Games and Tournament Questions for CAT Set-2 PDF

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Games and Tournament Questions for CAT Set-2 PDF

Download important CAT Games and Tournament Questions with Solutions PDF based on previously asked questions in CAT exam. Practice Games and Tournament Questions with Solutions for CAT exam.

Instructions

Directions for the next 5 questions:

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 determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.

Question 1:Â What is the total number of matches played in the tournament?

a)Â 28

b)Â 55

c)Â 63

d)Â 35

Question 2:Â The minimum number of wins needed for a team in the first stage to guarantee its advancement to the next stage is:

a)Â 5

b)Â 6

c)Â 7

d)Â 4

Question 3:Â What is the highest number of wins for a team in the first stage in spite of which it would be eliminated at the end of first stage?

a)Â 1

b)Â 2

c)Â 3

d)Â 5

Question 4:Â What is the number of rounds in the second stage of the tournament?â€™

a)Â 1

b)Â 2

c)Â 3

d)Â 4

Question 5:Â Which of the following statements is true?

a)Â The winner will have more wins than any other team in the tournament.

b)Â At the end of the first stage, no team eliminated from the tournament will have more wins than any of the teams qualifying for the second stage.

c)Â It is possible that the winner will have the same number of wins in the entire tournament as a team eliminated at the end of the first stage.

d)Â The number of teams with exactly one win in the second stage of the tournament is 4.

Instructions

Six teams are playing in a hockey tournament where each team is playing against every other team exactly once. At an intermediate stage, the status is as follows:

Notes:
â€¢ The team that scores more goals than it concedes wins the match, while if both the teams score the same no. of goals, the match is declared drawn.
â€¢ Ina match played between Team X and Team Y, if team X scores 1 and concedes none. then the score line would read: Team X â€” Team Y (1-0)

Question 6:Â Which of the following matches are yet to be played?

a)Â Team A – Team B and Team C – Team D

b)Â Team C – Team D and Team E – Team F

c)Â Team E – Team F and Team B – Team D

d)Â Team C – Team D and Team A – Team E

e)Â Team A – Team B and Team E – Team F

Question 7:Â Which of the following score line is a possible outcome in the tournament?

a)Â Team A – Team D (1-0)

b)Â Team A – Team E (2-1)

c)Â Team B – Team D (1-0)

d)Â Team C – Team F (2-0)

e)Â None of the above

Question 8:Â Which of the following score line is not a possible outcome in the tournament?

a)Â Team A – Team F (4-0)

b)Â Team B – Team F (4-0)

c)Â Team C – Team D (0-0)

d)Â Team C – Team E (2-0)

e)Â All of the above options are possible

In 1st stage there were 2 groups each group played 28 matches as $^8C_2$ = 28. So total 56 matches after 1st stage . IN 1st round of stage 2, 4 matches are played and in the next round we have 4 teams .The winner is one who defeats every team out of remaining 3Â matchesÂ . so 3 matches more needed. In total 56+4+3=63.

Let us first try to find the maximum number of points with which a team cannot advance to the second stage.

For this to happen the top five teams should have highest possible equal number of points and one team does not advance after the tie breaker.

To maximize the points of top 5 teams all of the top 5 teams should win their matches with the bottom 3 teams. Now each team has 3 points.

The top 5 teams play 5C2 = 10 matches among themselves. There are 10 points to be won from these 10 matches.

Now as all the top 5 teams should have equal number of points each team gets 2 points from these games.

In all each top 5 team gets 3+2 = 5 points each.

In this case after getting 5 points also one of the top 5 teams will not advance to the second round.

Thus the maximum number of points with which a team cannot advance to the second stage is 5.

Therefore at least 6 wins are required for a team to guarantee its advancement to the next stage.

There are 28 matches in the 1st round of 8 player group so in total 28 wins.To find this, we need the top 5 teams to win nearly equal matches. So Let each of the top 5 teams win 5 matches each and the remaining 3 matches are won by the bottom 2 teams. The qualifiers will be decided based on the tie breaking rules. Hence, even with 5 wins a team may end up not qualifying for the next round. Thus, option D is the correct answer.

2nd stage 1st round has 8 teams , 2nd round will have 4 teams and 3rd round 2 teams where the winner wins .

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Consider the below case.

If D wins the tournament he would have 5 wins. But if P loses in second round, he would have 7 wins. Hence option A is incorrect.

We can see that T has more wins than D. Hence option B is incorrect.

Consider the below scenario:

We can see that 2 teams have one win each in the second stage. Hence option D is incorrect.

Consider the following scenario.

If D wins the tournament he would have 5 wins. But T would lose the tournament with 5 wins. Hence option C is correct.