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**Specialized Curriculum:**Our tailored curriculum focuses on various types of games and tournaments questions frequently encountered in the CAT exam, providing a comprehensive understanding of strategies and approaches.**Practice Material:**Access a diverse range of practice exercises and CAT-level mock tests specifically designed to strengthen your skills in solving Games and Tournaments-based problems.**Expert Guidance:**Benefit from the expertise of our faculty, who provide comprehensive insights and methodologies for solving complex Games and Tournaments questions, enabling you to navigate through them with ease.

Quantifiers’ Games and Tournaments section is meticulously designed to equip you with the expertise needed to excel in this crucial segment of the CAT DILR section. Master the art of solving Games and Tournaments questions and elevate your CAT preparation to new heights.

Five friends – Ankit, Basant, Charan, David and Eshwar – played a game of dice, in which they throw a regular die and score points equal to the number shown up by the die. The game was played for five rounds and in each round, each player threw the die exactly once. It was observed that no two players scored the same number of points in any round. At the end of five rounds, the players with the top two scores were selected and it was decided that these two players will play the game for another two rounds, i.e., the 6th and the 7th rounds, and their scores in these two rounds will be added to their respective scores in the earlier rounds and the person with the highest total number of points will be declared the winner. It was also decided that the seventh round has to be held only if the player with the second highest number of points after the sixth round has a chance to win, if the seventh round is conducted. Further, it is known that no one scored 6 points in the last round that they played. mThe following table gives partial information about the points scored by the participants in different rounds:

**Q1. What is the minimum possible number of total points scored by Charan?**

- 4
- 5
- 6
- CBD

**Q3. What is the maximum possible difference between the points scored by Eshwar and Charan in the fourth round?**

- 0
- 3
- 2
- 1

**Correct Answer 1**

13

**Correct Answer 2**

b. 5

**Correct Answer 3**

4

**Correct Answer 4**

c. 3

The following scatter plot gives the information about the number of innings played and runs scored by ten different batsmen – Ashwin, Dhoni, Gambhir, Harbhajan, Jadega, Kohli, Raina, Sehwag and Yuvraj. The average of a batsman is defined as runs scored per innings played.

For example, the point (10, 150) in the scatter plot represents one of the ten batsmen (the names being intentionally left out) who played 10 innings and scored 150 runs.

Further, it is known that

- Sehwag did not score the highest number of runs and Kohli did not have a higher average than Dhoni had.
- Rohit and Jadeja were the batsmen whose averages were among the lowest two averages and Rohit played more matches than Gambhir did.
- Among all the possible pairs, Dhoni and Gambhir is the pair with the least difference in averages.
- Exactly three batsmen scored more runs than Ashwin did and neither Raina nor Yuvraj scored more runs than Harbhajan did.

**Q1**. **Which of the following statements is definitely false?**

- The average of Sehwag is less than 30, if he is not the one who played the least number of matches.
- Yuvraj scored more runs than Rohit did but less runs than Dhoni did.
- The number of runs scored by Harbhajan is more than the number of runs scored by Dhoni.
- The average of Yuvraj is less than that of Dhoni.

**Q2. Which of the following statements would help to uniquely determine the average of each of the ten batsmen?**

- The average of Yuvraj is less than that of Harbhajan, while the average of Raina is more than that of Harbhajan.
- The average of Sehwag is more than that of Yuvraj and less than that of Raina.
- The average of Raina is more than that of Yuvraj and Shewag, while the average of Sehwag is more than that of Dhoni

- (i) alone
- (ii) alone
- (i) and (iii) together
- (iii) alone

**Q3. What is the minimum possible number of players who scored more runs than Sehwag did?**

The table below is the league table at the half-way stage in an Asian football tournament. So far, every team has played every other team in its pool exactly once. The positions in the group have been determined in the sequence: maximum number of points, followed by higher goal difference in case of a tie in points. Every match has 3 possible results: Win, Loss or Tie (Draw). Each win fetches three points while a loss gives no point. In case of a tie, a point is given to both the teams. Some information is missing in the table.

The following additional information is available:-

All teams were on a different number of points.

UAE beat Oman 2-1 in their head-to-head encounter.

**Q1. Which team won the match between Japan and UAE?**

**Q2. How many matches ended in a tie until the halfway stage of the Qualifiers?**

**Q3. What was the minimum number of combined goals scored by both participating teams in any of the matches played so far?**

**Q4. What is the maximum possible combined number of goals in the match between South Korea and UAE?**

**Correct Answer 1**

Tie

**Correct Answer 2**

4 matches

**Correct Answer 3**

0

**Correct Answer 4**

4

To study the performance of three strikers – Villa, Torres and Messi – the coach of a football team analysed all the matches played by the team in the last season. The coach found that each of the three strikers played all the games in the last season and every goal scored by the team required the assistance/involvement of at least one of these three strikers. The total number of goals scored by the team in the last season was 37.

