CAT 2003 Slot 1 — QA Question 15
Answer the following question based on the information given below.
A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1, the south end point of OR to E2, the east endpoint of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and km/hr on all the chord roads.
Twenty-seven persons attend a party. Which one of the following statements can never be true?
Answer & solution
- A
There is a person in the party who is acquainted with all the twenty-six others.
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.
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).