CGPSC Prelims CSAT 2024 Solved Paper 2

Concept:The problem is a logical puzzle about floor occupancy.We need to check if the number of occupied flats on the IV floor is uniquely determined from the given constraints.Explanation:Let the number of flats on floors II, III, and IV be $n_2$, $n_3$, and $n_4$.Given $n_2 = 4$ and total flats = $13$, so $n_3 + n_4 = 9$.Each floor has between $3$ and $6$ flats, so possible pairs for $(n_3, n_4)$ are $(3,6)$, $(4,5)$, $(5,4)$, $(6,3)$.Since no floor can have more than $4$ occupied flats (only $4$ professions exist and no two same profession on a floor), and III floor is fully occupied, $n_3 \le 4$.Thus $n_3$ can be $3$ or $4$.Total occupants: $3$ managers, $2$ teachers, $2$ lawyers, and $1$ doctor.So total occupied flats = $3 + 2 + 2 + 1 = 8$.Total unoccupied = $13 - 8 = 5$.Using the condition that the lawyer on II floor has exactly one neighbor, we can construct multiple valid arrangements.For example, if $n_3=3, n_4=6$, one arrangement gives $o_4 = 3$ (occupied on IV) and another gives $o_4 = 2$.If $n_3=4, n_4=5$, we can have $o_4 = 1$ or $o_4 = 2$.Since different valid configurations yield different numbers of occupied flats on IV floor, the exact number cannot be determined.Answer:The number of flats occupied on the IV floor is not uniquely determined.Hence the answer is Data inadequate.