If \(a, b,\) and \(c\) are positive integers, what is the remainder when \(a - b\) is divided by \(6?\)

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If \(a, b,\) and \(c\) are positive integers, what is the remainder when \(a - b\) is divided by \(6?\)

(1) \(a = c^3\)
(2) \(b = (c - 2)^3\)

Answer: C

Source: Manhattan GMAT