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CAT 2024 Slot 2 DILR · Set 5 of 5Logical ReasoningModerate DifficultyQ18–Q22 · 2 MCQ + 3 TITA

CAT 2024 Slot 2 DILR Set 5: Arrangements (5 Questions) with Solutions

The Arrangements set from the official CAT 2024 Slot 2 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2024 Slot 2 DILR · Questions 18–22
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.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q18. Arrangements

MCQ · +3 / −1
What best can be concluded about the number of players coached by Zara?
  1. A) Exactly 2
  2. B) Either 2 or 3
  3. C) Exactly 3
  4. D) Either 2 or 3 or 4
Correct Answer
A) Exactly 2
Step-by-step solution
📌 Core Concept
The ratings are forced by the 1 to 7 scale and the average of 4. That fixes the coach of each player and gives Zara's count.
🔢 Step-by-Step Solution
1
Clue 3 says only Players 5 and 7 share a rating and everyone else is unique. So the eight ratings use all of 1 to 7, with one value repeated. Clue 4 gives a total of 8×4=328 \times 4 = 32. Since 1+2+⋯+7=281+2+\dots+7 = 28, the repeated value is 32−28=432-28=4, so Players 5 and 7 each got 4.
2
Clue 1 of the coach rules: Yuki trains only even players and Zara only odd players. Players 1 and 4 share a coach (clue 2), and that coach must be Xena, because Player 1 is odd (not Yuki) and Player 4 is even (not Zara).
3
Players 2, 3 and 5 have three different coaches (clue 2). Player 3 and Player 5 are odd, so each is Xena's or Zara's, and they must differ. That leaves Player 2 with Yuki.
4
If Player 5 were Xena's, then Player 7 (same coach as Player 5) would be Xena's too, and Player 3 would be Zara's. Then Players 1, 5 and 7 are all Xena's, so Zara would have only Player 3. That breaks the rule that each coach trains at least two players.
5
So Player 3 is Xena's and Players 5 and 7 are Zara's. Zara's only possible odd players are 1, 3, 5, 7, and 1 and 3 are Xena's, so Zara trains exactly Players 5 and 7.
Quick Check
Zara's average is 4, Yuki's must be 6 and Xena's 3. This is consistent with the full solution (Xena: 1, 3, 4, 8; Yuki: 2, 6).
Correct Answer: A

Q19. Arrangements

TITA · +3 / 0
What was the rating of Player-7?
Correct Answer
4
Step-by-step solution
📌 Core Concept
The total rating and the uniqueness condition fix the shared rating of Players 5 and 7.
🔢 Step-by-Step Solution
1
Clue 3 says Players 5 and 7 have the same rating and all other players have unique ratings. So the eight ratings take every value from 1 to 7, with exactly one value repeated.
2
Clue 4 gives a total of 8×4=328 \times 4 = 32.
3
The values 1 to 7 add up to 28, so the repeated value is 32−28=432 - 28 = 4.
4
Player 7 shares Player 5's rating, so Player 7 got 4.
Quick Check
Clue 7 needs Player 4's rating to be less than Player 5's. With Player 5 at 4, Player 4 is 2, which works.
Correct Answer: 4

