Last Updated on November 17, 2017 by MBAUniverse.com News Desk

# CAT 2017 Must read Expert Tips: 2- How to prepare Data Interpretation & add 40 percentile in new CAT syllabus, exam pattern

This is the expert tip-2 to add more percentile in CAT 2017 score through DI part of questions in CAT 2017 with tips from experts how to prepare and quickly solve the CAT questions in revised new CAT syllabus and exam pattern for the Data Interpretation

Next 10 days of preparation and practice for CAT 2017 exam day on November 26, calls for specific strategy in new and revamped CAT syllabus and exam pattern. The CAT 2017 exam pattern, as revealed in CAT 2017 official Mock test released by IIMs on October 30, has brought more impact on Data Interpretation (DI) part of DILR section in CAT 2017 exam than on any other section.

In the CAT 2017 Expert tips series, this is the expert tip-2 to add more percentile in CAT 2017 score through DI part of questions in CAT 2017 with tips from experts how to prepare and quickly solve the CAT questions in revised new CAT syllabus and exam pattern for the Data Interpretation questions in CAT 2017. Prof S K Agarwal-expert on CAT preparation and Prof. Nishit Sinha, IIM Lucknow alumnus and author of titles on QA, LRDI and VARC, published by Pearson share insights on how to prepare, approach and quickly crack the questions on DI in CAT 2017.

Important links:

CAT 2017 must-read expert Tips-1: 5 things to note in new syllabus, changed exam pattern

CAT 2017: Prepare devising your own Exam day strategy; suggest CAT toppers

CAT 2017: Prepare smart avoid 24 hours study plan; dont expect miracles in CAT percentile jump

Not only the weightage on Data Interpretation questions in CAT 2017 has increased but also there is an increase in number of questions on Data Interpretation part of DILR section. The increased role of DI questions in CAT 2017 exam can help you improve your sectional percentile score by 40 points or so, if the answers marked by you go correct.

DI in CAT 2017: Ratio of questions increased

Ratio of questions on Data Interpretation (DI) part in DILR section of CAT 2017 appears to have been increased by IIMs as reflected in CAT 2017 Mock test released by IIMs.

In the past also, DI questions have remained a hard nut to crack for CAT aspirants. Many CAT test takers with 99+ percentile lost the race to IIMs only because they could not score even the qualifying percentile of 70 or 80 in newly created DILR section in CAT since 2015.

DI questions are rated as more time consuming in CAT exam and this year IIMs have increased the questions on DI. This is high time that equal weightage is awarded to DI questions in your study schedule while preparing for CAT 2017.

Important changes in DI part of DILR section in CAT 2017 syllabus:

DILR in CAT 2017 will have 32 total questions

Share of DI questions in the revamped CAT 2017 exam pattern increased to 20

There are 4 No-negative marking questions in DI part in CAT 2017 out of 32

Whether a publishing error or deliberate, IIMs have posted a few MCQs as no negative marking questions in DI part of DILR section of official CAT 2017 Mock test

16 MCQs on Data Interpretation to carry 1/3 negative marking

If MCQ with no penalty, how it is beneficial?

In case you find the MCQ type of questions without negative marking in DI section of CAT 2017 exam as revealed in CAT official Mock test, you should be happy as you will get answer options also to choose from in this section without any fear of loss of marks.

Check the topics you have prepared!

The key topics on which DI questions in CAT 2017 will be based on, are Table Analysis-data comparison; Bar graphs analysis, ratio, percentage; Pie chart; Line graph; Table Data Analysis among others.

If you have prepared well on these DI topics, you should attempt variety of questions to crack DI with high score in CAT 2017.

Add 40 percentile with no penalty and increased ratio of DI questions

The composition of Data Interpretation questions would be a major part in the form of MCQs and 4 questions as Non-MCQs. If you are able to crack all the 4 no penalty questions correct and can accurately solve 3-4 more questions in DI, you may improve your percentile in DILR section by 40% or more making a clear way to crack CAT 2017 with high score.

DI-real game changer: Experts view

Prof Nishit K Sinha, Prof Arun Sharma and Prof S K Agarwal, all experts on CAT 2017 preparation and authors of the best-selling books on DI, VARC, LR & Quant preparation are unanimous that in the changed CAT exam structure, you cannot supplement your score of Quant to DI score and now it is difficult to neglect or overlook Data Interpretation questions, if you wish to be shortlisted by highly ranked top IIM Ahmedabad, Bangalore and Calcutta.

