Logic

Functions 1. a 2. d Functions 2 1. d 2. a 3. b Five Machines 1. a 2. a ABC Gold Cup 1. c 2. b 3. d 4. c 5. c

(CAT 2000) Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup. The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage, teams in each group are ranked on the basis of total points to dete...

(CAT 2000) There are five machines — A, B, C, D, and E — situated on a straight line at distances of 10 m, 20 m, 30 m, 40 m and 50 m respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw materials are located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the ne...

(CAT 2000) For three distinct real numbers x, y and z, let f(x, y, z) = Min(Max(x, y), Max(y, z), Max(z, x)) g(x, y, z) = Max(Min(x, y), Min(y, z), Min(z, x)) h(x, y, z) = Max(Max(x, y), Max(y, z), Max(z, x)) j(x, y, z) = Min(Min(x, y), Min(y, z), Min(z, x)) m(x, y, z) = Max(x, y, z) n(x, y, z) = Min(x, y, z) 1. Which of the following is necessarily greater than 1? a. [h(x, y, z) – f(x, y, z)] / j(x, y, z) b. j(x, y, z) / h(x, y, z) c. f(x, y, z) / g(x, y, z) d. [f(x, y, z) + h(x, y, z) – g(x, y, z)] / j(x, y, z) 2. Which of the following expressions is necessarily equal to 1? a. [f(x, y, z) – m(x, y, z)] / [g(x, y, z) – h(x, y, z)] b. [m(x, y, z) – f(x, y, z)] / [g(x, y, z) – n(x, y, z)] c. [j(x, y, z) – g(x, y, z)] / h(x, y, z) d. [f(x, y, z) – h(x, y ,z)] / f(x, y, z) 3. Which of the following expressions is indeterminate? a. [f(x, y, z) – h(x, y, z)] / [g(x, y, z) – j(x, y, z)] b. [f(x, y, z) + h(x, y, z) + g(x, y, z) + j(x, y, z)] / [j(x, y, z) + h(x, y, z...

(CAT 2000) A, B and C are three numbers. Let @ (A, B) = Average of A and B, / (A, B) = Product of A and B, and × (A, B) = The result of dividing A by B. 1. The sum of A and B is given by a. / (@ (A, B), 2) b. × (@ (A, B), 2) c. @ (/ A, B), 2) d. @ (× (A, B), 2) 2. Average of A, B and C is given by a. @ (/ (@ (/ (B, A), 2), C), 3) b. × (@ (/ (@ (B, A), 3), C), 2) c. / (×(× (@ (B, A), 2), C), 3) d. / (× (@ (/ (@ (B, A) 2), C), 3), 2) For answers click here .