You are invited to a welcome party with 25 fellow team members. Each of the fellow members shakes hands with you to welcome you. Since a number ofpeople in the room haven't met each other, there's a lot ofrandom handshaking among others as well. Ifyou don't know the total number of handshakes, can you say with certainty that there are at least two people present who shook hands with exactly the same number of people?

It is widely assumed that people need to engage in intellectual activities such as solving crossword puzzles or mathematics problems in order to maintain mental sharpness as they age. in fact, however, simply talking to other people—that is, participating in social interaction, which engages many mental and perceptual skills—suffices. evidence to this effect comes from a study showing that the more social contact people report, the better their mental skills. which of the following, if true, most seriously weakens the force of the evidence cited? (a) as people grow older, they are often advised to keep exercising their physical and mental capacities in order to maintain or improve them. (b) many medical conditions and treatments that adversely affect a person's mental sharpness also tend to increase that person's social isolation. (c) many people are proficient both in social interactions and in solving mathematical problems. (d) the study did not itself collect data but analyzed data bearing on the issue from prior studies. (e) the tasks evaluating mental sharpness for which data were compiled by the study were more akin to mathematics problems than to conversation.