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CAT 2021 Slot 3 DILR · Set 2 of 4Logical ReasoningModerate DifficultyQ7–Q12 · 2 MCQ + 4 TITA

CAT 2021 Slot 3 DILR Set 2: Arrangements (6 Questions) with Solutions

The Arrangements set from the official CAT 2021 Slot 3 DILR paper: the caselet, all 6 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 2021 Slot 3 DILR · Questions 7–12
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external "subject matter experts" (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below.
If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it.
A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal.
The following facts are also known.
1
Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.
2
Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
3
Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.
4
Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q7. Arrangements

TITA · +3 / 0
How many questions were DEFINITELY created by Amal?
Correct Answer
3
Step-by-step solution
📌 Core Concept
The creator is identified by who reviewed a question and in what order. A creator never reviews their own question, and each creator has a distinctive review path.
🔢 Step-by-Step Solution
1
List the reviewers of each question from facts 2 to 4. Q01 and Q05: Komal only. Q10: Amal only. Q03 and Q11: Amal and Komal. Q06 and Q13: Amal and Bimal. Q07, Q09 and Q12: Bimal and Komal. Q02, Q04 and Q08: all three.
2
An Amal-created question goes first to Bimal and then, only if he disapproves, to Komal. So a question seen only by Bimal and Komal must be Amal's.
3
Q07, Q09 and Q12 were reviewed by exactly Bimal and Komal, so Amal created all three. Neither an SME question (always seen by Amal first) nor a Komal question (Amal first) nor a Bimal question (Komal first, then Amal) fits this pattern.
4
Q07 was accepted, which fits Bimal disapproving and Komal approving. Q09 and Q12 were rejected, which fits both disapproving.
5
No other question is forced to Amal. Q03 and Q11 (Amal and Komal) point to Bimal. Q01, Q05 and Q10 are single-reviewer cases for Bimal or Komal. Q06 and Q13 could be SME or Komal. Q02, Q04 and Q08 are SME.
6
So the questions definitely created by Amal are Q07, Q09 and Q12, which is 3.
Quick Check
Amal never reviewed Q07, Q09 or Q12, which is consistent with Amal being their creator.
Correct Answer: 3

Q8. Arrangements

TITA · +3 / 0
How many questions were DEFINITELY created by Komal?
Correct Answer
1
Step-by-step solution
📌 Core Concept
The creator is identified from the review pattern. Komal's questions go first to Amal, and then to Bimal only if Amal disapproves.
🔢 Step-by-Step Solution
1
The reviewers of each question, from facts 2 to 4, are as follows. Q01 and Q05: Komal only. Q10: Amal only. Q03 and Q11: Amal and Komal. Q06 and Q13: Amal and Bimal. Q07, Q09 and Q12: Bimal and Komal. Q02, Q04 and Q08: all three.
2
For a Komal question, Komal never reviews. Amal reviews first, and Bimal reviews only after a disapproval by Amal. So a Komal question is reviewed by Amal alone, or by Amal and then Bimal.
3
Q10 was reviewed by Amal alone and accepted. An SME question always goes to Bimal too, and an Amal question would not be reviewed by Amal. A Bimal question would need Komal first. So Q10 was created by Komal.
4
Q06 and Q13 (Amal and Bimal) could be Komal's, with Amal disapproving and Bimal deciding. They could equally be SME questions on which both reviewers agreed. So neither is certain.
5
Q02, Q04 and Q08 involve Komal as a reviewer, so they cannot be hers.
6
Only Q10 is definitely Komal's, which gives 1.
Correct Answer: 1

Q9. Arrangements

TITA · +3 / 0
How many questions were DEFINITELY created by the SMEs?
Correct Answer
3
Step-by-step solution
📌 Core Concept
Only an SME question must be reviewed by both Amal and Bimal and then sometimes by Komal. A question reviewed by all three reviewers can therefore only be an SME question.
🔢 Step-by-Step Solution
1
Q02, Q04 and Q08 were reviewed by Amal, Bimal and Komal (facts 2 to 4).
2
Rule out the reviewer-created cases. If Amal created it, she would not review it. If Bimal created it, he would not review it. If Komal created it, she would not review it. Only an SME question can be seen by all three.
3
This fits the SME path: Amal and Bimal disagree, so Komal decides. Q02 was rejected because Komal disapproved. Q04 and Q08 were accepted because Komal approved.
4
The other questions can be placed without being SME. Q07, Q09 and Q12 are Amal's. Q03 and Q11 are Bimal's. Q01 and Q05 are Bimal's, since Komal reviewed them alone. Q10 is Komal's.
5
Q06 and Q13 (Amal and Bimal only) could be SME or Komal, so neither is certain.
6
The definite SME questions are Q02, Q04 and Q08, which is 3.
Correct Answer: 3

