GAMES AND TOURNAMENTS

Importance of the topic in various exams

Logical reasoning questions in various MBA entrance exams test the ability of candidates in concluding scrutinizing and studying all aspects of the problem. Objective thinking and rational ability of the test taker are also tested. For a career as a manager, it is important to take important decisions, set goals, and take novel solutions. Games and tournaments questions are a popular part of several MBA entrances including CAT, they may be related to cricket or tennis or football, or any other popular sport. These problems also come in a variety of ways such as round robbins, knockout tournaments, maximum and minimum, triangles, scoreboard, etc.   

Below are the details about the games and tournaments questions for different MBA competitive exams across the years:-

CAT

 

Games and Tournaments
YearNo of QuestionsGood attemptsDifficulty Level
2019

 

Slot 143Moderate
Slot 232Moderate
2018

 

Slot 143Easy
Slot 244Moderate
2017

 

Slot 143Easy
Slot 243Easy

XAT

Games and Tournaments
YearNo of QuestionsGood attemptsDifficulty Level
2020

 

3

 

2

 

Moderate

 

 

 

 

 

 

 

 

 

2018

 

2

 

1

 

Moderate

 

ATMA

Games and Tournaments
YearNo of QuestionsGood attemptsDifficulty Level
2020

 

4

 

3

 

Easy

 

 

 

 

 

 

 

 

 

2018

 

5

 

4

 

Easy

 

SNAP

Games and Tournaments
YearNo of QuestionsGood attemptsDifficulty Level
2019
5
4
Moderate
 
 
 
 
2017
4
3
Moderate

List of Concepts in that Chapter

The list of concepts that are covered in the Games and Tournaments section is as follows: –

  • Understanding the basic information of popular games such as tennis (most asked), cricket, hockey, football, and other team-based games
  • Having prior knowledge and familiarity with terms will help candidates in quickly understanding what is being asked and how to approach the questions
  • The data may be given in the form of a table or a pattern format such as triangles,
  • Questions usually ask winners, ties, scores of players at the end, probable team combinations, the total number of matches, matches required to win, etc.
  • Several other concepts like arithmetic progression, geometric progressions, and permutations and combinations are usually included along with games and tournaments questions 
 

Some Questions from Previous Papers

Some of the important CAT questions on Games and Tournaments that appeared in the previous papers are: –

1. A new game show on TV has 100 boxes numbered 1, 2, ….., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ….., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b, and so on. There is no particular order in which the prizes are placed in the boxes

(CAT 2019 slot 1)

Q.1 What is the minimum possible number of different types of prizes?

 

Q.2 What is the maximum possible number of different types of prizes?

 

Q.3 Which of the following is not possible?

1. There are exactly 45 items of type c.

2. There are exactly 30 items of type b

3. There are exactly 75 items of type e.

4. There are exactly 60 items of type d.

 

Q.4 You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100.

What is the maximum possible number of different types of items?

1. 5

2. 4

3. 3

4. 6

 

1. Minimum possible number is when there is 1 of type a and 99 of type b which is in accordance to the condition.

2. Maximum possible number is when 1 of a, 2 of b, 4 of c, 8 of d, 16 of e, 32 of f,

Now left boxes woud be 100 – (1+2+…32) = 37

Now if one more type is to be added then we need at least 64 which is not available thus maximum possible is 6.

3. Lets try to prove the given options possible using easy numbers.

op1:never possible

op2: 1,30,69 is possible

op3: 1,2,4,18.75 is possible

op4: 1,9,30,60 is possible.

4. There have to be then at least 31 + `1 + 43 = 75 gifts of same type,

Thus maximum possible number of boxes = 5 when all types are lest 1,2,4,18,75

 

2. Six players – Tanzi, Umeza, Wangdu, Xyla, Yonita, and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round, every player shot an arrow at a target. Hitting the center of the target (called bull’s eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2, and 1. Every bull’s eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.

A player’s total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing

(CAT 2019 slot 1)

The following additional facts are known.
 
 
1. Tanzi, Umeza and Yonita had the same total score
2. Total scores for all players, except one, were in multiples of three.
3. The highest total score was one more than double of the lowest total score
4. The number of players hitting bull’s eye in Round 2 was double of that in Round 3.
5. .Tanzi and Zeneca had the same score in Round 1 but different scores in Round 3.
Q.1 What was the highest total score?
1. 25
2. 23
3. 24
4. 21
 
Q.2 What was Zeneca’s total score?
1. 21
2. 24
3. 22
4. 23
 
 
Q.3 Which of the following statements is true?
1. Zeneca’s score was 23.
2. Xyla was the highest scorer.
3. Xyla’s score was 23.
4. Zeneca was the highest scorer
 
 
Q.4 What was Tanzi’s score in Round 3?
1. 3
2. 4
3. 1
4. 5
 

As from the table given we can see that Xyla had played all the six rounds in means he had scored 5 points in each of first 3 rounds.

Similarly Tanzi and Yonita each had hit one bull’s eye score in first three rounds, Umeza and Zeneca had two bull’s eye score in first 3 rounds while Wangdu didn’t had any bull’s eye score.

