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