If X = P*N^K + P where P, N and K are positive integers, is X

\(X = P*N^K + P\)

\(X = P(N^K + 1)\)

Question Is X divisible by 2 ?

In other words, we want to know if X is even.

As X is a product of two integers , if either P or \((N^K + 1)\) is even, X is even.

Statement 1

(1) N + KN = 915

N(1+K) = odd

As its given that P, N and K are positive integers, we can conclude that the individual elements P and (K+1) are odd. (odd * odd = odd)

As, 1+ K = odd ⇒ K is even.

Let's move back to our base equation

\(X = P(N^K + 1)\)

As N is odd, \(N^K \) is odd, and \((N^K + 1)\) is even. Therefore we have one even term in the product. Hence the entire product is divisible by 2.

Sufficient. We can eliminate B, C and E.

Statement 2

\(P^{35} + 35^P\) = Even

\(35^P\) = odd

\(P^{35}\) = Even - Odd = Odd

P is odd.

We have no information on \((N^K + 1)\).

Hence this statement alone is not sufficient to answer the question "Is X divisible by 2"

Option A