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CAT Exam  >  CAT Notes  >  100 DILR Questions for CAT Preparation  >  Practice Question - 79 (Games and Tournaments)

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation PDF Download

The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.

The management of a university hockey team was evaluating performance of four women players - Amla, Bimal, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.

  1. Only one goal was scored in every even numbered match.
  2. Harita scored more goals than Bimal.
  3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
  4. Bimal scored a goal in Match 1 and one each in three other consecutive matches.
  5. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
  6. The match in which the highest number of goals was scored was unique and it was not Match 5.

Q1: How many goals were scored in Match 7?
(a) 3
(b) 2
(c) 1
(d) Cannot be determined

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Ans: (c)
A total of 12 goals were scored in 8 matches and each player scored at least one goal and no of goals scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5).
From statement 4 we know that Bimal scored 4 goals and since Harita scored more goals than Bimal so we can say that Harita scored 5 goals and the only case possible for total goals scored by each of the players is (1,2,4,5).
Now using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which Bimal scored will be 5th, 6th and 7th matches as Harita scored in 4th and 8th matches and we get the following table:

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

From statement 5 and 6, we can conclude that the highest number of goals were scored in Match 1.
Let the no. of goals scored in 3rd and 7th match be a each and no. of goals scored in 1st and 5th match be b and c respectively.
Therefore, 2a + b + c = 8
If a = 1, then b + c = 6 therefore possible solutions for b and c will be 2 and 4 only
If a = 2, then b + c = 4 therefore possible solution for b and c will be 1 and 3 only but since highest goals scored is in Match 1 so then no. of goals scored in match 1 must be 3 and Harita must have scored 3 goals in match 1 as Harita scored 5 goals in exactly 3 matches. Therefore, we can see this is not possible because then the no. of goals scored in Match 1 becomes 4.
Therefore the only possible solution is a = 1, b = 4 and c = 2

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

The remaining 3 goals were scored in the match 2, 3 and 5 by Amla and Sarita in some order.

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Q2: Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?
(a) 5, 1, 0, 1
(b) 3, 1, 2, 1
(c) 3, 2, 1, 2
(d) 4, 1, 2, 1

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Ans: (d)
A total of 12 goals were scored in 8 matches and each player scored at least one goal and no of goals scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5).
From statement 4 we know that Bimal scored 4 goals and since Harita scored more goals than Bimal so we can say that Harita scored 5 goals and the only case possible for total goals scored by each of the players is (1,2,4,5).
Now using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which Bimal scored will be 5th, 6th and 7th matches as Harita scored in 4th and 8th matches and we get the following table:

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

From statement 5 and 6, we can conclude that the highest number of goals were scored in Match 1.
Let the no. of goals scored in 3rd and 7th match be a each and no. of goals scored in 1st and 5th match be b and c respectively.
Therefore, 2a + b + c = 8
If a = 1, then b + c = 6 therefore possible solutions for b and c will be 2 and 4 only
If a = 2, then b + c = 4 therefore possible solution for b and c will be 1 and 3 only but since highest goals scored is in Match 1 so then no. of goals scored in match 1 must be 3 and Harita must have scored 3 goals in match 1 as Harita scored 5 goals in exactly 3 matches. Therefore, we can see this is not possible because then the no. of goals scored in Match 1 becomes 4.
Therefore the only possible solution is a = 1, b = 4 and c = 2

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

The remaining 3 goals were scored in the match 2, 3 and 5 by Amla and Sarita in some order.

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Q3: Which of the following statement(s) is/are true?
Statement 1: Amla and Sarita never scored goals in the same match.
Statement 2: Harita and Sarita never scored goals in the same match.
(a) Statement-1 only
(b) Statement-2 only
(c) Both the statements
(d) None of the statements

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Ans: (c)
A total of 12 goals were scored in 8 matches and each player scored at least one goal and no of goals scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5).
From statement 4 we know that Bimal scored 4 goals and since Harita scored more goals than Bimal so we can say that Harita scored 5 goals and the only case possible for total goals scored by each of the players is (1,2,4,5).
Now using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which Bimal scored will be 5th, 6th and 7th matches as Harita scored in 4th and 8th matches and we get the following table:

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

From statement 5 and 6, we can conclude that the highest number of goals were scored in Match 1.
Let the no. of goals scored in 3rd and 7th match be a each and no. of goals scored in 1st and 5th match be b and c respectively.
Therefore, 2a + b + c = 8
If a = 1, then b + c = 6 therefore possible solutions for b and c will be 2 and 4 only
If a = 2, then b + c = 4 therefore possible solution for b and c will be 1 and 3 only but since highest goals scored is in Match 1 so then no. of goals scored in match 1 must be 3 and Harita must have scored 3 goals in match 1 as Harita scored 5 goals in exactly 3 matches. Therefore, we can see this is not possible because then the no. of goals scored in Match 1 becomes 4.
Therefore the only possible solution is a = 1, b = 4 and c = 2

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

The remaining 3 goals were scored in the match 2, 3 and 5 by Amla and Sarita in some order.

