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CAT 2019 Slot 1 DILR · Set 2 of 8Logical ReasoningEasy DifficultyQ5–Q8 · 4 MCQ

CAT 2019 Slot 1 DILR Set 2: Arrangements (4 Questions) with Solutions

The Arrangements set from the official CAT 2019 Slot 1 DILR paper: the caselet, all 4 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 2019 Slot 1 DILR · Questions 5–8
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.
The following additional facts are known.
i) No composer who assigned item to Princess, assigned any item to Queen.
ii) No composer who assigned item to Rani, assigned any item to Samragni.
iii) The first performance was by Princess; this item was assigned by Badal.
iv) The last performance was by Rani; this item was assigned by Gagan.
v) The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q5. Arrangements

MCQ · +3 / −1
Which of the following is true?
  1. A) The third performance was composed by Ashman
  2. B) The second performance was composed by Dyu.
  3. C) The second performance was composed by Gagan
  4. D) The third performance was composed by Dyu
Correct Answer
B) The second performance was composed by Dyu.
Step-by-step solution
📌 Core Concept
Fix the composer sequence of all eight performances using the position constraints and the equal-gap rule, then test each option.
🔢 Step-by-Step Solution
1
The first items are performances 1 to 4 and the second items are performances 5 to 8, both in the same dancer order. Princess is 1st (Badal) and Rani is last, so Rani's first item is 4th and her second item is 8th (Gagan).
2
The four first items have four different composers, so positions 1 to 4 hold Ashman, Badal, Gagan and Dyu once each. Rani's two items must come from different composers, so position 4 is not Gagan.
3
Each composer assigns two items, and Ashman's two items are consecutive. One item lies in positions 1 to 4 and the other in 5 to 8, so they must be positions 4 and 5. Hence Ashman has positions 4 and 5.
4
The second round then has Ashman at 5 and Gagan at 8, leaving Badal and Dyu for positions 6 and 7. The first round has Badal at 1, Ashman at 4, and Gagan and Dyu in positions 2 and 3.
5
Try Badal at 6, giving a gap of 5 from position 1. Dyu must also have a gap of 5, so Dyu is at 2 and 7. Gagan is then at 3 and 8, also a gap of 5. This works.
6
Try Badal at 7, giving a gap of 6. Dyu at 6 would have a gap of only 3 or 4, so this fails.
7
The order is Badal, Dyu, Gagan, Ashman, Ashman, Badal, Dyu, Gagan.
Why Not the Others
A: The 3rd performance is Gagan's, not Ashman's.
C: The 2nd performance is Dyu's, not Gagan's.
D: The 3rd performance is Gagan's, not Dyu's.
Correct Answer: B

Q6. Arrangements

MCQ · +3 / −1
Which of the following is FALSE?
  1. A) Queen did not perform in any item composed by Gagan
  2. B) Samragni did not perform in any item composed by Ashman
  3. C) Rani did not perform in any item composed by Badal
  4. D) Princess did not perform in any item composed by Dyu
Correct Answer
A) Queen did not perform in any item composed by Gagan
Step-by-step solution
📌 Core Concept
First fix the composer order of the eight performances, then assign dancers using the two exclusion clues.
🔢 Step-by-Step Solution
1
The first items are performances 1 to 4 and the second items are performances 5 to 8, in the same dancer order. Princess is 1st (Badal) and Rani is 4th, with her second item 8th (Gagan).
2
Ashman's items must be consecutive, one in the first round and one in the second, so they are positions 4 and 5. The equal-gap rule then fixes the composer order: Badal, Dyu, Gagan, Ashman, Ashman, Badal, Dyu, Gagan. Every composer except Ashman has a gap of 5.
3
Princess performs 1 and 5, so her composers are Badal and Ashman. Rani performs 4 and 8, so her composers are Ashman and Gagan.
4
By clue i, Queen cannot use Badal or Ashman. Queen performs in position 2 or 3 in the first round, and her second item is the matching position 6 or 7. Position 6 is Badal, so Queen must be the 3rd dancer, performing 3 and 7 (Gagan and Dyu).
5
Samragni is therefore the 2nd dancer, performing 2 and 6 (Dyu and Badal). This agrees with clue ii, since Rani (Ashman, Gagan) shares no composer with her.
6
Queen performs 3 and 7, which are Gagan's and Dyu's items, so she did perform in an item composed by Gagan.
Why Not the Others
B: Samragni has Dyu and Badal, so the statement is true.
C: Rani has Ashman and Gagan, so the statement is true.
D: Princess has Badal and Ashman, so the statement is true.
Correct Answer: A

Q7. Arrangements

MCQ · +3 / −1
The sixth performance was composed by:
  1. A) Gagan
  2. B) Badal
  3. C) Ashman
  4. D) Dyu
Correct Answer
B) Badal
Step-by-step solution
📌 Core Concept
Ashman's consecutive items and the equal-gap rule for the other composers fix the full composer sequence.
🔢 Step-by-Step Solution
1
Performances 1 to 4 are the first items, one per dancer, and 5 to 8 are the second items in the same dancer order. Princess is 1st (Badal) and Rani is last, so her second item is 8th (Gagan) and her first item is 4th. Her first item cannot be Gagan's, since her two items come from different composers.
2
Each composer has two items. Ashman's must be consecutive, with one in the first round and one in the second, so they are positions 4 and 5.
3
Position 5 is Ashman's. Position 8 is Gagan's. Positions 6 and 7 are therefore Badal and Dyu in some order. Gagan and Dyu share positions 2 and 3 in the first round.
4
If Badal is 6th, his gap from position 1 is 5. Dyu then needs a gap of 5, so Dyu is at 2 and 7. Gagan is at 3 and 8, again a gap of 5. This is consistent.
5
If Badal is 7th, his gap is 6. Dyu at 6 would have a gap of only 3 or 4, so this fails.
6
The sequence is Badal, Dyu, Gagan, Ashman, Ashman, Badal, Dyu, Gagan. The 6th performance is Badal's.
Why Not the Others
A: Gagan has positions 3 and 8.
C: Ashman has positions 4 and 5.
D: Dyu has positions 2 and 7.
Correct Answer: B

Q8. Arrangements

MCQ · +3 / −1
Which pair of performances were composed by the same composer?
  1. A) The third and the seventh
  2. B) The first and the seventh
  3. C) The first and the sixth
  4. D) The second and the sixth
Correct Answer
C) The first and the sixth
Step-by-step solution
📌 Core Concept
Build the composer sequence for all eight performances, then compare the positions named in each option.
🔢 Step-by-Step Solution
1
The first items (positions 1 to 4) use four different composers, and the second items (5 to 8) follow the same dancer order. Princess is 1st (Badal) and Rani is last (Gagan), so her first item is 4th and is not Gagan's.
2
Ashman's two items are consecutive and must straddle the two rounds, so they are positions 4 and 5. This leaves Badal and Dyu for positions 6 and 7.
3
Badal at 6 gives a gap of 5. Dyu must match it, so Dyu is at 2 and 7. Gagan is then at 3 and 8, also a gap of 5. Badal at 7 would give a gap of 6, which Dyu cannot match, so that case fails.
4
The sequence is Badal, Dyu, Gagan, Ashman, Ashman, Badal, Dyu, Gagan.
5
The 1st and 6th performances are both Badal's.
Why Not the Others
A: The 3rd is Gagan and the 7th is Dyu.
B: The 1st is Badal and the 7th is Dyu.
D: The 2nd is Dyu and the 6th is Badal.
Correct Answer: C
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CAT 2019 Slot 1 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Kozhikode

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