If you have to score 80-85 percentile in Quant and VRC sections, you will have to score same percentile in CAT 2017 in DI section also to get shortlisted by IIMs. The actual cut off percentile in DILR section in CAT 2017 may be higher than the announced cut off, depending upon the merit status and scoring pattern. If you score a percentile of 97 in Quant; 96 in VRC but lag behind to 69 in DILR, despite scoring a high percentile of 97 or 98 in CAT 2017, you will not get shortlisted by IIMs as they need a minimum of 70 to 80 percentile in each of the 3 sections

You cannot expect to score high sectional percentile without attempting more questions on Data Interpretation

Neglecting DI part can slide down your sectional percentile score much lower than minimum qualifying 70 or 80 percentile

One set of 4 DI questions can add to your percentile up by 20 to 24 points in equated scoring system

Consistent practice can get you expertise on DI questions. There are limited topics on which DI questions are formed.

DI: Best Preparation strategy

Best preparation for DI part in CAT 2017 can be done quickly, if

You prepare a numerical chart

Instead of depending upon on screen calculator, practice more to do your own calculations

Solve previous years CAT question papers as much as possible

Prepare by using elimination method. Since Data Interpretation generally has several types of questions available as many forms of data could be given to you in CAT 2017 question paper, including line charts, pie charts, histograms, tables, you need to be sure that you first are able to understand exactly what the question is asking you and then try to eliminate as many calculations as you can.

Avoid getting indulged into the web of long calculations and try to arrive at the closest approximate value

Dont spend more than 7 minutes to solve a DI set of 4 questions

Using Elimination in DI question: Example

If a question is asking about the growth of sales from 10 years ago to now and the options are something like 56%, 112%, 180%, 204%, then its not necessary to get the exact percentage answer, you can estimate to find out whether the sales were 1.5 times, a little more than double, little less than triple or a little more than triple of their previous value. If you can do this effectively, you can save a lot of time that otherwise would be spent in calculations, even if you have a calculator.

How to solve DI questions on Games and tournament; expert tips

According to CAT expert and IIM Lucknow alumnus Prof Nishit Sinha author of titles on QA, LRDI and VARC, widely published by Pearson, the Games based questions are often asked in CAT and other MBA entrance examinations. In his view, although process of solving these questions largely depends upon the kind of rules followed in the question set, it is pertinent to understand the basics involved in almost all such questions.

First know the Types of tournament:

There are two types of standard tournaments:

Round Robin League Tournament (also known as League Tournament)

Knockout Tournament (also known as Elimination Tournament).

Round Robin League Tournament

In Round Robin League tournament, each team plays with every other team. For example, if there are 5 teams namely A, B, C, D and E, total matches will be = AB, AC, AD, AE, BC, BD, BE, CD, CE, DE. (AB means a match between A and B and so on. There cannot be a match between team A and team A, hence AA does not make sense).

So, if there are 5 teams, total number of matches = 10

In general, if there are n teams, total number of matches = ?(n@ C@ 2)

Where =?(n@ C@ 2)=(n(n-1))/2

?(n@ C@ 2) is also equal to [1 + 2 + 3 + 4 + ...................+(n-2) + (n-1)].

For example, if there are six teams in a round robin league tournament, total number of matches = 5+ 4 + 3 + 2 + 1 = 15. This is also equal to =?(6@ C@ 2)= (6(6-1))/2 = (65)/2 = 15.

Knockout Tournament

In Knockout Tournament, initially the teams / players are paired up, and one match takes place for every pair. Winner of the match advances to the next round and loser of the match gets eliminated from the tournament.

For example, if there are 32 players participating in the tournament, then in the 1st round, there are going to be 16 pairs of players, and one match per pair is scheduled. For every match, ONLY one player from every pair will be advanced to the next round. So 16 players will be advanced to the next round and 16 players will be eliminated (out of total 32 players initially).

Similarly, in the 2nd round, there are going to be 8 pairs = total 8 matches = 8 players advancing to the next round and so on.

Note the key facts

(a) - In case of Knockout Tournament, total number of matches for the champion to be emerging out of the tournament- if there are n players participating in the tournament = (n-1) matches.

