CAT 2024 Question Paper | DILR Slot 2

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.

Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.

The following additional information is known.
1. Xena trained more players than Yuki.
2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
4. The average of the ratings of all the players was 4.
5. Player-2 got the highest rating.
6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
7. Player-4's rating was double of Player-8's and less than Player-5's.

Question 7 :What was the rating of Player-6?

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Video Explanation

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Explanatory Answer

Each coach trained at least two players. So, the number of players trained by these coaches can be either 3+3+2=8 or 4+2+2=8. Since Xena trained more players than Yuki:

Xena	Yuki	Zara
3	2	3
4	2	2

Yuki trained only even numbered players and Zara trained only odd numbered players. Since Player 1 and Player 4 were trained by the same coach, it should be Xena. The coaches who trained Player-2, Player-3 and Player-5 are all different. Hence Player-2 must be trained by Yuki (only even numbered players).

	XENA	YUKI (Only Even)	ZARA (Only Odd)	Rating
Player 1	✓
Player 2		✓•
Player 3
Player 4	✓•
Player 5
Player 6
Player 7
Player 8

Now, Zara can train only odd numbered players. Player 3 and Player 5 cannot be trained by the same Person. Player 7 must be trained by Zara. Player 5 also must be trained by Zara which makes Player 3 trained by Xena. Player 6 or Player 8 will be trained by Yuki.

	XENA	YUKI (Only Even)	ZARA (Only Odd)	Rating
Player 1	✓
Player 2		✓
Player 3	✓
Player 4	✓•
Player 5			✓
Player 6
Player 7			✓•
Player 8

Therefore, the number of players trained by the coaches are fixed.

Xena	Yuki	Zara
4	2	2

Player 5 and Player 7 got trained by the same coach and both got the same ratings. All other players got a unique rating.

The average of the ratings of all the players is 4. Total ratings is 8*4 = 32.
The sum of ratings will be 1 + 2 + 3 + 4 + 5 + 6 + 7 + x = 32. Therefore x = 4. Therefore Player 5 and Player 7 got a rating of 4.

Player 2 got the highest rating which is 7.

Player 4 rating was double of Player 8 and less than Player 5. Player 4 should get an even number rating less than 4 which is 2.

Player 4 rating is 2 and Player 8 rating is 1.

Player	XENA	YUKI (Only Even)	ZARA (Only Odd)	Ratings
Player 1	✓			3 or 5 or 6
Player 2		✓		7
Player 3	✓			3 or 5 or 6
Player 4	✓•			2
Player 5			✓	4
Player 6				3 or 5 or 6
Player 7			✓•	4
Player 8				1
Average	x	2x	2x-2	4

Sum of the ratings = 32.

4x + 2(2x) + 2(2x - 2) = 32;
4x + 4x + 4x - 4 = 32;
12x = 36 => x = 3

Average of ratings given by Yuki to two players is 6. One of them is Player 2 whose rating is 7. Therefore, the other player should have got rating 5. Hence Player 6’s rating is 5. Since Player 6 is trained by Yuki, Player 8 has to be trainer by Xena.

Final Table

Player	XENA	YUKI (Only Even)	ZARA (Only Odd)	Ratings
Player 1	✓•			3 or 6
Player 2		✓•		7
Player 3	✓•			3 or 6
Player 4	✓•			2
Player 5			✓•	4
Player 6		✓•		5
Player 7			✓•	4
Player 8	✓•			1
Average	3	6	4	4

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The question is "What was the rating of Player-6?"

Answer: The rating of Player-6 is 5.

Hence, the answer is '5'

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