Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. If x is a positive even integer and y is a positive odd integer, which of the following will be even?
Explanation: (B) Let x be Even (E) and y be Odd (O). (A) \(x^3 + y^2 = E^3 + O^2 = E + O = O\) (Odd). (B) \(3x + y + y^2 = O \cdot E + O + O^2 = E + O + O = E + E = E\) (Even). (C) \((x-y)(x+y) = x^2 - y^2 = E^2 - O^2 = E - O = O\) (Odd). (D) \(xy + y^2 = E \cdot O + O^2 = E + O = O\) (Odd). Only (B) is always even.
