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

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