(Photo credit: US Army)
In Logical Reasoning, very often we encounter problems based on games or tournaments. The first thing that as a CAT taker you need to realize is that the tournament-based format of questions offers the examiners a multitude of options to test you about. So, there cannot be a one-size-fits-all way of solving such kind of questions. However, if you looked at the CAT papers of the past few years you can spot some patterns. Let us discuss a couple of them.
Type 1: These questions are typically in the form of a set where the data will be either in the standard tabular format or a format which you would never find on Cricinfo or for that matter any other ESPN-like website. The different for the sake of being different format essentially tests a candidates ability to infer data presented in unusual ways.
Example,
Each diagram communicates the number of runs scored by the three top scorers from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The percentage number in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game.
You can get the complete set of questions from here.
I will not get into the details of solving this particular set. Once you interpret the information, the questions are really simple. The catch in this question (this type of questions) is to interpret the given data.
Let us view this same information in a different way,
Pakistan South Africa Australia Runs by Kaif 28 51 Runs by Rahul 49 55 Runs by Saurav 75 50 Runs by Virender 130 Runs by Yuvraj 40 87 Runs by Top 3 Top 3 as a %age of total 90% 70% 80% Total runs
As you can see, the triangular format is just a twisted way of representing simple tabular data. It is just a little more intimidating to see the triangles in a pressure situation and that intimidation is exactly what you should avoid. With some very simple addition and calculation operations, you would be able to solve this problem set.
Bottom line: Even if it takes a couple of extra minutes, it is best to represent information using a format that you are more comfortable with.
Type 2: For some reason, Tennis appears to be a favorite among CAT exam setters. Actually Tennis does offer some very interesting possibilities such as seeds, unconventional scoring and the knockout feature. Knockouts are inherent feature of the sport of Tennis and hence used frequently by exam setters.
Note: In a knockout tournament,
No of matches = No of players 1
Let us look at few ideas related to questions on seeded players. Lets say in a tournament there are n players and they are seeded (ranked) from 1 to n. Typically this n is a power of 2 such as 32, 64 or 128.
In the first round the highest seeded player plays the lowest seeded player, the second highest seeded player plays the second lowest seeded player and so on. To put it into perspective,
Round 1 Match 1 Seed 1 Vs Seed n
Round 1 Match 2 Seed 2 Vs Seed (n-1)
Round 1 Match 3 Seed 3 Vs Seed (n-2)
.
.
.
Round 1 Match n/2 Seed n/2 Vs Seed (n/2) + 1
In the second round, the winner of Match 1 plays the winner of Match n/2; winner of Match 2 plays the winner of Match n/2 1 and so on.
In this kind of a question, an upset happens when a lower seeded player beats a higher seeded player.
The questions are typically of the format,
Q: Who will play match 36 in Round 1?
A: It will be played between the 36th highest seed and the 36th lowest seed.
The 36th lowest seed can be sometimes difficult to figure out but you can figure it out easily by calculating (n+1) 36.
Note: The rth match in Round 1 will be played between Seed r and Seed n+1-r
Q: If there are no upsets, then in Round 2 who will play the 5th match?
A: One way of solving this question would be to figure out the winners of Round 1 and then figuring out the 5th from the top and the bottom.
If there is no upset, then seed 5 will be there. The other player would be (n/2+1 5)
Note: If there are no upsets, then the rth match in the pth round will be played between,
Seed r and Seed (n/2p – 1) + 1 – r
Q: Who will meet Seed 37 in the Quarter-finals of a tournament in which 64 players are taking part? Other than Seed 37s matches, there were no other upsets.
We first need to analyze which round would be the quarterfinal,
Round 1 (32 matches), Round 2 (16 matches), Round 3 (8 matches pre-quarter), Round 4 (4 matches quarterfinals).
In Round 1, Seed 37 must have defeated 64 + 1 37 = 28
In Round 2, Seed 37 played the match that Seed 28 would have played. Seed 28 would have played against Seed 32 + 1 28 = Seed 5
In Round 3 (pre-quarters), Seed 37 played the match that Seed 5 would have played. Seed 5 would have played against Seed 16 + 1 5 = Seed 12 and won it.
In Round 4 (quarterfinals), Seed 37 would meet the player that Seed 5 would have met. Seed 5 would have met 8 + 1 – 5 = 4.
Hence, Seed 37 will meet Seed 4 in the quarterfinals.
As a matter of fact, even the above solution is not the most optimal one. Because once you realize that Seed 37 defeated Seed 5, he would keep meeting the opponents that Seed 5 would have met.
I think I have taken enough of your time with this lengthy post but this time would be well spent if such a question appears in CAT or some other management entrance exam.
Ravi Handa, an alumnus of IIT Kharagpur, has been teaching for CAT and various other competitive exams for around a decade. He currently runs an online CAT coaching and CAT Preparation course on his website http://www.handakafunda.com