Gates Foundation IT Program Manager interview questions

Applied online and then was contacted by contracted IT HR. Interviewed with the hiring manager we seemed to get along and I thought a clear understanding of the position was established. Next steps was an all day onsite interview with all teams this position would work with. At the end of the day met with Department Head. I sensed when asked once again what my "strategy" would be for the position that I would not be selected. I could only go with the job description and what I learned from the team members. I have had this kind of subjective question which resulted in the same declination before. Wondering if other female/minorities have encountered this tactic.