(b)- If there are odd number of players participating, then one of the players will get bye and promoted to the next round without actually playing in that round. Remaining players will be paired up.

Understand with example

Following Example on the lines of CAT 2016 exam will make you learn more about how to approach Games based Questions:

Direction for questions 1 4: Read the passage below and solve the questions based on it.

Following table gives the result of due North soccer competition. Matches were played round robin (each team playing against another once) and the teams participated were Bihar, Punjab and Haryana. The table has some data missing:

Match played

Won

Drawn

Lost

Goals for

Goals against

Bihar

2

1

2

4

Punjab

2

3

7

Haryana

2

1

Q1.What is the total number of matches played in the competition?

1. 3 2. 6 3. 9 4. None of these

Q2.What did the score card read in favor of Punjab in Punjab-Haryana match?

1.

2 5

2.

1 5

3.

1 4

4.

1 6

Q3.How many matches did Punjab lose?

1.

0

2.

1

3.

2

4.

0 or 1

Q4.How many goals did Haryana score?

1.

5

2.

1

3.

3

4.

7

How to quickly Solve in CAT 2017

You may find one question set with 4-5 questions based on games. You must know the quick and accurate approach to solve these question sets.

In this set of questions, we are 1st required to calculate total number of matches. Let us understand the scheme of matches in a Round Robin League tournament.

Method 1 - In a round robin league tournament, each team plays against other team once. So if there are five teams A, B, C, D and E (let us assume), total number of matches are going to be the following:

AB, AC, AD, AE

BC, BD, BE

CD, CE,

DE

Hence total number of matches = 4 + 3 + 2 + 1 = 10.

In general, if there are n teams, then total number of matches = (n-1) + (n-2)+.+3 + 2 + 1 = (n(n-1))/2

Method 2 - each team plays one match with every other team. So, number of matches played by each team = 4. So total number of matches = 5 teams 4 matches = 20 matches. But each of these matches has been counted twice for example match AB and BA both have been counted.

So total number of unique matches = 20/2= 10 matches.

Method 3 Using Permutation and Combination

There is a match for every set of two players. So, if there are n players, total number of matches = nC2.

In this question, there are three teams Bihar, Punjab and Haryana.

Hence total number of matches = 2 + 1 (Using method 1)

This is also equal to (n(n-1))/2 = (3(3-1))/2 = 3 matches.

Hence answer to Q1.Total number of matches played in the competition = 3 matches. Hence option (1) is the answer.

SECONDLY,

Total Goals for by all the teams = Total Goals Against all the teams

Now total goals against = 4 + 7 + 1 = 12 goals

This gives us the number of Goals for Haryana = 12 (2+3) = 7

Match played

Won

Drawn

Lost

Goals for

Goals against

Bihar

2

1

2

4

Punjab

2

3

7

Haryana

2

7

1

Now, Bihar has drawn one of its matches, so it has either won or lost the other match.

Since it has drawn one of its two matches, possible score for Bihar is:

Match 1 (Draw)

Match 2 (Lost)

Hypothesis

Possibility 1

0--0

2--4

Hypothesis 1

Possibility 2

1--1

1--3

Hypothesis 2

Possibility 3

2--2

0--2

Hypothesis 3

2-2 = Goals for 2 and goals against 2.

It can be seen that Bihar is losing its second match.

Testing Hypothesis 1:

Hereafter, we will have to go ahead with hypothesis 1. Using the conditions given, then, we will verify if the assumptions that we have assumed are correct or not.

Assume that Bihar has its match drawn with Punjab and lost its match against Haryana.

Since Punjab and Haryana both have played one match with Bihar at this stage, total number of matches occurred so far = 2. And next match will be between Punjab and Haryana.

Using the score card of Punjab Goals for 3 and Goals against 7.

Since one of its matches was drawn with Bihar (score 0 0), hence score of 2nd match against Haryana would be = 3-7

Match 1 (Drawn with Bihar)

Match 2 (Lost to Haryana )

Punjab

0--0

3--7

Now Finally, we will have to evaluate if the goals for / against obtained in two matches against Haryana (one against Bihar and another against Punjab) support the figure given in the original table given in the question.

