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

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) ...
(C) ...
(D) ...
(E) ...

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

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Posted: 05/14/2012 16:13
If p=5 and q=7 then pq+1=31
If p=q=1 then pq/2=1/2
If p=3 and q=7 then pq= 21
The answer should none of the above right? Or am I missing something?
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Posted: 05/14/2012 16:27
Alex, in your first example, pq + 1 = 35 + 1 = 36, not 31.

Acc to the facts given, p and q are odd numbers (since there is a remainder of 1 when they are divided by 2 or 6). The product of odd numbers are always odd numbers, so when you add 1, you always get an even number.
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