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)))
Choose the correct answer:
A) I only	B) I and II only	C) I and III only	D) II and III only	E) I, II, and III
2 is the only even prime number. Now, the sum of first 10 prime numbers = 9*odd + 2 = odd. Thus P(10) = odd.   Again, the sum of the first n -odd primes = (n-1)*odd+2 = even.Thus, p(P(10)) = even.   Similarly, the sum of the first m - even primes = (m-1)*odd+2 = odd.   I and III.   ANSWER:I and III only
<result>C</result>
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)))