Remainders

[swerve]

If \(p\) and \(q\) are positive 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. \(pq/2\) is an integer
III. \(pq\) is a multiple of \(12\)

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

The OA is A