Question number 10. Two brothers, Gervase and Protase, answered truthfully a question regarding the number of members on the debate team, which they are both part. Gervase said, all the team members except five are women. Protase said, among any six randomly chosen members of our team, there are always at least four women. How many members belong to the debate team? What we have so far is that the two brothers are on the team, so there are at least two men and out of all the team members, all except five are men, so that means five, exactly five are women. And so this tells us that we have at least seven members. Then looking at the second statement, out of any six randomly chosen members, always four are women, so always four of six are women. And if we try to increase the number of the members on the team past seven, we can add either a man or a woman. So adding a woman is not allowed because then we would increase the number of women past five and that is breaking the first statement. And if we add one more man, then we could choose three men and three women and violate the second statement. So adding a woman violates the first statement and adding a man violates the second statement, both of which are true, therefore we conclude that there are at most seven members. And together, combining this information, we see that there are exactly seven, so the answer is B.

debate team

seven members

women

men

composition