25+ Games and Tournaments CAT Questions PDF Download with Answers for Practice

Overview: Get ready to practice the 25+ commonly asked "Games and tournaments CAT questions" with us. Boost your preparation by practicing these questions!

Cracking the Common Admission Test (CAT) often feels like a high-stakes game in itself, and among the many challenging sections, Games and Tournaments questions for CAT stand out as a particularly intriguing and often perplexing area. 

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These CAT questions on games and tournaments demand a keen understanding of logical deduction, strategic thinking, and the ability to visualize complex scenarios. 

Read on to know more about it!

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What are Games and Tournaments CAT Questions?

Games and Tournaments CAT Questions test a candidate’s ability to analyze and interpret complex game formats, match schedules, and tournament outcomes. These questions often involve ranking players or teams, league formats, knockout rounds, and point-based systems.

The questions usually appear in the form of Logical Reasoning sets, where candidates need to solve 4–6 sub-questions based on a single game or tournament setup. These CAT questions are time-consuming and require structured thinking.

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Games And Tournaments CAT Questions 2024

1. A tournament has 8 teams. Each team plays every other team exactly once. How many matches are played in the tournament?

A. 14

B. 28

C. 56

D. 16

Correct Answer: 28
Explanation: For a round-robin tournament, the number of matches is calculated using combinations, specifically nC2, where 'n' is the number of teams. This formula ensures that each team plays every other team exactly once, without repetition.

2. In a chess tournament, each player plays every other player twice. If 7 players participate, how many games are played in total?

A. 7

B. 21

C. 49

D. 42

Correct Answer: 42

Explanation: When each player plays every other player twice, the number of games is 2 * nC2, where n is the number of players. For 7 players, this is 2 * (7*6)/2 = 42.

3. A league has 10 teams. In the first phase, each team plays every other team once. In the second phase, the top 4 teams play each other once. What is the total number of matches played across both phases?

A. 60

B. 45

C. 51

D. 55

Correct Answer: 51

Explanation: The first phase has 10C2 = 45 matches. The second phase has 4C2 = 6 matches. Total matches = 45 + 6 = 51.

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4. In a knockout tournament, there are 32 participants. How many matches are played to determine the winner?

A. 32

B. 31

C. 64

D. 16

Correct Answer: 31

Explanation: In a knockout tournament, each match eliminates one participant, so to determine a single winner from 'n' participants, 'n-1' matches are required.

5. A game involves rolling two fair dice. Player A wins if the sum of the dice is 7. Player B wins if the sum is 10. If neither sum occurs, no one wins. What is the probability that Player A wins?

A. 5/ 36

B. 1/ 6

C. 1/ 9

D. 1/ 12

Correct Answer: 1/ 6

Explanation: The total number of outcomes when rolling two dice is 36. The outcomes that sum to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) – 6 outcomes. So the probability is 6/36 = 1/6.

6. In a game, a coin is tossed three times. Player X wins if there are exactly two heads. Player Y wins if there are exactly three tails. What is the probability that Player X wins?

A. 3/ 8

B. 1/ 2

C. 1/ 8

D. 7/ 8

Correct Answer: 3/ 8

Explanation: The total possible outcomes are 2^3 = 8 (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT). Outcomes with exactly two heads are HHT, HTH, THH – 3 outcomes. So the probability is 3/8.

7. Four players, P, Q, R, S, play a game. Each player has a unique number from 1 to 4. They simultaneously reveal their numbers. If a player's number matches their position in a predetermined sequence (e.g., P is 1st, Q is 2nd, R is 3rd, S is 4th), they score a point. What is the probability that exactly two players score a point?

A. 1/ 24

B. 1/ 3

C. 1/ 8

D. 1/ 4

Correct Answer: 1/ 4

Explanation: This problem involves derangements. Total permutations are 4! = 24. Number of ways to choose 2 players to score points = 4C2 = 6. The remaining 2 players must not score (derangement of 2 elements, D2 = 1). So, 6 * 1 = 6 favourable outcomes. Probability = 6/24 = 1/4.

