If a and b are odd integers, which of the following must also be an odd integer?

Question

1. (A+1)b
2. (A+1)+b
3. (A+1)-b

Answer 1

If a is odd, then a+1 must be even.  So it can't be #1 because an even number times anything is always even.

 

What about 2 and 3?  Well, adding or subtracting an odd number to an even number always results in an odd number.  That's what's being done in both 2 (adding b -- an odd number -- to A+1 -- an even number) and 3 (subtracting b from A+1).  So both 2 and 3 would be odd.