If a, b, and c are integer and ab + c is odd, which of the must be true?
I. a + c is odd
II. b + c is odd
III. abc is even Choose the correct choice from the following
A) I only
B) II only
C) III only
D) I and III only
E) II and III only
Personally I'd approach this question in another way.   ab+c=odd, means:   1. ab=even (which means that at least one of them is even) and c=odd   OR:   2. ab=odd (which means that both are odd) and c=even   We can see that in both cases at least one is even thus option III (abc=even) is always true.   Now, for I: if c=odd(case 1) and a=odd(so b=even) then a+c=even≠odd, so this option is not always true.   Exactly the same for option II: if c=odd (case 1) and b=odd (so a=even) then b+c=even≠odd, so this option is not always true.   Answer: III only (III only).
<result>C</result>
If a, b, and c are integer and ab + c is odd, which of the must be true?
I. a + c is odd
II. b + c is odd
III. abc is even