 

So this information can be tabulated as below: (Name of players have been represented by first letter of their name )

s number of player hitting bull’s eye in round 2 is double that of the number in round 3. And 2 players have already scored 4 points in Round 2 so maximum possible people hitting bulls eye in Round 3 can be 2 and in round 2 can be 4.
Thus a = 5 as c and d can not be 5.
Possible score of U = 5+5+1+2 + b = 13+b as it should be multiple of 3 so b = 2 thus x = 15
Thus Tanzi’s score in round 3 , c = 15 – 5 – 4 – a = 15 – 5 -4-5 = 1
Also W must have minimum score as his maximum possible score = 12 (if he scores 4 in each of first 3 rounds)Let it be m and X must have maximum possible score let it be n.
As m <= 12 and n >= 22
As n= 2m + 1
S n can be 23 or 25 .
But if n = 23 , m = 11 (which is not possible as only one of the all total score is not multiple of 3)
Thus n = 25 and m = 12
As Z has four scores of 5 so his 5th score will be either 1 or 4. But it can not be 1 as T’s score was 1.
Now the complete table will look like,

3. Ten players, as listed in the table below, participated in a rifle shooting competition comprising of 10 rounds. Each round had 6 participants. Players numbered 1 through 6 participated in Round 1, players 2 through 7 in Round 2,…, players 5 through 10 in Round 5, players 6 through 10 and 1 in Round 6, players 7 through 10, 1 and 2 in Round 7 and so on. The top three performances in each round were awarded 7, 3, and 1 point respectively. There were no ties in any of the 10 rounds. The table below gives the total number of points obtained by the 10 players after Round 6 and Round 10.

(CAT 2019 slot 2)

The following information is known about Rounds 1 through 6:
 
1. Gordon did not score consecutively in any two rounds.
2. Eric and Fatima both scored in a round.
 
The following information is known about Rounds 7 through 10:
1. Only two players scored in three consecutive rounds. One of them was Chen. No other player scored in any two consecutive rounds
2. Joshin scored in Round 7, while Amita scored in Round 10.
3. No player scored in all the four rounds.
 
Q.1 What were the scores of Chen, David, and Eric respectively after Round 3?
 1. 3, 3, 0
2. 3, 3, 3
3. 3, 6, 3
4. 3, 0, 3
 
 
Q.2 Which three players were in the last three positions after Round 4?
 1. Hansa, Ikea, Joshin
2. Bala, Chen, Gordon
3. Bala, Ikea, Joshin
4. Bala, Hansa, Ikea
 
 
Q.3 Which player scored points in maximum number of rounds?
1. Ikea
2. Chen
3. Amita
4. Joshin
 
 
Q.4 Which players scored points in the last round?
1. Amita, Chen, Eric
2. Amita, Bala, Chen
3. Amita, Eric, Joshin
4. Amita, Chen, David
 

Now as B had scored 2 points till round 6 and he had played only in round 1 and in round 2 till that thus he must have scored 1 – 1 points in each round.

So A can score 1 in round 6 and 7 in round 1 as he had played only in two rounds and had 8 points.

Similarly, Joshin (J) must have scored 7 points each in round 5 and round 6.

Now from the information known about Rounds 7 through 10: from point 1 and 2, C must score 1 points each in round 8, 9 and 10 as hi points has been increased 3 (from 3 to 6) and J must score 3 points in round 7.

Now the only possibility for I is to score 1, 7 and 7 points in round 7, 8 and 9 respectively.

Now A can not score in two consecutive rounds and his points has been increased from 8 to 18 so it is the only possibility that he score 7 points in round 7 and 3 points in round 10. Thus B will score 3 points in round 9 and H in round 8.

Now all the question can be answered:

 

1. Score of Chen, David, and Eric respectively after Round 3 =3, 3,3

2. option a)

3. option a)

4. option a)

 

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How to prepare for the concept of Games and Tournaments

Level 1 

It is important to have a basic understanding of the sports being asked so that a lot of time is not spent on recognizing the terms and jargon being used. Although a definition of most terms and the process being followed is included in the questions through practice a student needs to know terms like knockout and seeding for tennis and similarly for other sports. The questions are not always sport-related and may include other games with novel rules as well. Then the student needs to patiently understand the rules and apply them. It may take a little time but jump directly to questions isn’t advised.

Level 2

At this level, the student should focus on solving the questions correctly and without looking at the solutions. In the last few years for CAT, it was a little difficult to distinguish between the data interpretation and logical reasoning sections, as most of the concepts were intermingled. So, it is important to practice questions of different types from both sections. Also, the student should practise questions of varying difficulties without looking at the solutions beforehand. The questions where difficulty was faced should be revised after a week again and if the difficulty is faced again, then the concept should be revised.

Level 3

At level 3, as the difficulty of the DILR section in several exams has been increasing especially in CAT so it’s important to practice and practice. A mixture of different levels of difficulty should be attempted through section-wise tests. Attempting too many easy or too many difficult questions is not advised. Taking up a mock test series from a coaching institute will be beneficial. An important part of attempting mocks and particularly in the DILR section is understanding which questions to attempt and which to leave, this should be instilled at the current stage.