Q10. Arrangements

TITA · +3 / 0
How many questions were DEFINITELY disapproved by Bimal?
Correct Answer
4
Step-by-step solution
📌 Core Concept
Work out the creator of each question and then the decisions its review path forces. Count only the questions where Bimal's disapproval is certain.
🔢 Step-by-Step Solution
1
Q07, Q09 and Q12 were reviewed only by Bimal and Komal, so Amal created them. Bimal reviews first and Komal reviews only if Bimal disapproves. Since Komal saw them, Bimal disapproved all three.
2
Q06 was reviewed by Amal and Bimal only and was rejected. An approval by either would have been accepted (Komal's or Amal's path) or sent to Komal (SME path), but Komal did not review it. Both therefore disapproved, so Bimal disapproved Q06.
3
That already gives Q06, Q07, Q09 and Q12.
4
The other Bimal reviews do not force a disapproval. On Q13 (accepted, no Komal), Bimal must have approved. On Q02, Q04 and Q08, which are SME questions, Amal and Bimal disagree, but which of them disapproved is not fixed.
5
So the questions Bimal definitely disapproved are Q06, Q07, Q09 and Q12, which is 4.
Quick Check
Bimal reviewed Q02, Q04, Q06, Q07, Q08, Q09, Q12 and Q13. Four of these are forced disapprovals, one (Q13) is forced approval, and three are uncertain.
Correct Answer: 4

Q11. Arrangements

MCQ · +3 / −1
The approval ratio of a reviewer is the ratio of the number of questions (s)he approved to the number of questions (s)he reviewed. Which option best describes Amal's approval ratio?
  1. A) lies between 0.25 and 0.75
  2. B) 0.25
  3. C) either 0.25 or 0.75
  4. D) lies between 0.25 and 0.50
Correct Answer
A) lies between 0.25 and 0.75
Step-by-step solution
📌 Core Concept
For Amal, fix the decisions that are forced and treat the others as unknowns. This gives the lowest and highest possible approval ratio.
🔢 Step-by-Step Solution
1
Amal reviewed 8 questions: Q02, Q03, Q04, Q06, Q08, Q10, Q11 and Q13.
2
Q03 was reviewed by Amal and Komal, so Bimal created it. Komal reviewed first and disapproved, and Amal then reviewed it. It was accepted, so Amal approved it.
3
Q10 was reviewed by Amal alone and accepted, so Amal approved it.
4
Q06 was rejected without Komal, so both reviewers disapproved. Amal disapproved it.
5
Q11 was a Bimal question rejected after Komal's disapproval, so Amal also disapproved it.
6
Q13 was accepted with only Amal and Bimal reviewing. If it was an SME question, both approved. If it was Komal's, Amal disapproved and Bimal approved. Either is possible.
7
Q02, Q04 and Q08 are SME questions on which Amal and Bimal disagreed, so Amal's decision on each is unknown.
8
The minimum is 2 approvals (Q03 and Q10), a ratio of 2/8=0.252/8 = 0.25. The maximum is 2+1+3=62 + 1 + 3 = 6 approvals, a ratio of 6/8=0.756/8 = 0.75. Both extremes are possible.
9
So the ratio can fall anywhere from 0.25 to 0.75.
Why Not the Others
B: 0.25 is only the minimum, not the only value.
C: Intermediate values such as 0.5 are also possible.
D: It cannot be limited to 0.50 or below, since up to 6 of 8 approvals is possible.
Correct Answer: A

Q12. Arrangements

MCQ · +3 / −1
How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?
  1. A) 5
  2. B) 2
  3. C) 4
  4. D) 7
Correct Answer
A) 5
Step-by-step solution
📌 Core Concept
Identify every question created by Amal or Bimal. Then check whether a reviewer other than the creator must have disapproved it.
🔢 Step-by-Step Solution
1
Q07, Q09 and Q12 were reviewed only by Bimal and Komal, so Amal created them. Komal saw them only because Bimal disapproved. Each was therefore disapproved by at least one other reviewer. That is 3.
2
Q03 and Q11 were reviewed by Amal and Komal only. These can only be Bimal's questions, since Komal reviews first and Amal reviews only after a disapproval. Komal disapproved both, so they count. That is 2 more, giving 5.
3
Q01 and Q05 were reviewed by Komal alone and accepted. They are Bimal's questions that Komal approved. Nobody disapproved them, so they do not count.
4
Q10 was reviewed by Amal alone, which makes it Komal's question. It is not Amal's or Bimal's, so it is not counted.
5
The remaining questions are SME or Komal questions, so none is created by Amal or Bimal.
6
The total is 3+2=53 + 2 = 5.
Why Not the Others
B: 2 counts only the Bimal questions.
C: 4 leaves out one of the forced cases.
D: 7 wrongly includes Q01 and Q05, which Komal approved.
Correct Answer: A
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CAT 2021 Slot 3 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Ahmedabad

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