What must be true about the male and female lineups if no two of the same gender can be adjacent?

The correct answer is that there must be at least as many females as males. This is necessary to ensure that no two individuals of the same gender can be adjacent in the lineup.

To visualize why this is true, consider a simple arrangement where you have a certain number of males. For every male, there needs to be enough females to separate them. If you have fewer females than males, after placing a male, you might run out of females to separate them, which would result in at least two males being adjacent—this directly contradicts the requirement that no two individuals of the same gender can be next to each other.

For example, if you have three males, you would need at least three females to place them in between each male and on both ends of the lineup (M-F-M-F-M for three males and three females). If the number of females was less than males, say only two females for three males, you could not create a valid lineup without having at least one pair of males adjacent.

Therefore, maintaining a count of at least as many females as males is essential for achieving the stipulated arrangement, fulfilling the condition of non-adjacency for individuals of the same gender.