Bihars score against Haryana = 2 4 ?Score read in favour of Haryana = 4 2 (i.e. Haryana scored 4 goals and Bihar scored 2 goals) ---------------------(1)

Punjabs score against Haryana = 3 7 ? Score read in favour of Haryana = 7 -3 (i.e. Haryana scored 7 goals and Punjab scored 3 goals) ------------------(2)

Using the information given above in (1) and (2):

Haryana scored a total of 4 + 7 = 11 goals against these two teams. Looking at the information given in the table, Haryana has scored only 7 goals against both the teams taken together.

So, the hypothesis that Bihar drawn its match against Punjab with 0-0 is wrong.

Testing Hypothesis 2:

Similarly we will test our 2nd Hypothesis that Bihar drawn its match against Punjab with 1-1.

Testing Hypothesis 3:

Now checking the hypothesis that Bihar drawn its match against Punjab with score 2-2.

Using the score card of Punjab Goals for 3 and Goals against 7.

Since one of its matches was drawn with Bihar (score 0 0), hence score of 2nd match against Haryana would be = 3-7

Match 1 (Drawn with Bihar)

Match 2 (Lost to Haryana )

Punjab

2--2

15

Bihars score against Haryana = 0 2 ? Score read in favour of Haryana = 2 0 (i.e. Haryana scored 2 goals and Bihar scored 0 goal) ---------------------(1)

Punjabs score against Haryana = 1 5 ? Score read in favour of Haryana = 5 -1 (i.e. Haryana scored 5 goals and Punjab scored 1 goal) ------------------(2)

Using the information given above in (1) and (2):

Haryana scored a total of 5 + 2 = 7 goals against these two teams. Looking at the information given in the table, Haryana has scored 7 goals against both the teams taken together. At the same time, Punjab and Bihar taken together have scored 0 + 1 = 1 goal against Haryana. This also suits the tally given in the table (in original question).

So Hypothesis 3 is correct.

Hence the final table is like:

Match played

Won

Drawn

Lost

Goals for

Goals against

Bihar

2

0

1

1

2

4

Punjab

2

0

1

1

3

7

Haryana

2

2

0

0

7

1

(New findings are in bold and italics)

Now all the questions from Q2 to Q4 can be answered.

Answers:

Q1

Q2

Q3

Q4

1

2

2

4

You may find a different CAT 2017 exam on November 26 with a changed pattern based on revamped CAT syllabus as regards to type of questions and their scoring pattern. So make sure that your preparation remains more result oriented than time consuming. Experts at MBAUniverse.com will bring out next important expert tip to crack CAT 2017 with an improved percentile shortly.

Stay tuned to MBAUniverse.com for more updates and expert tips on CAT 2017

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Take CAT 2017MockFull Length:To assess your preparation in revised CAT 2017 exam pattern with 100 questions.

CAT Previous Year Question Papers, Answer With Solution:

CAT 2008 | CAT 2007 | CAT 2006 | CAT 2005 | CAT 2004

Section 1: Verbal Ability & Reading Comprehension

CAT 2017: Quiz 1

CAT 2017: Quiz 2

Section 2: Data Interpretation and Logical Reasoning

CAT 2017: Quiz 1

CAT 2017: Quiz 2

Section 3: Quantitative Ability

CAT 2017: Quiz 1

CAT 2017: Quiz 2

In the CAT 2017 Expert tips series, this is the expert tip-2 to add more percentile in CAT 2017 score through DI part of questions in CAT 2017 with tips from experts how to prepare and quickly solve the CAT questions in revised new CAT syllabus and exam pattern for the Data Interpretation questions in CAT 2017. Prof S K Agarwal-expert on CAT preparation and Prof. Nishit Sinha, IIM Lucknow alumnus and author of titles on QA, LRDI and VARC, published by Pearson share insights on how to prepare, approach and quickly crack the questions on DI in CAT 2017.

Important links:

CAT 2017 must-read expert Tips-1: 5 things to note in new syllabus, changed exam pattern

CAT 2017: Prepare devising your own Exam day strategy; suggest CAT toppers

CAT 2017: Prepare smart avoid 24 hours study plan; dont expect miracles in CAT percentile jump

Not only the weightage on Data Interpretation questions in CAT 2017 has increased but also there is an increase in number of questions on Data Interpretation part of DILR section. The increased role of DI questions in CAT 2017 exam can help you improve your sectional percentile score by 40 points or so, if the answers marked by you go correct.

DI in CAT 2017: Ratio of questions increased

Ratio of questions on Data Interpretation (DI) part in DILR section of CAT 2017 appears to have been increased by IIMs as reflected in CAT 2017 Mock test released by IIMs.

