If A, B, C, and D are integers such that A - C + B is even and D + B - A is odd, which of the following expressions is always odd?
Choose the correct choice from the following choices: A) A + D B) B + D C) C + D D) A + B E) A + C
Even matrix method takes more than two mins in this problem since you have to jot down the even and odd values.   Try subtracting the equations   (A - C + B) - (D + B - A) = 2A-(C+D)   Even - Odd = Odd   So 2A-(C+D) is odd   2A is always even , so the subtrahend should always be odd, so C+D is odd.   ANSWER:C + D
<result>C</result>
If A, B, C, and D are integers such that A - C + B is even and D + B - A is odd, which of the following expressions is always odd?