Section-1: Numerical Logic Solved QuestionLogical Reasoning Discussion

 Q. Twenty-seven persons attend a party. Which one of the following statements can never be true?
 ✖ A. There is a person in the party who is acquainted with all the twenty-six others. ✔ B. Each person in the party has a different number of acquaintances. ✖ C. There is a person in the party who has an odd number of acquaintances. ✖ D. In the party, there is no set of three mutual acquaintances.

Solution:
Option(B) is correct

Consider option A: 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 B: 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 C: There may be a person in the party who has an odd number of acquaintances.

Consider option D: It may happen that a group of three people are mutual acquaintances.

Hence, option B.