If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?
1. wx + yz is odd
2. wz + xy is odd
Pls. give me your reasoning! Thanks
B. Just think about it.
Only way for WX+YZ to be odd is if and only if either WX or YZ are odd. Both cannot be odd or even. 1 must be completely odds. Thus that means W*X or Y*Z both of one of these are odd.
However we could have 3 of the variables as odds.
Ex/ 12/4+3/1 or just 12/3+3/1 thus we have a Y and N situation.
2: Again one of these must be odd. Thus WZ or XY are odd and W and Z or X and Y are both odd.
Notice that something changes here though. We must have a third odd in this case. Because we cannot have an odd number in the numerator divided by an even number in the denominator... This will not result in an integer!!!
Thus we have 3 odds. Doesnt matter which of the variables, but just notice that. Thus we have O/O+E/O ---> O+Even. We have an odd number.