From the analysis, the coach obtained the following information about the three strikers.

- Messi was involved in 20 goals scored by the team, which was the maximum number for any striker within the team.
- The number of goals scored, in which Messi was the only striker involved, was equal to the number of goals scored in which Torres was involved such that that Torres was not the only striker involved in the goal scoring.
- The number of goals in which Torres was the only striker involved was double the number of goals in which all the three strikers were involved.
- Villa was involved in the scoring of 17 goals.
- The number of goals in which Villa was the only striker involved was one less than the number of goals in which Torres was the only striker involved.
- The number of goals in which Villa was not the only striker involved in goal scoring was 10.

After the analysis, the coach awarded points to the three strikers, based on the following conditions.

- If only 1 striker was involved in a particular goal, 3 points were awarded to the striker
- If 2 strikers were involved in a particular goal, 2 points each were awarded to both the strikers.
- If 3 strikers were involved in a particular goal, 1 point was awarded to each striker

**Q1. In how many goals was Messi the only striker involved in scoring the goal?**

**Q2. How many points were awarded to Torres, for the goals in which Villa and Torres were involved in goal scoring?**

**Q3. In how many goals was Torres not involved?**

Eight teams play against each other exactly once in a Cricket World Cup. The following is also known about the matches that have been completed.

- Each team is awarded 2 points on a win.
- A loss is awarded no points.
- There is no draw in the tournament.
- No team ended with the same points at the end of the tournament.
- It is known that if a team loses a match against an opponent, it also loses the match against those whom the opponent has already lost to.
- The incomplete points table is as shown in the table below where the rows represents the performance of a team w.r.t the other teams.

- H
- D
- F
- Cannot be Determined

**Q2. How many points did H score?**

**Q3. What is the difference between the final points of B and E?**

**Q4. How many points have C, F and H scored together?**

**Correct Answer 1**

b. D

**Correct Answer 2**

8

**Correct Answer 3**

CBD/999

**Correct Answer 4**

26

Nine participants participated in an inter-school quiz. A total of five rounds were held in this tournament. In any round, the winner got 5 points, the 1st runner up got 3 points and the 2nd runner up got 1 point. In any round the number of participants was five, such that the 1st participant to enter the tournament plays only the first round, the 2nd participant plays the first two rounds, the 3rd participant plays first three rounds and so on till the 5th participant plays all the five rounds. The next participant plays one round less than the previous participant and this continues till Ajinkya, who plays only one round. The 1st participant to enter the tournament was Akshay followed by Amit and so on in the order given in the bar chart below. Ajosh was the only participant to have scored in consecutive rounds. There were no ties for any of the positions in any of the five rounds. The graph below gives the points tally at the end of five stipulated rounds. Ajinkya was not able to score any point in the quiz

- Abhilash
- Ajay
- Amar
- Cannot be Determined

- 2 : 3
- 1 : 3
- 3 : 1
- Cannot be Determined

- Round 2
- Round 3
- Round 4
- Both Rounds 2 and 4

**Q4. The winners in round 3, 4 and 5 in some order are**

- Ajosh, Amar, Anil
- Ajosh, Anil
- Anil, Abhilasha, Ajay
- Abhilasha, Ajosh, Amar

**Correct Answer 1**

d. Cannot be Determined

**Correct Answer 2**

8

**Correct Answer 3**

d. Both Rounds 2 and 4

**Correct Answer 4**

Six persons P, Q, R, S, T and U play in a tournament called “high Rollers”. Every game involved two players. Each of the participants played with every other participant exactly once. In the game both the players rolled an unbiased die each. The player who gets the larger number on the top surface of the die wins the game. Every game resulted in a win/ loss. The player who wins, gets as many coins as the number on the top surface of his die. The total number of games won by each person is distinct.
Further it is known that:

- Q won his game against P.
- R won the maximum number of coins, more than any one else.
- U lost only two games, one against S and the other against R.
- T did not lose more than three games.

- 1
- 2
- 3
- Either a or b
- Cannot be determined

- T won 5 games
- R won 5 games
- S won 5 games
- No player was undefeated
- None of the above

- 32
- 33
- 34
- 35
- 17

- 11
- 4
- 10
- 5
- CBD

**Correct Answer 1**

- 1

**Correct Answer 2**

5. None of the above.

**Correct Answer 3**

2. 33

**Correct Answer 4**

3. 10

**Correct Answer 1**

(A) Arsenal

**Correct Answer 2**

(B) Man Utd

**Correct Answer 3**

(D) 6

**Correct Answer 4**

(D) Man Utd

The points table of the English Premier League 2007-08 after 37 games played by each team is given. Each team is yet to play one more match. Three points are awarded for a win, one point for a draw and no points for a loss. In case two or more teams are level on points after the last round of matches, the team with a higher goal difference (GD = GF − GA) is ranked higher

