p and q are integers. If p is divided by 2, the remainder is 1; and if ... ...

p and q are integers. If p is divided by 2, the remainder is 1; and if q is divided by 6, the remainder is 1. Which of the following must be true.   I. pq + 1 is even.  II. image is an integer. III. pq is a multiple of 12.


(A) I only
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set F: Number Theory