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Games And Tournaments CAT Questions 2023

8. A game involves drawing 3 cards from a standard deck of 52 cards. Player A wins if all three cards are spades. Player B wins if all three cards are aces. What is the probability that Player A wins?

A. 286/ 22100

B. 11/ 850

C. 13/ 52

D. 1/ 5525

Correct Answer: 11/ 850

Explanation: Number of ways to choose 3 spades from 13 is 13C3 = (13*12*11)/(3*2*1) = 286. The total ways to choose 3 cards from 52 is 52C3 = (52*51*50)/(3*2*1) = 22100. Probability = 286/22100 = 11/850.

9. In a series of games between two teams, X and Y, the first team to win 3 games wins the series. If Team X has a 60% chance of winning any single game, what is the probability that Team X wins the series in exactly 4 games?

A. 0.216

0.2592

0.3456

0.1296

Correct answer: 0.2592

Explanation: Team X must win 3 games and lose 1. The last game must be won by X. So, in the first 3 games, X must win 2 and lose 1. The number of ways this can happen is 3C2. Probability = 3C2 * (0.6)^2 * (0.4)^1 * 0.6 (for the 4th win) = 3 * 0.36 * 0.4 * 0.6 = 0.2592.

10. A game involves drawing balls from an urn containing 5 red and 5 blue balls. Two balls are drawn without replacement. Player A wins if both balls are red. Player B wins if both balls are blue. What is the probability that Player A wins?

A. 5/ 10

B. 2/ 9

C. 1/ 2

D. 1/ 9

Correct answer: 2/ 9

Explanation: The probability of drawing two red balls is (5/10) * (4/9) = 20/90 = 2/9.

11. Three players, X, Y, and Z, are playing a game. In each round, one player is eliminated. The probability of X being eliminated in a round is 0.4, Y being eliminated is 0.3, and Z being eliminated is 0.3. What is the probability that X is the first player to be eliminated?

A.0.3

B.0.4

C.0.12

D.0.7

Correct answer: 0.4

Explanation: Since elimination is independent and mutually exclusive, the probability of X being the first to be eliminated is simply their elimination probability in any given round.

12. In a game show, there are 3 doors. Behind one door is a car, and behind the other two are goats. You pick a door. The host, who knows where the car is, opens one of the other two doors, always revealing a goat. Then, the host offers you the option to switch to the remaining unopened door. What is the probability of winning the car if you switch?

A. 1/ 3

B. 1

C. 1/ 2

D. 2/ 3

Correct answer: 2/ 3

 Explanation: By switching, you are essentially betting that your initial choice was incorrect (which has a 2/3 probability). The host's action provides information, concentrating the probability of the car being behind the unchosen, unopened door to 2/3.

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13. A game involves picking a number from 1 to 10. If the number is prime, you win. If it's a multiple of 3, you lose. Otherwise, it's a draw. What is the probability of winning?

A.0.4

B.0.5

C.0.6

D.0.3

Correct answer: 0.4

Explanation: The prime numbers between 1 and 10 are 2, 3, 5, 7. There are 4 prime numbers. So, the probability of winning is 4/10 = 0.4.

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Games And Tournaments CAT Questions 2022

14. In a game, two players take turns rolling a die. The first player to roll a 6 wins. What is the probability that the first player wins?

A. 5/ 11

B. 6/ 11

C. 1/ 2

D. 1/ 6

Correct answer: 5/ 11

Explanation:  Let p be the probability of rolling a 6 (1/6) and q be the probability of not rolling a 6 (5/6). The first player wins if they roll a 6 on their first turn, or on their second turn after both missed, and so on. This is a geometric series: p + (q*q)p + (q*q*q*q)p + ... = p / (1 - q^2) = (1/6) / (1 - 25/36) = (1/6) / (11/36) = 6/11.

15. A game involves two players, A and B, drawing cards from a deck. Player A draws first, then B, then A again, and so on. The first player to draw a King wins. If there are 4 Kings in a standard 52-card deck and cards are not replaced, what is the probability that Player A wins?

