The brothers Tom and Jason gave truthful answers to the questions about the number of members their chess club has . Tom said “ All the members of our club, except 5 girls are boys,”Jason said : “ Every six members always includes at least four girls. “ what is the least number of members in their chest club?
Let's analyze the statements given by Tom and Jason separately.
Statement 1: Tom said, "All the members of our club, except 5 girls, are boys."
From this statement, we can infer that there are at least 5 girls in the chess club.
Statement 2: Jason said, "Every six members always includes at least four girls."
From this statement, we can deduce that for every group of 6 members, at least 4 of them are girls.
To find the minimum number of members in the chess club, we need to determine the smallest possible group size that satisfies both statements.
If there are 6 members in the chess club (group size = 6), then from Jason's statement, at least 4 of them must be girls. However, this contradicts Tom's statement, which mentions that there are only 5 girls (not at least 4) in the club.
If there are 7 members in the chess club (group size = 7), then from Jason's statement, at least 4 of them must be girls. This is valid as long as the 5 girls mentioned by Tom are part of this group of 7. The remaining 2 members could be boys. Therefore, with 7 members, both statements can be true.
Hence, the least number of members in their chess club is 7.