**(CAT 2008)**

**Directions for Questions 1 and 2: **

Marks (1) if Q can be answered from A alone but not from B alone.

Marks (2) if Q can be answered from B alone but not from A alone.

Marks (3) if Q can be answered from A alone as well as from B alone.

Marks (4) if Q can be answered from A and B together but not from any of them alone.

Marks (5) if Q cannot be answered even from A and B together.

In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:

(a) If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.

(b) If the number of players, say n, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n − 1) players are grouped into (n − 1)/2 pairs. The players in each pair play a match against each other and the winners moves on to the next round. No player gets more than one bye in the entire tournament.

Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n + 1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament.

**[1] Q: What is the number of matches played by the champion? **

A: The entry list for the tournament consists of 83 players.

B: The champion received one bye.

**[2] Q: If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n? **

A: Exactly one player received a bye in the entire tournament.

B: One player received a bye while moving on to the fourth round from third round

**(CAT 2008)**

**Directions for Questions 1 and 2: **

Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.

**[1] Which of the following cannot be true? **

(A) At least two horses finished before Spotted

(B) Red finished last

(C) There were three horses between Black and Spotted

(D) There were three horses between White and Red

(E) Grey came in second

**[2] Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true? **

(A) Spotted came in first

(B) Red finished last

(C) White came in second

(D) Black came in second

(E) There was one horse between Black and White

**(CAT 2008)**

**Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surface resting on the base of the cone. Find the largest possible total surface area (in sq. cm) of the cylinder.**

(A) 100π/3

(B) 80π/3

(C) 120π/7

(D) 130π/9

(E) 110π/7

**(CAT 2008)**

**Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to **

(A) 6:15 am

(B) 6:30 am

(C) 6:45 am

(D) 7:00 am

(E) 7:15 am

**(CAT 2008)**

**Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the circle of the other. What is the area (in sq cm) of the intersecting region?**

(A) π/3 - √3/4

(B) 2π/3 + √3/2

(C) 4π/3 - √3/2

(D) 4π/3 + √3/2

(E) 2π/3 + √3/2