Final answer:
The lowest percentage of voters that must be women for Candidate B to win in an election sharply divided along gender lines is 50%, given that all women support Candidate B and all men do not.
Step-by-step explanation:
To determine the lowest percentage of voters that must be women on election day for Candidate B to win, assuming that voting is sharply divided along gender lines, we can use an illustrative example. Let's say in this scenario, women overwhelmingly support Candidate B. For Candidate B to achieve a simple majority, we should consider the extreme case in which all men vote against Candidate B and all women vote for Candidate B.
In this case, Candidate B would need just over 50% of the votes to win. If we assume a 50-50 split in the electorate, then the lowest percentage of voters who are women for B to win would theoretically be just over 50%. However, if women are more likely to vote than men, which is suggested by real-world voting patterns, the proportion of women voters needed could be lower.
Without specific numbers for preferences in this scenario, the safe answer would be that at least 50% of voters must be women for Candidate B to win, since any number below 50% would automatically give men (assuming they all vote against Candidate B) a majority.