In the past also, DI questions have remained a hard nut to crack for CAT aspirants. Many CAT test takers with 99+ percentile lost the race to IIMs only because they could not score even the qualifying percentile of 70 or 80 in newly created DILR section in CAT since 2015.

DI questions are rated as more time consuming in CAT exam and this year IIMs have increased the questions on DI. This is high time that equal weightage is awarded to DI questions in your study schedule while preparing for CAT 2017.

Important changes in DI part of DILR section in CAT 2017 syllabus:

DILR in CAT 2017 will have 32 total questions

Share of DI questions in the revamped CAT 2017 exam pattern increased to 20

There are 4 No-negative marking questions in DI part in CAT 2017 out of 32

Whether a publishing error or deliberate, IIMs have posted a few MCQs as no negative marking questions in DI part of DILR section of official CAT 2017 Mock test

16 MCQs on Data Interpretation to carry 1/3 negative marking

If MCQ with no penalty, how it is beneficial?

In case you find the MCQ type of questions without negative marking in DI section of CAT 2017 exam as revealed in CAT official Mock test, you should be happy as you will get answer options also to choose from in this section without any fear of loss of marks.

Check the topics you have prepared!

The key topics on which DI questions in CAT 2017 will be based on, are Table Analysis-data comparison; Bar graphs analysis, ratio, percentage; Pie chart; Line graph; Table Data Analysis among others.

If you have prepared well on these DI topics, you should attempt variety of questions to crack DI with high score in CAT 2017.

Add 40 percentile with no penalty and increased ratio of DI questions

The composition of Data Interpretation questions would be a major part in the form of MCQs and 4 questions as Non-MCQs. If you are able to crack all the 4 no penalty questions correct and can accurately solve 3-4 more questions in DI, you may improve your percentile in DILR section by 40% or more making a clear way to crack CAT 2017 with high score.

DI-real game changer: Experts view

Prof Nishit K Sinha, Prof Arun Sharma and Prof S K Agarwal, all experts on CAT 2017 preparation and authors of the best-selling books on DI, VARC, LR & Quant preparation are unanimous that in the changed CAT exam structure, you cannot supplement your score of Quant to DI score and now it is difficult to neglect or overlook Data Interpretation questions, if you wish to be shortlisted by highly ranked top IIM Ahmedabad, Bangalore and Calcutta.

If you have to score 80-85 percentile in Quant and VRC sections, you will have to score same percentile in CAT 2017 in DI section also to get shortlisted by IIMs. The actual cut off percentile in DILR section in CAT 2017 may be higher than the announced cut off, depending upon the merit status and scoring pattern. If you score a percentile of 97 in Quant; 96 in VRC but lag behind to 69 in DILR, despite scoring a high percentile of 97 or 98 in CAT 2017, you will not get shortlisted by IIMs as they need a minimum of 70 to 80 percentile in each of the 3 sections

You cannot expect to score high sectional percentile without attempting more questions on Data Interpretation

Neglecting DI part can slide down your sectional percentile score much lower than minimum qualifying 70 or 80 percentile

One set of 4 DI questions can add to your percentile up by 20 to 24 points in equated scoring system

Consistent practice can get you expertise on DI questions. There are limited topics on which DI questions are formed.

DI: Best Preparation strategy

Best preparation for DI part in CAT 2017 can be done quickly, if

You prepare a numerical chart

Instead of depending upon on screen calculator, practice more to do your own calculations

Solve previous years CAT question papers as much as possible

Prepare by using elimination method. Since Data Interpretation generally has several types of questions available as many forms of data could be given to you in CAT 2017 question paper, including line charts, pie charts, histograms, tables, you need to be sure that you first are able to understand exactly what the question is asking you and then try to eliminate as many calculations as you can.

Avoid getting indulged into the web of long calculations and try to arrive at the closest approximate value

Dont spend more than 7 minutes to solve a DI set of 4 questions

Using Elimination in DI question: Example

If a question is asking about the growth of sales from 10 years ago to now and the options are something like 56%, 112%, 180%, 204%, then its not necessary to get the exact percentage answer, you can estimate to find out whether the sales were 1.5 times, a little more than double, little less than triple or a little more than triple of their previous value. If you can do this effectively, you can save a lot of time that otherwise would be spent in calculations, even if you have a calculator.

