CAT 2025 Lesson : Teams & Events - Case 1

Direction for Questions 1 to 2: Read the information provided and answer the questions which follow.

In ISL football competition, eight football teams - Atletico De Kolkata, Chennaiyan FC, Delhi Dynamos, FC Goa, FC Pune City, Kerala Blasters, Mumbai City FC and North-East United FC - participated where each team played against every other team exactly once. Every win earned three points for the teams and a loss earned 0. If there was a draw, each team was rewarded one point. Now, as per the fixtures, following are some of the observations:

(a) Out of the seven matches played by Chennaiyan FC, it won five and the other two matches were drawn.
(b) FC Pune City won the match against FC Goa and Kerala Blasters but lost the match against Delhi Dynamos and Chennaiyan FC.
(c) Atletico De Kolkata drew a match against FC Goa, Chennaiyan FC and FC Pune City.
(d) None of the teams lost all the matches.
[IIFT 2017]

1) If Chennaiyan FC won the match against FC Goa, what could have been the maximum score of FC Goa?

(1) 11
(2) 12
(3) 13
(4) 14

2) What could be the minimum absolute difference between the scores of FC Pune City and Chennaiyan FC?

(1) 0
(2) 1
(3) 3
(4) 4

Solution

The Eight football teams Atletico De Kolkata, Chennaiyan FC, Delhi Dynamos, FC Goa, FC Pune City, Kerala Blasters, Mumbai City FC, and North-East United FC can be represented as A, C, D, G, P, K, M, and N. A team gets 3 points for a win, 1 point each for a draw, and 0 points for a loss.

The total number of matches in the competition is $^{8}\mathrm{C}_{2}$ = $\dfrac{8 \times 7}{2}$ = 28 matches. Each team played 7 matches against other teams.

'>' represents 'defeated' and '=' represents 'drew with'. For example, C > G means Chennaiyan FC defeated FC Goa.



1) From (a), (b), and (c) it is given that G lost a match against P, and drew a match with K. G can get a maximum of 4 wins against A, D, M, and N. It is also given in the question that C > G and with the 4 wins and 1 drawn match the maximum score of FC Goa should be 13 points (4 $\times$ 3 + 1).

Answer: (3) 13

2) From (a) it is given that the total points of C must be 17 points. To achieve the minimum score difference between C and P, we should consider the maximum score that P can attain in the competition.

From (b) it is given that P had lost its match against D and C, and a drew match against K. So P can score 12 points by winning against the four teams (A, G, M, and N) and 1 point from the drew match against K. P can score a maximum of 13 points in the tournament.

The minimum difference between C and P = 17 – 13 = 4 points.

Answer: (4) 4

Answer:
1) (3) 13
2) (4) 4