ab + c = odd implieskalpanas wrote:Example: If a, b and c are integers and a.b + c is odd, what is true?
I. a + c is odd
II. b + c is odd
III. a.b.c is even
The answer provided for this is III.is this right?
Case 1: ab = even, c = odd
If a = even, b = even, then a + c = even + odd = odd, b + c = even + odd = odd, abc = even
If a = odd, b = even, then a + c = odd + odd = even, b + c = even + odd = odd, abc = even
If a = even, b = odd, then a + c = even + odd = odd, b + c = odd + odd = even, abc = even
Case 2: ab = odd, c = even
If a = odd, b = odd, then a + c = odd + odd = even, b + c = odd + even = odd, abc = even
It can be seen that abc = even in all the cases.
The correct answer is III.