How to solve DI questions on Games and tournament; expert tips

According to CAT expert and IIM Lucknow alumnus Prof Nishit Sinha author of titles on QA, LRDI and VARC, widely published by Pearson, the Games based questions are often asked in CAT and other MBA entrance examinations. In his view, although process of solving these questions largely depends upon the kind of rules followed in the question set, it is pertinent to understand the basics involved in almost all such questions.

First know the Types of tournament:

There are two types of standard tournaments:

Round Robin League Tournament (also known as League Tournament)

Knockout Tournament (also known as Elimination Tournament).

Round Robin League Tournament

In Round Robin League tournament, each team plays with every other team. For example, if there are 5 teams namely A, B, C, D and E, total matches will be = AB, AC, AD, AE, BC, BD, BE, CD, CE, DE. (AB means a match between A and B and so on. There cannot be a match between team A and team A, hence AA does not make sense).

So, if there are 5 teams, total number of matches = 10

In general, if there are n teams, total number of matches = ?(n@ C@ 2)

Where =?(n@ C@ 2)=(n(n-1))/2

?(n@ C@ 2) is also equal to [1 + 2 + 3 + 4 + ...................+(n-2) + (n-1)].

For example, if there are six teams in a round robin league tournament, total number of matches = 5+ 4 + 3 + 2 + 1 = 15. This is also equal to =?(6@ C@ 2)= (6(6-1))/2 = (65)/2 = 15.

Knockout Tournament

In Knockout Tournament, initially the teams / players are paired up, and one match takes place for every pair. Winner of the match advances to the next round and loser of the match gets eliminated from the tournament.

For example, if there are 32 players participating in the tournament, then in the 1st round, there are going to be 16 pairs of players, and one match per pair is scheduled. For every match, ONLY one player from every pair will be advanced to the next round. So 16 players will be advanced to the next round and 16 players will be eliminated (out of total 32 players initially).

Similarly, in the 2nd round, there are going to be 8 pairs = total 8 matches = 8 players advancing to the next round and so on.

Note the key facts

(a) - In case of Knockout Tournament, total number of matches for the champion to be emerging out of the tournament- if there are n players participating in the tournament = (n-1) matches.

(b)- If there are odd number of players participating, then one of the players will get bye and promoted to the next round without actually playing in that round. Remaining players will be paired up.

Understand with example

Following Example on the lines of CAT 2016 exam will make you learn more about how to approach Games based Questions:

Direction for questions 1 4: Read the passage below and solve the questions based on it.

Following table gives the result of due North soccer competition. Matches were played round robin (each team playing against another once) and the teams participated were Bihar, Punjab and Haryana. The table has some data missing:

Match played

Won

Drawn

Lost

Goals for

Goals against

Bihar

2

1

2

4

Punjab

2

3

7

Haryana

2

1

Q1.What is the total number of matches played in the competition?

1. 3 2. 6 3. 9 4. None of these

Q2.What did the score card read in favor of Punjab in Punjab-Haryana match?

1.

2 5

2.

1 5

3.

1 4

4.

1 6

Q3.How many matches did Punjab lose?

1.

0

2.

1

3.

2

4.

0 or 1

Q4.How many goals did Haryana score?

1.

5

2.

1

3.

3

4.

7

How to quickly Solve in CAT 2017

You may find one question set with 4-5 questions based on games. You must know the quick and accurate approach to solve these question sets.

In this set of questions, we are 1st required to calculate total number of matches. Let us understand the scheme of matches in a Round Robin League tournament.

Method 1 - In a round robin league tournament, each team plays against other team once. So if there are five teams A, B, C, D and E (let us assume), total number of matches are going to be the following:

AB, AC, AD, AE

BC, BD, BE

CD, CE,

DE

Hence total number of matches = 4 + 3 + 2 + 1 = 10.

In general, if there are n teams, then total number of matches = (n-1) + (n-2)+.+3 + 2 + 1 = (n(n-1))/2

Method 2 - each team plays one match with every other team. So, number of matches played by each team = 4. So total number of matches = 5 teams 4 matches = 20 matches. But each of these matches has been counted twice for example match AB and BA both have been counted.

So total number of unique matches = 20/2= 10 matches.

Method 3 Using Permutation and Combination

There is a match for every set of two players. So, if there are n players, total number of matches = nC2.

