Twenty-seven persons attend a party. Which one of the following statements can never be true?
Explanation:
Consider option 1: There may be a person in the party who is acquainted with all the twenty-six others and rest may have the same or different number of acquaintances.
Consider option 2: For all people to have a different number of acquaintances, the first person will have a maximum of 26 acquaintances, the second person will have 25 acquaintances and so on. Continuing in this manner, the last person will have 0 acquaintances, which is not possible.
Consider option 3: There may be a person in the party who has an odd number of acquaintances.
Consider option 4: In the case that none of the people attending the party know each other, then option 4 will be true, and hence it is not the correct option.
Hence, option (b).
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