In the world championship tournament of ‘Shoot-a-player’, played every 4 years by all the qualifying states, each match is played among 3 participant states. Each state is represented by their national champion. Each match is an elimination match in which one participant is eliminated and the other two qualify for the next match. The game is played by participants who use guns (with fake bullets) to shoot each other. The 3 participants in a match stand on 3 corners of an equilateral triangular field, and can start shooting at each other as soon as the start whistle is blown by the referee. The first participant to get hit is eliminated. The match stops at that instant and the other two qualify for the next round. During the final match of the competition, the participant who shoots out one of the other two becomes the champion while the other remaining non-eliminated participant is declared the runners up.
If, during a given year, there were 1000 states at the start of the tournament, and all of them participated in at least one match, what is the number of matches played in the whole tournament?
- Insufficient data
Let us try to find the correct answer. At first instinct, you may feel that the data given is insufficient since it’s not mentioned what happens to the 1000th player since you cannot divide the 1000 equally into groups of three.
Let us forget this question for a while and try to answer the following one. We will learn something from this one which will help us solve this seemingly complex question above.
In Wimbledon Tennis tournament each year, in Men’s singles draw, 128 men participate. Each match is played between 2 players; the loser is eliminated while the winner qualifies for the next round. This is continued till there is only one player left undefeated, the champion. How many matches are played in the Men’s singles in a given year at Wimbledon?
This, you can easily work out, right? The correct answer is b. 127.
If you needed to write anything on paper to find out this answer, then you have understood the question, and have done all the calculations correctly but you haven’t DEDUCED the answer SMARTLY. Had you done that, it would have saved you all the calculations.
Before answering any QA question, you need to think of two things: What is required to be found out and what information is provided.
For this question,
What is required: number of matches played
What is provided:
- Each match played between 2 players and results in an elimination (which means there aren’t any draws)
- A total of 128 players with one winner in the end.
When you concern yourself with ‘what is provided’, it is of prime importance to think about only the relevant information and chuck the rest. It is a vital skill to be able to distinguish cheese from chalk.
Have you got the answer without any calculations now? Here goes the ideal thought process: in order to have one winner, we need 127 eliminations, and for 127 eliminations, how many matches do we need? 127. Bingo!
That’s how easy this was. Now let’s go back to the previous question and try answering it.
What is needed and what useful information is provided in that question?
What is needed: Number of matches played in the whole tournament?
What is provided:
- 1000 initial participants
- Each match played among 3 players
- 1 elimination per match, 2 ‘not eliminated’ till the end
See, you don’t need to know how the groupings are done in order to answer this question. I am sure you have got your answer by now. It is d. 998.
How? Well, a match each for each one of the 998 eliminations: We have only one player being eliminated per match and we need 998 eliminations in total to be left with 2 in the end. Hence, a minimum of 998 matches need to be played.
Now, as usual, we dig into the morals from the story.
Practice Rule: Think Smart
Thinking smart is a priceless proficiency and its importance cannot be over emphasized. Thinking of smart solutions in the face of adversity or scarcity is inherent in us Indians, i.e. doing more with less. We call it ‘Jugaad’. Even the major MNCs believe that Jugaad Innovation is the next big thing and are trying to embrace the philosophy.
While the term ‘Jugaad’ sometimes has slightly pejorative connotations, I am not referring to that here. I am referring to the art of thinking smart, the art whereby you look at all the options provided in the question, look at all the data given and think logically, but also cleverly.
Contrary to popular belief, the art of thinking smart can begroomed by practice. You shouldn’t take out your paper and pen and start crunching numbers as soon as you think you have understood the question.
It is imperative to go step by step. First, think of what is needed (i.e. what is it you need to cull out) and what information is provided in the question that will help you cull out what you require.
Then think of marrying the two with minimum possible calculations. Use logic. Use your common sense. The information provided might not satiate all your superfluous inquisitiveness (like how to form groups of 3 out of a 1000 participating states), but it might be just enough for you to correctly answer the question asked.
If you were asked to find the answer to: 999,999,998 + 998,999,987 – 999,999,997 – 998,999,987, will you add the first two and last two separately and then subtract? That is what you would do at school, following the BODMAS rule. Or will you look at the numbers carefully and come up with the answer to be 1? The same will be asked in CAT with the only difference of the patterns not being this conspicuous. You will not be able tomerely glanceat the question and crack the code and not all questions will have a code. However, you will need to think to be able to decipher the question after which it will become a matter of seconds till you get the answer or you figure out how to get it with the minimum amount of number crunching.
Pearl of Wisdom: The practice rule ‘think smart’ must be tried only while you are practicing or during the mock exams that you write and never during the actual CAT if you already have found a longer yet circuitous way to solve the question. You should never waste time in the actual test by trying to search for patterns when you have already found a way, albeit tedious, to solve a question.
Imagine you had come across the Wimbledon question during actual CAT and you haven’t realized this logic of deducing the answer by ‘number of eliminations’; would you have wasted time trying to find if there is any such way or would you have just calculated the answer traditionally? I hope you would have done the latter because that would be the smarter thing to do.
Then why think smart during the practice tests, you might wonder. Well, imagine that you had come across the Wimbledon question during a practice test and had answered it traditionally (by using the factorization method), checked the answer, found a match, felt euphoric and moved on.
In CAT, you come across the ‘Shoot-a-player’ question. Will you be able to solve it by the traditional method? No. To rub salt to your own wound, in all likelihood, you will mark the ‘data insufficient’ option because you had come across a similar question during a practice test and the way you had solved it cannot be done here (since 1000 cannot be factorized by 3). In this case, you would have been better off without coming across the Wimbledon question during practice. Then, maybe you wouldn’t have attempted the question, thus not losing one precious mark. Guess this is what they call the winner’s curse.
The solution is not ‘not practicing’. It is trying to think smart during the preparation phase. If only had you thought about the Wimbledon question non-traditionally during practice, in the hypothetical situation cited above, then you would have been able to answer the ‘Shoot-a-player’ question in the hypothetical actual CAT and got 4 solid marks.
The bottom-line is, after you have solved a question during your preparation phase, try thinking if you could have solved it faster or in a better way. Do the same for the mock CATs that you take (not during the mock CATs though, but after coming back home, while analyzing the paper).