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Q4: Which of the following statement(s) is/are false?
Statement 1: In every match at least one player scored a goal.
Statement 2: No two players scored goals in the same number of matches.
(a) None of the statements
(b) Statement-1 only
(c) Both the statements
(d) Statement-2 only

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Ans: (a)
A total of 12 goals were scored in 8 matches and each player scored at least one goal and no of goals scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5).
From statement 4 we know that Bimal scored 4 goals and since Harita scored more goals than Bimal so we can say that Harita scored 5 goals and the only case possible for total goals scored by each of the players is (1,2,4,5).
Now using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which Bimal scored will be 5th, 6th and 7th matches as Harita scored in 4th and 8th matches and we get the following table:

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

From statement 5 and 6, we can conclude that the highest number of goals were scored in Match 1.
Let the no. of goals scored in 3rd and 7th match be a each and no. of goals scored in 1st and 5th match be b and c respectively.
Therefore, 2a + b + c = 8
If a = 1, then b + c = 6 therefore possible solutions for b and c will be 2 and 4 only
If a = 2, then b + c = 4 therefore possible solution for b and c will be 1 and 3 only but since highest goals scored is in Match 1 so then no. of goals scored in match 1 must be 3 and Harita must have scored 3 goals in match 1 as Harita scored 5 goals in exactly 3 matches. Therefore, we can see this is not possible because then the no. of goals scored in Match 1 becomes 4.
Therefore the only possible solution is a = 1, b = 4 and c = 2

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

The remaining 3 goals were scored in the match 2, 3 and 5 by Amla and Sarita in some order.

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Q5: If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true?
Statement 1: Amla scored goals in consecutive matches.
Statement 2: Sarita scored goals in consecutive matches.
(a) Statement-2 only
(b) None of the statements
(c) Statement-1 only
(d) Both the statements

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

Ans: (b)
A total of 12 goals were scored in 8 matches and each player scored at least one goal and no of goals scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5).
From statement 4 we know that Bimal scored 4 goals and since Harita scored more goals than Bimal so we can say that Harita scored 5 goals and the only case possible for total goals scored by each of the players is (1,2,4,5).
Now using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which Bimal scored will be 5th, 6th and 7th matches as Harita scored in 4th and 8th matches and we get the following table:

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

From statement 5 and 6, we can conclude that the highest number of goals were scored in Match 1.
Let the no. of goals scored in 3rd and 7th match be a each and no. of goals scored in 1st and 5th match be b and c respectively.
Therefore, 2a + b + c = 8
If a = 1, then b + c = 6 therefore possible solutions for b and c will be 2 and 4 only
If a = 2, then b + c = 4 therefore possible solution for b and c will be 1 and 3 only but since highest goals scored is in Match 1 so then no. of goals scored in match 1 must be 3 and Harita must have scored 3 goals in match 1 as Harita scored 5 goals in exactly 3 matches. Therefore, we can see this is not possible because then the no. of goals scored in Match 1 becomes 4.
Therefore the only possible solution is a = 1, b = 4 and c = 2

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

The remaining 3 goals were scored in the match 2, 3 and 5 by Amla and Sarita in some order.

Practice Question - 79 (Games and Tournaments) | 100 DILR Questions for CAT Preparation

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FAQs on Practice Question - 79 (Games and Tournaments) - 100 DILR Questions for CAT Preparation

1. What are the common formats of games and tournaments used in competitive settings?
Ans. The common formats of games and tournaments include knockout (or elimination) tournaments, round-robin tournaments, and Swiss system tournaments. Knockout tournaments eliminate participants after a loss, while round-robin tournaments allow each participant to compete against all others. The Swiss system combines elements of both, pairing participants with similar scores over several rounds without eliminating anyone.
2. How do point systems work in games and tournaments?
Ans. Point systems in games and tournaments typically award points based on performance. For example, in round-robin formats, participants might earn points for wins, ties, or losses, contributing to their overall ranking. A common system awards 3 points for a win, 1 point for a draw, and 0 points for a loss, which helps determine standings and qualifications for subsequent rounds.
3. What is the significance of seeding in tournament formats?
Ans. Seeding is crucial in tournament formats as it determines the matchups based on participants' rankings or past performance. Higher-seeded players or teams face lower-seeded ones in the early rounds, which aims to prevent the strongest competitors from eliminating each other too soon. This system enhances fairness and maintains spectator interest by ensuring that top contenders progress further in the tournament.
4. How do tie-breakers work in tournaments?
Ans. Tie-breakers are used in tournaments when participants have equal points or scores at the end of the competition. Common tie-breakers include head-to-head results, differential points, or additional playoff matches. These criteria help determine rankings or advance participants when standard point systems do not yield a clear winner.
5. What strategies can participants employ to succeed in tournaments?
Ans. Participants can employ various strategies to succeed in tournaments, such as studying opponents' previous performances, managing time effectively during matches, and adapting their gameplay based on the tournament format. Additionally, maintaining physical and mental stamina, practicing under tournament conditions, and developing a flexible game plan can enhance their chances of success.
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Sep 26, 2025 Last updated
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