If, for all positive integer values of \(n,\) \(P(n)\) is defined as the sum of the smallest \(n\) prime numbers, then

If, for all positive integer values of \(n,\) \(P(n)\) is defined as the sum of the smallest \(n\) prime numbers, then which of the following quantities are odd integers?

I. \(P(10)\)
II. \(P(P(10))\)
III. \(P(P(P(10)))\)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Answer: C

Source: Manhattan GMAT