Expected CAT Questions: Quants

Q1: Let r be the radius of the circular tracks. Length and breadth of the rectangular track are 4r and 2r respectively. Length (perimeter) of the rectangular track = 12r Length of the two circular tracks (figure of eight) = 4r If A and B have to reach their starting points at the same time, (12r/a)=4*pi*r/b (where a and b are the speeds of A and B respectively) (b/a)=4pi/12 (b-a)*100/a = 4.7% Hence, option 4. Q2: Let there be g girls and b boys. Number of games between two girls = gC2 Number of games between two boys = bC2 ∴ g(g – 1)/2 = 45 ∴ g2 – g – 90 = 0 ∴ (g – 10)(g + 9) = 0 ∴ g = 10 Also, b(b – 1)/2 = 190 ∴ b2 – b – 380 = 0 ∴ (b + 19)(b – 20) = 0 ∴ b = 20 ∴ Total number of games = (g + b)C2 = 30C2 = 435 ∴ Number of games in which one player is a boy and the other is a girl = 435 – 45 – 190 = 200 Hence, option 1.