This relationship is valid only if a<0 and the exponent on the lefthand side is EVEN (so that the lefthand side becomes positive), while the exponent on the righthand side is ODD (so that the righthand side stays negative).
In each statement, for the exponent on the righthand side to be ODD, n itself must be odd.
Thus, each statement on its own is SUFFICIENT.
The correct answer is
D.
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