A. 7/ 13

B. 6/ 13

C. 1/ 2

D. 4/ 52

Correct Answer:  7/ 13

Explanation: This is a complex probability calculation involving conditional probabilities and summing possibilities. The exact probability can be derived using conditional probabilities for each turn. It involves summing infinite series or using a recursive approach.

16. In a two-player game, a fair coin is tossed repeatedly. Player 1 wins if the sequence HHH appears. Player 2 wins if the sequence TTH appears. Who has a higher probability of winning?

A. Player 2

B. Cannot be determined

C. Player 1

D. Both have equal probability.

Correct answer: Player 2

Explanation: This is a classic problem in probability, and surprisingly, TTH has a higher probability of appearing first than HHH. This is due to the overlapping nature of the sequence HHH, where TTH can 'reset' the count more effectively.

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17. A game has 5 rounds. In each round, two players, A and B, compete. Player A has a 0.6 probability of winning a round. The overall winner is decided by the best of 5 rounds. What is the probability that Player A wins the game in exactly 3 rounds?

A. 0.216

B. 0.36

C. 0.432

D. 0.144

Correct answer: 0.216

Explanation: This is the probability that Player A wins all 3 rounds: 0.6 * 0.6 * 0.6 = 0.216.

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18. Consider a game where two players, A and B, take turns drawing one card from a deck of 10 cards numbered 1 to 10. The first player to draw an even number wins. If cards are not replaced, what is the probability that Player B wins?

A. 5/ 18

B. 5/ 10

C. 4/ 9

D. 5/ 9

Correct Answer: 5/ 18

Explanation: Player B wins if A draws an odd number AND B draws an even number. P(A draws odd) = 5/10. P(B draws even | A draws odd) = 5/9. So, P(B wins on their first turn) = (5/10) * (5/9) = 25/90 = 5/18.

19. In a tournament, there are 6 teams. Each team plays every other team twice. What is the total number of matches played?

A. 60

B. 30

C.36

D. 15

Correct Answer: 30

Explanation: If each team plays every other team twice, the number of matches is 2 * (nC2), where n is the number of teams. So, 2 * (6C2) = 2 * (6*5)/2 = 2 * 15 = 30.

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Games And Tournaments CAT Questions 2021

20. In a game, two players take turns rolling a fair six-sided die. The first player to roll a prime number (2, 3, 5) wins. What is the probability that the first player wins?

A. 3/ 5

B. 2/ 3

C. 1/ 3

D. 1/ 2

Correct Answer: 3/ 5

Explanation: Let P(prime) = 3/6 = 1/2. Let P(not prime) = 3/6 = 1/2. Player 1 wins if they roll a prime on their turn. P(P1 wins) = P(prime) + P(not prime on P1's 1st turn) * P(not prime on P2's 1st turn) * P(prime on P1's 2nd turn) + ... This is a geometric series sum: (1/2) / (1 - (1/2)*(1/2)) = (1/2) / (1 - 1/4) = (1/2) / (3/4) = 2/3.

21. In a knockout tournament with 'n' teams, what is the maximum number of byes that can be given in the first round?

A. n/ 2

B. The next power of 2 minus n

C. N-1

D. N

Correct Answer: the next power of 2 minus n

Explanation: Byes are given to make the number of teams a power of 2 for a smooth knockout bracket. If 'n' is not a power of 2, the number of byes is the smallest power of 2 greater than 'n', minus 'n'.

22. A game involves drawing 2 balls from a bag containing 3 red, 4 blue, and 5 green balls. Player A wins if both balls are of the same color. Player B wins if both balls are of different colors. What is the probability that Player A wins?

A. 19/ 66

B. 47/ 66

C. 1/ 2

D. 1/ 3

Correct Answer: 1/ 3

Explanation: Total balls = 12. P(2 red) = (3C2)/(12C2) = 3/66. P(2 blue) = (4C2)/(12C2) = 6/66. P(2 green) = (5C2)/(12C2) = 10/66. P(A wins) = (3+6+10)/66 = 19/66.