Q20. Arrangements

TITA · +3 / 0
What was the rating of Player-6?
Correct Answer
5
Step-by-step solution
📌 Core Concept
Fix the ratings of Players 2, 4, 5, 7 and 8 first, then use the average condition for Yuki to find Player 6.
🔢 Step-by-Step Solution
1
The ratings use 1 to 7 with 4 repeated, so Players 5 and 7 each got 4. Clue 5 gives Player 2 the highest rating, 7.
2
Clue 7 says Player 4 is double Player 8 and below Player 5's 4. So Player 4 is 2 and Player 8 is 1.
3
The ratings 3, 5 and 6 remain for Players 1, 3 and 6.
4
The coach assignments are forced. Xena has Players 1 and 4. Player 2 goes to Yuki. Player 3 goes to Xena, and Players 5 and 7 go to Zara. This leaves Players 6 and 8 for Xena or Yuki.
5
Zara's average is 4. Clue 6 then makes Yuki's average 4+2=64+2=6, and Xena's average is 6/2=36/2=3.
6
Yuki has Player 2 (rating 7). With Player 6 only, (7+P6)/2=6(7+P_6)/2 = 6, so P6=5P_6 = 5. With Player 8 only, the average is (7+1)/2=4(7+1)/2 = 4, which fails. With both, (7+P6+1)/3=6(7+P_6+1)/3 = 6 gives P6=10P_6=10, which is impossible.
7
So Player 6 got 5.
Quick Check
Xena trains Players 1, 3, 4, 8. Her ratings sum to 9+2+1=129+2+1 = 12, an average of 3, as clue 6 requires.
Correct Answer: 5

Q21. Arrangements

TITA · +3 / 0
For how many players the ratings can be determined with certainty?
Correct Answer
6
Step-by-step solution
📌 Core Concept
Work out which ratings are forced and which are only known as a pair.
🔢 Step-by-Step Solution
1
The repeated rating is 4, so Players 5 and 7 each got 4. That fixes two players.
2
Clue 5 gives Player 2 the rating 7.
3
Clue 7 gives Player 4 a rating of 2 and Player 8 a rating of 1. That fixes two more players.
4
The average condition for Yuki, whose players are 2 and 6, forces Player 6 to be 5.
5
That is six players fixed: Players 2, 4, 5, 6, 7 and 8.
6
The ratings 3 and 6 remain for Players 1 and 3. Xena's average of 3 needs P1+P3=9P_1+P_3 = 9, and both splits 3+63+6 and 6+36+3 give that sum. No clue separates them, so Players 1 and 3 stay undetermined.
7
Six players have ratings that can be determined with certainty.
Correct Answer: 6

Q22. Arrangements

MCQ · +3 / −1
Who all were the players trained by Xena?
  1. A) Player-1, Player-4, Player-6, Player-8
  2. B) Player-1, Player-3, Player-4, Player-6
  3. C) Player-1, Player-3, Player-4, Player-8
  4. D) Player-1, Player-3, Player-4
Correct Answer
C) Player-1, Player-3, Player-4, Player-8
Step-by-step solution
📌 Core Concept
The clues about coaches and averages fix who trained whom.
🔢 Step-by-Step Solution
1
Players 1 and 4 share a coach, and only Xena can train both (Player 1 is odd, Player 4 is even). So Xena has Players 1 and 4.
2
Players 3 and 5 are odd, so each is Xena's or Zara's. Clue 2 makes Players 2, 3 and 5 have three different coaches, so Players 3 and 5 differ and Player 2 goes to Yuki.
3
Suppose Player 5 were Xena's. Player 7 would then also be Xena's, and Zara would be left with only Player 3. Each coach must train at least two players, so this fails.
4
So Player 3 is Xena's, and Players 5 and 7 are Zara's.
5
Players 6 and 8 go to Xena or Yuki. The ratings are P2=7P_2=7, P4=2P_4=2, P8=1P_8=1, P5=P7=4P_5=P_7=4. Zara's average is 4, so Yuki's average is 6 and Xena's is 3.
6
Yuki with Players 2 and 8 gives (7+1)/2=4(7+1)/2=4, which fails. Yuki with Players 2, 6 and 8 would need P6=10P_6=10, which fails. Yuki with Players 2 and 6 gives P6=5P_6=5 and an average of 6, which works.
7
Player 8 therefore goes to Xena. Xena trains Players 1, 3, 4 and 8, and Yuki's count of 2 is below Xena's 4, as clue 1 requires.
Why Not the Others
A: Player 3 must be Xena's, and Player 6 must be Yuki's.
B: It leaves out Player 8 and wrongly includes Player 6.
D: Xena needs four players, and Player 8 cannot go to Yuki.
Correct Answer: C
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CAT 2024 Slot 2 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Calcutta

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