CAT Question Bank  Games & Tournaments

Q28) Two teams P and Q contest in a game of tug of war. Team P has ‘n’ players with an average weight of ‘a’ kgs, ‘a’ being an integer. Team Q also has ‘n’ players with an average weight of ‘a’ kgs. The rule of the game is that the team that wins two rounds consecutively wins the game. However, once a team wins a round, the other team adds one more player to their team such that their average weight increases by 1 kg for the next round. The game progressed as follows.
Round 1: Team Q won
Round 2: Team P won
Round 3: Team Q won
Round 4: Team P won
Round 5: Team Q won
Round 6: Team P won
Round 7: Team P won
Which of the following can be the sum of the weights of the new players added in team P?
(a) 248
(b) 250
(c) 249
(d) 247[OA: C]

First player to be added brings in an excess of 1 kg for each player (including himself) over the average, a.
This means his weight is a+n+1.
The second player to be added brings in an excess of 1 for all including himself over the previous average, a+1. This means his weight is a+1+n+2
Third player weighs a+2+n+3.
Total weight is 3a + 3n + 9. This is divisible by 3. So the total can be 249.
[@rajesh_balasubramanian ]

Q29) Ram and Shyam were playing a game that involved picking up marbles from a table. Each player in his turn has to pick up at least 2 or at most 7 marbles, except when there is only one marble left on the table in which case, he has to pick up that marble. The game ends when all the marbles on the table are picked up. If the game starts with 62 marbles and it is Ram's turn to play, then how many marbles should he pick up so as to ensure his win?
Assume that both play intelligently so as to win the game.
Assume that the player who picks the last marble LOSES the game.
a. 4 or 3
b. 6 or 7
c. 5 or 4
d. 2 or 1

Q30) In a soccer tournament n teams play against one another exactly once. The win fetches 3 points, draw 1 each and loss 0. After all the matches were played, it was noticed that the top team had unique number of maximum points and unique least number of wins. What can be the minimum possible value of n?
a) 5
b) 6
c) 7
d) 8
e) none of these

@rowdyrathore Shouldnt it be smallest value of n greater than 5 , or any other limiting factor?

@rowdyrathore We select two points out of 98 to make a chord, given by 98C2. This gives 4753 , which leaves a remainder on dividing by 3 .thus anthony wins.

@rowdyrathore The rth match in Round 1 will be played between Seed ‘r’ and Seed ‘n+1r’
so 7th match will be played between seed 7 and seed 32+17=26
and 10 th match will be played between seed 10 and seed 32+110=23

@rowdyrathore please provide solution

@RowdyRathore what is the answer??