**Q1. On the final day Manheader United draw with Arsenail without scoring. Also, Chelski and Heartpool win their matches against Fillham and Overton, 6-1 and 4-0 respectively, then what is the sum of the goal differences of the teams ranked 1 and 4 at the end of the league?**

- Arsenail and Chelski
- Arsenail and Heartpool
- Heartpool and Manheader United
- Chelski and Heartpool

**Q3. On the final day, Manheader United loses 0-2 against Braxton Villa and Arsenail and Chelski draw against Sunderbans and Wiggle, 4-4 and 2-2 respectively. If Heartpool has conceded three goals in their match against Overton, then what is the minimum number of goals they need to score to become the champions?**

- Manheader United win 3-0, Chelski lose 1-0
- Chelski win 2-0, Manheader United draw 2-2
- Heartpool win 2-1, Manheader United win 3-2
- Chelski win 6-5, Manheader United lose 5-0

**Correct Answer 1**

**Correct Answer 2**

b. Arsenail and Heartpool

**Correct Answer 3**

5

**Correct Answer 4**

d. Chelski win 6-5, Manheader United lose 5-0

Each of five friends – A, B, C, D and E – placed bets among themselves. Each person placed at most one bet with every other person and none of the bets ended as a draw. The money involved in each bet is called as the *stake* of that bet and the person who wins the bet gets the *stake* of that bet from the person who lost the bet. The total money got by any person in all the bets he won is called as his *gain* and the total money lost by any person in all the bets that he lost is called as his *loss*. The following information is also known:

- No two persons won the same number of bets and no two persons lost the same number of bets.
- For any person, the
*stakes*of any two bets are different. - The
*stake*of any bet is an integer amount (in Rs.) and is neither less than Rs.4 nor more than Rs.21. - Neither the
*gain*of any person who won at least one bet nor the*loss*of any person who lost at least one bet is less than Rs.20 or more than Rs.40. - The sums of the
*stakes*(in Rs.) of all the bets placed by each of A, B, C, D and E are 55, 37, 40, 55 and 53 respectively. - The number of bets won by D is equal to the number of bets lost by A. The number of bets lost by C is more than the number of bets lost by D.
- E won Rs.17 against A and the
*stake*involved in the bet between C and D is Rs.4. The*gain*of A is equal to the*loss*of D.

**Q2. ****The stake (in Rs.) in the bet between B and C is **

**Q3. What is the total loss (in Rs.) of A?**

**Q4. What is the amount (in Rs.) that A lost to D?**

The following is the table of points drawn at the end of all the matches in a six-nation Hockey tournament, in which each country played with every other country exactly once. The table gives the positions of the countries in terms of their respective total points scored (i.e., in the decreasing order of their total points). Each win was worth three points, each draw one point, and there were no points for a loss. Some information in the table has been intentionally left out. The results of none of the individual matches are known, except that Pakistan beat India and no two teams finished with the same number of points.

- Australia
- Netherlands
- South Korea
- Spain

- India Vs South Korea
- Spain Vs Netherlands
- Netherlands Vs South Korea
- Spain Vs South Korea

**Correct Answer 1**

6

**Correct Answer 2**

0

**Correct Answer 3**

c. South Korea

**Correct Answer 4**

d. Spain Vs South Korea

In a shooting competition, each player, in his turn, takes three shots at the target. The competition starts with the first player taking three shots, followed by the second player taking three shots, and so on. After the last player has taken his three shots, the turn comes back to the first player who again takes three shots, followed by the second player and so on. For each shot, if a player hits the target, he is awarded 3 points while no point is awarded to or deducted from the scores of each of the other players. If he misses, 1 point is deducted from his score and 1 point is awarded to each of the other competitors. The first player(s) to reach at net score of 100 points or more will be declared the winner(s) of the competition. Once the winner(s) is/are decided, the competition ends. Exactly five players – A, B, C, D and E – participated in the competition, with their turns not necessarily being in the same order. At the end of the competition, D alone won the competition and had the same number of misses as that of A. The net score of C was 74 points and he registered the same number of hits as that of B. The net scores of the players whose turns were third, fourth and the fifth, were in descending order. There were a total of 86 hits and 54 misses.

**Q1. What was the number of hits registered by E?**

**Q2. ****Who had the second least number of misses?**

**Q3. ****The player whose turn was fourth is**

**Q4. Difference between net score of A and B is ______**

**Q5. Net score of A is _______**

**Correct Answer 1**

14

**Correct Answer 2**

B

**Correct Answer 3**

B

**Correct Answer 4**

15

**Correct Answer 5**

95

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