I'm guessing they picked an integer A for the average of the men's and women's percentages, and then a smaller (positive or negative) integer D for the deviatio

I'm guessing they picked an integer A for the average of the men's and women's percentages, and then a smaller (positive or negative) integer D for the deviation from this average for each sex. Then they could use A+D as the score for the women and A-D as the score for the men. If one of these is even (or odd) then so must the other be. It might be worth checking to see the distribution of D, compared to real variation between men and women.