2. Which of the following numbers is odd for any integer values of $k$ ?
(A) $2007+k^{3}$;
(B) $2007+7 k$;
(C) $2007+2 k^{2}$;
(D) $2007+2007 k$;
(E) $2007 k$.
2. Ans: (C)
Because $2 k^{2}$ is always even, thus $2007+2 k^{2}$ is always odd. For other statements, either $k=1$ or $k=0$ gives a counterexample.