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

Question

If  X = P*N^K + P  where P, N and K are positive integers, is X divisible by 2?

(1) N + KN = 915
(2)  P^{35} + 35^P  is Even

Kvivekee · Answer

Statement 2 is sufficient

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divyadna · Answer

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gmatophobia · Answer

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

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