Is the product of integers \(M\) and \(N\) even?

[VJesus12]

Is the product of integers \(M\) and \(N\) even?

(1) \(N\) can be expressed as a difference of squares of two consecutive prime numbers at least one of which is odd. \(M\) can be expressed as a product of two natural numbers \(P\) and \(Q,\) where \(2P + 1= Q.\)

(2) \(N\) can be expressed as a difference of squares of two consecutive prime numbers that lie at a distance of \(2\) units. \(M\) is the sum of all the numbers from \(1\) to \(Z\) where \(Z+1\) is a multiple of \(4.\)

Answer: B

Source: e-GMAT