In this question, there are three teams Bihar, Punjab and Haryana.

Hence total number of matches = 2 + 1 (Using method 1)

This is also equal to (n(n-1))/2 = (3(3-1))/2 = 3 matches.

Hence answer to Q1.Total number of matches played in the competition = 3 matches. Hence option (1) is the answer.

SECONDLY,

Total Goals for by all the teams = Total Goals Against all the teams

Now total goals against = 4 + 7 + 1 = 12 goals

This gives us the number of Goals for Haryana = 12 (2+3) = 7

Match played

Won

Drawn

Lost

Goals for

Goals against

Bihar

2

1

2

4

Punjab

2

3

7

Haryana

2

7

1

Now, Bihar has drawn one of its matches, so it has either won or lost the other match.

Since it has drawn one of its two matches, possible score for Bihar is:

Match 1 (Draw)

Match 2 (Lost)

Hypothesis

Possibility 1

0--0

2--4

Hypothesis 1

Possibility 2

1--1

1--3

Hypothesis 2

Possibility 3

2--2

0--2

Hypothesis 3

2-2 = Goals for 2 and goals against 2.

It can be seen that Bihar is losing its second match.

Testing Hypothesis 1:

Hereafter, we will have to go ahead with hypothesis 1. Using the conditions given, then, we will verify if the assumptions that we have assumed are correct or not.

Assume that Bihar has its match drawn with Punjab and lost its match against Haryana.

Since Punjab and Haryana both have played one match with Bihar at this stage, total number of matches occurred so far = 2. And next match will be between Punjab and Haryana.

Using the score card of Punjab Goals for 3 and Goals against 7.

Since one of its matches was drawn with Bihar (score 0 0), hence score of 2nd match against Haryana would be = 3-7

Match 1 (Drawn with Bihar)

Match 2 (Lost to Haryana )

Punjab

0--0

3--7

Now Finally, we will have to evaluate if the goals for / against obtained in two matches against Haryana (one against Bihar and another against Punjab) support the figure given in the original table given in the question.

Bihars score against Haryana = 2 4 ?Score read in favour of Haryana = 4 2 (i.e. Haryana scored 4 goals and Bihar scored 2 goals) ---------------------(1)

Punjabs score against Haryana = 3 7 ? Score read in favour of Haryana = 7 -3 (i.e. Haryana scored 7 goals and Punjab scored 3 goals) ------------------(2)

Using the information given above in (1) and (2):

Haryana scored a total of 4 + 7 = 11 goals against these two teams. Looking at the information given in the table, Haryana has scored only 7 goals against both the teams taken together.

So, the hypothesis that Bihar drawn its match against Punjab with 0-0 is wrong.

Testing Hypothesis 2:

Similarly we will test our 2nd Hypothesis that Bihar drawn its match against Punjab with 1-1.

Testing Hypothesis 3:

Now checking the hypothesis that Bihar drawn its match against Punjab with score 2-2.

Using the score card of Punjab Goals for 3 and Goals against 7.

Since one of its matches was drawn with Bihar (score 0 0), hence score of 2nd match against Haryana would be = 3-7

Match 1 (Drawn with Bihar)

Match 2 (Lost to Haryana )

Punjab

2--2

15

Bihars score against Haryana = 0 2 ? Score read in favour of Haryana = 2 0 (i.e. Haryana scored 2 goals and Bihar scored 0 goal) ---------------------(1)

Punjabs score against Haryana = 1 5 ? Score read in favour of Haryana = 5 -1 (i.e. Haryana scored 5 goals and Punjab scored 1 goal) ------------------(2)

Using the information given above in (1) and (2):

Haryana scored a total of 5 + 2 = 7 goals against these two teams. Looking at the information given in the table, Haryana has scored 7 goals against both the teams taken together. At the same time, Punjab and Bihar taken together have scored 0 + 1 = 1 goal against Haryana. This also suits the tally given in the table (in original question).

So Hypothesis 3 is correct.

Hence the final table is like:

Match played

Won

Drawn

Lost

Goals for

Goals against

Bihar

2

0

1

1

2

4

Punjab

2

0

1

1

3

7

Haryana

2

2

0

0

7

1

(New findings are in bold and italics)

Now all the questions from Q2 to Q4 can be answered.

Answers:

Q1

Q2

Q3

Q4

1

2

2

4

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