CAT 2024 Question Paper | DILR Slot 1

CAT Questions

CAT 2024 DILR did not have a change in pattern. Atleast two sets were doable in each slot and one of the four sets was extremely tough. Choice of Sets became a crucial factor. Overall this section was at a medium to high level of difficulty.

The game of QUIET is played between two teams. Six teams, numbered 1, 2, 3, 4, 5, and 6, play in a QUIET tournament. These teams are divided equally into two groups. In the tournament, each team plays every other team in the same group only once, and each team in the other group exactly twice. The tournament has several rounds, each of which consists of a few games. Every team plays exactly one game in each round.

The following additional facts are known about the schedule of games in the tournament.
1. Each team played against a team from the other group in Round 8.
2. In Round 4 and Round 7, the match-ups, that is the pair of teams playing against each other, were identical. In Round 5 and Round 8, the match-ups were identical.
3. Team 4 played Team 6 in both Round 1 and Round 2.
4. Team 1 played Team 5 ONLY once and that was in Round 2.
5. Team 3 played Team 4 in Round 3. Team 1 played Team 6 in Round 6.
6. In Round 8, Team 3 played Team 6, while Team 2 played Team 5.

Question 13 : What is the number of the team that played Team 6 in Round 3?

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Video Explanation

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Explanatory Answer

• Each team plays 2 matches in the same group and 6 matches with the other group.
• Therefore each plays a total of 8 matches. There are exactly 8 rounds. Each round has 3 matches.
• There are totally 24 matches.
• Team 1 and Team 5 are in the same group, since they play against each other only once.
• Team 4 played against Team 6 in Round 1 and Round 2. Therefore, they are in different groups.
• In Round 8, each team played against a team from the other group in Round 8. Since two of the matches are (Team 3 Vs Team 6) and (Team 2 Vs Team 5). The other match should be (Team 1 Vs Team 4). Therefore Team 1 and Team 4 are also in different groups.
• Forming the teams in groups A and B

Group A	Group B
1	4
5	2
6	3

ROUNDS	MATCH 1	MATCH 2	MATCH 3
1	4 vs. 6
2	4 vs. 6	1 vs. 5
3	3 vs. 4
4*
5#	3 vs. 6	2 vs. 5	1 vs. 4
6	1 vs. 6
7*
8#	3 vs. 6	2 vs. 5	1 vs. 4

* implies matches in Round 4 and Round 7 are identical.

# implies matches in Round 5 and Round 8 are identical.

• We know that Team 4 is in a different group from Team 1, 5 and 6.
• Team 4 already played two matches against Team 1 in rounds 8 and 5. Also it played two matches against Team 6 each in the rounds 1 and 2. So it has to play two matches against Team 5. These two matches can placed in any two of the rounds 4,6 or 7. Also matches in Round 4 and Round 7 are identical. Therfore two matches of Team 4 against Team 5 are played in round 4 and round 7.
• In Round 2 , match 3 is definitely between Team 2 and Team 3 because the other 4 Teams have already one match.

ROUNDS	MATCH 1	MATCH 2	MATCH 3
1	4 vs. 6
2	4 vs. 6	1 vs. 5	2 vs. 3
3	3 vs. 4
4*	4 vs. 5
5#	3 vs. 6	2 vs. 5	1 vs. 4
6	1 vs. 6
7*	4 vs. 5
8#	3 vs. 6	2 vs. 5	1 vs. 4

• It is clear from the above table, Team 4 has played in all the rounds except Round 6. Hence only Team it can play against is Team 2 in Round 6. Therefore the third match in Round 6 is between Team 3 and Team 5.
• Team 2 has to play two macthes against Team 6. These two matches can placed in any two of the rounds 3,4 or 7. Also matches in Round 4 and Round 7 are identical. Therfore two matches of Team 2 against Team 6 are played in round 4 and round 7. This automatically fills the 3rd match (Team 1 against Team 3) in round 4 and round 7.
• Team 1 has to play two matches against Team 2. These two matches fits exactly in Round 1 and Round 3.
• This automatically fills the 3rd match in Round 1 and Round 3. Round 1 – Match 3 ( Team 3 against Team 5) Round 3- Match 3 ( Team 5 against Team 6)

ROUNDS	MATCH 1	MATCH 2	MATCH 3
1	4 vs. 6	1 vs. 2	3 vs. 5
2	4 vs. 6	1 vs. 5	2 vs. 3
3	3 vs. 4	1 vs. 2	5 vs. 6
4*	4 vs. 5	2 vs. 6	1 vs. 3
5#	3 vs. 6	2 vs. 5	1 vs. 4
6	1 vs. 6	4 vs. 2	3 vs. 5
7*	4 vs. 5	2 vs. 6	1 vs. 3
8#	3 vs. 6	2 vs. 5	1 vs. 4

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The question is " What is the number of the team that played Team 6 in Round 3? "

Answer: From the table it is evident that Team 6 played Team 5 in Round 3.

Hence, the answer is '5'

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