CAT 2025 Lesson : Teams & Events - Case 4

Directions for questions 12 to 15: Answer the following questions based on the information given below.

In a sports event, six teams (A, B, C, D, E and F) are competing against each other. Matches are scheduled in two stages. Each team plays three matches in Stage-I and two matches in Stage-II. No team plays against the same team more than once in the event. No ties are permitted in any of the matches. The observations after the completion of Stage-I and Stage-II are as given below.

Stage-I:
- One team won all the three matches.
- Two teams lost all the matches.
- D lost to A but won against C and F.
- E lost to B but won against C and F.
- B lost at least one match.
- F did not play against the top team of Stage-I.

Stage-II:
- The leader of Stage-I lost the next two matches.
- Of the two teams at the bottom after Stage-I, one team won both matches, while the other lost both matches.
- One more team lost both matches in Stage-II.
[CAT 2008]

12) The two teams that defeated the leader of Stage-I are:

(1) F & D
(2) E & F
(3) B & D
(4) E & D
(5) F & D

13) The only team(s) that won both the matches in Stage-II is (are):

(1) B
(2) E & F
(3) A, E & F
(4) B, E & F
(5) B & F

14) The teams that won exactly two matches in the event are:

(1) A, D & F
(2) D & E
(3) E & F
(4) D, E & F
(5) D & F

15) The team(s) with the most wins in the event is (are):

(1) A
(2) A & C
(3) F
(4) E
(5) B & E

Solution

Each team in the event plays exactly one match with the other teams and also plays three matches in Stage-I and two matches in Stage-II. '>' represents 'defeated'. For example, A > D means A wins a match against D.

Stage-I



Using the information in (3), (4) and (5), we can start filling the following table.
From (3), we can infer that A defeated D and D defeated both C and F in stage-I.
From (4), we can infer that B defeated E and E defeated both C and F in stage-I.



It is given in statement (2) for stage-I that exactly two teams lost in all matches. Therefore, C and F must be two teams that lost in all the matches. B lost at least one match in stage-I, so A is the only team that won all three matches in stage-I.



F does not play with the top team which is A and also lost all the matches on stage-I like C. So it must lose a match against B. This shows that A won its other two matches against B and C.



Stage-II



A should have lost its match against E and F because it has already played against D, B, and C in stage-I. F won its match against A, so C must be the 2^nd team that lost all its matches in stage-II. Since C already played against D, E and A in stage-I, it should have lost the two matches against B and F.



From (3), we can infer that D should be the 3^rd team that lost the two matches in stage-II with B and E.



12) The following table shows the results of stage-II matches.



From the above table it is clear that E and F are the two teams that defeated A in stage-II.

Answer: (2) E & F

13) The following table shows the results of stage-II matches.



B, E, and F are the three teams won all the matches in stage-II.

Answer: (4) B, E & F

14) The following table shows the results of stage-I matches.



The following table shows the results of stage-II matches.



The total number of wins of each team in the event as calculated in the above two tables is given below.



From the above tables, it is clear that D and F are the only two teams won exactly two matches in the whole event.

Answer: (5) D & F

15) The following table shows the results of stage-I matches.



The following table shows the results of stage-II matches.



The total number of wins of each team in the event as calculated in the above two tables is given below.



From these tables it is clear that B and E has four wins each in the end of the event.

Answer: (5) B & E

Answer: 12) (2) E & F;
13) (4) B, E & F;
14) (5) D & F;
15) (5) B & E