23. In a game, you bet on the outcome of rolling two fair dice. If the sum is even, you win \$10. If the sum is odd, you lose \$8. What is the expected value of playing this game once?

A. \$1

B. \$2

C. -\$1

D. \$0

Correct Answer: \$1

Explanation: There are 18 even sums and 18 odd sums when rolling two dice (a total of 36 outcomes). P(even sum) = 18/36 = 1/2. P(odd sum) = 18/36 = 1/2. Expected Value = (1/2) * 10 + (1/2) * (-8) = 5 - 4 = \$1.

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24. A tournament has 9 teams. The tournament format is a round-robin league followed by a knockout stage among the top 4 teams. How many matches are played in total if the knockout stage determines a single winner?

A. 40

B. 39

C. 42

D. 36

Correct answer: 39

Explanation: Round-robin: 9C2 = 36 matches. Knockout stage for 4 teams: 4-1 = 3 matches. Total = 36 + 3 = 39.

25. In a game, two players, A and B, take turns drawing a card from a deck of 5 cards (1, 2, 3, 4, 5). The first player to draw a card that is a multiple of 2 or 3 wins. Cards are not replaced. What is the probability that Player A wins?

A. 1/ 2

B. 2/ 5

C. 3/ 10

D. 3/ 5

Correct answer: 3/ 5

Explanation: This is the initial probability of drawing a multiple of 2 or 3 (2,3,4) from 5 cards.

26. A tournament has a unique scoring system. For every match won, a team gets 3 points. For a draw, 1 point. For a loss, 0 points. If 5 teams play a round-robin tournament (each team plays every other team once), and there are no draws, what do all teams accumulate the maximum possible total points?

A. 30

B. 15

C. 45

D. 20

Correct answer: 30

Explanation: Number of matches = 5C2 = 10. Since there are no draws, each match results in 3 points being awarded (3 for winner, 0 for loser). So, total points = 10 matches * 3 points/match = 30.

27. In a game played on a grid, a player starts at (0,0) and can only move right or up. If the player needs to reach (3,2), how many distinct paths are there?

A. 24

B. 10

C. 6

D. 12

Correct answer: 10

Explanation: To reach (3,2) from (0,0), you need to make 3 moves to the right (R) and 2 moves up (U). The total number of moves is 3+2 = 5. This is a permutation with repetition problem, solved by 5! / (3! * 2!) = 10.

28. In a game, there are 5 contestants. In each round, the contestant with the lowest score is eliminated. If there are no ties, how many rounds are needed to determine a single winner?

A. 1

B. 4

C. 3

D. 2

Correct answer: 3

Explanation: In the first round, 1 is eliminated (4 remain). In the second, 1 is eliminated (3 remain). In the third, 1 is eliminated (2 remain). In the fourth, 1 is eliminated (1 winner remains). So, n-1 rounds are needed for 'n' contestants to determine a single winner, which is 5-1 = 4 rounds. Oh wait, it is a single winner from 5 contestants, so after 4 eliminations, 1 winner remains. So, 4 rounds.

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Importance of Games and Tournaments in CAT 2025

• The DILR section of CAT has consistently included Games and Tournaments sets in recent years.
• These questions not only challenge your reasoning but also test your ability to work under pressure.
• Mastering Games and Tournaments CAT Questions can give you a significant edge in your overall percentile.

Conclusion

Mastering Games and Tournaments questions for CAT is less about rote memorization and more about developing a robust logical framework. 

By working through these 25+ commonly asked CAT questions on games and tournaments, you've not only encountered a wide variety of problem types but also honed your analytical skills, learned to identify key patterns, and applied effective problem-solving strategies. 

Remember, consistent practice and a clear understanding of the underlying principles are your greatest allies. Keep reviewing these question types, challenge yourself with variations, and approach each problem with a systematic mindset. 

With dedication, you'll be well-equipped to tackle even the trickiest Games and Tournaments CAT questions that come your way, giving you a significant edge in achieving your dream B-school.