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.
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?
1 answer