MAT Exam 2024 Paper

Concept:Use the compulsory book-pairing rules and fill all 10 slots with books that give the most points per slot.Explanation:Let $m, q, p, f$ be the number of management, mathematics, physics, and fiction books.We must have $f \ge 2m$ and $p \ge 2q$, with $m \ge 1$ and $q \ge 1$.The minimum compulsory set is: $m=1$, $q=1$, $f=2$, $p=2$.This uses $1+1+2+2=6$ books and gives $4+3+4+2=13$ points.So 4 more books can be carried.Adding 1 mathematics book forces 2 extra physics books, using 3 slots and adding $3+2(2)=7$ points.The last remaining slot is best used for 1 more physics book, adding $2$ points.Thus the best combination is $m=1$, $q=2$, $p=5$, $f=2$.Check: $p=5 \ge 2q=4$, and $f=2 \ge 2m=2$.Total books: $1+2+5+2=10$.Points: $4(1)+3(2)+2(5)+1(2)=22$.Answer:$22$ points, i.e. Option C.