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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.   is an integer. III.  pq is a multiple of 12.
(A) I only    
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Press: Set E - Number Theory

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