CAT 2021 Slot 3 · DILR · Set 4: Reviewers Selecting Questions

The full set and all 6 questions (Q15–Q20) from CAT 2021 Slot 3, with answers and solutions.

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 known about the review process after its completion.

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.

Question 15 · Caselet DI

How many questions were DEFINITELY created by Amal?

Answer & solution

Answer: 3

Solving the set

Step 1 – Possible review paths for each type of creator:

Creator	Who reviews, in order	Possible reviewer sets
SME	Amal, Bimal; Komal only if they split	{A, B} or {A, B, K}
Amal	Bimal; Komal only if Bimal disapproves	{B} or {B, K}
Bimal	Komal; Amal only if Komal disapproves	{K} or {K, A}
Komal	Amal; Bimal only if Amal disapproves	{A} or {A, B}

Step 2 – Match each question's reviewer set (facts 2–4) with these paths and its result (fact 1).

Question	Reviewed by	Result	Creator	Decisions
Q01	Komal	Accepted	Bimal	K approved
Q02	Amal, Bimal, Komal	Rejected	SME	A/B split, K disapproved
Q03	Amal, Komal	Accepted	Bimal	K disapproved, A approved
Q04	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q05	Komal	Accepted	Bimal	K approved
Q06	Amal, Bimal	Rejected	SME or Komal	A and B disapproved
Q07	Bimal, Komal	Accepted	Amal	B disapproved, K approved
Q08	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q09	Bimal, Komal	Rejected	Amal	B and K disapproved
Q10	Amal	Accepted	Komal	A approved
Q11	Amal, Komal	Rejected	Bimal	K and A disapproved
Q12	Bimal, Komal	Rejected	Amal	B and K disapproved
Q13	Amal, Bimal	Accepted	SME or Komal	SME: both approved; Komal: A disapproved, B approved

This question

Questions with reviewer set {Bimal, Komal} can only be Amal's: Q07, Q09, Q12. No other question fits Amal's path. So 3.

Hence, the answer is 3.

Question 16 · Caselet DI

How many questions were DEFINITELY created by Komal?

Answer & solution

Answer: 1

Solving the set

Step 1 – Possible review paths for each type of creator:

Creator	Who reviews, in order	Possible reviewer sets
SME	Amal, Bimal; Komal only if they split	{A, B} or {A, B, K}
Amal	Bimal; Komal only if Bimal disapproves	{B} or {B, K}
Bimal	Komal; Amal only if Komal disapproves	{K} or {K, A}
Komal	Amal; Bimal only if Amal disapproves	{A} or {A, B}

Step 2 – Match each question's reviewer set (facts 2–4) with these paths and its result (fact 1).

Question	Reviewed by	Result	Creator	Decisions
Q01	Komal	Accepted	Bimal	K approved
Q02	Amal, Bimal, Komal	Rejected	SME	A/B split, K disapproved
Q03	Amal, Komal	Accepted	Bimal	K disapproved, A approved
Q04	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q05	Komal	Accepted	Bimal	K approved
Q06	Amal, Bimal	Rejected	SME or Komal	A and B disapproved
Q07	Bimal, Komal	Accepted	Amal	B disapproved, K approved
Q08	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q09	Bimal, Komal	Rejected	Amal	B and K disapproved
Q10	Amal	Accepted	Komal	A approved
Q11	Amal, Komal	Rejected	Bimal	K and A disapproved
Q12	Bimal, Komal	Rejected	Amal	B and K disapproved
Q13	Amal, Bimal	Accepted	SME or Komal	SME: both approved; Komal: A disapproved, B approved

This question

Only Q10 (reviewed by Amal alone) must be Komal's. Q06 and Q13 ({Amal, Bimal}) could be Komal's or an SME's.

Hence, the answer is 1.

Question 17 · Caselet DI

How many questions were DEFINITELY created by the SMEs?

Answer & solution

Answer: 3

Solving the set

Step 1 – Possible review paths for each type of creator:

Creator	Who reviews, in order	Possible reviewer sets
SME	Amal, Bimal; Komal only if they split	{A, B} or {A, B, K}
Amal	Bimal; Komal only if Bimal disapproves	{B} or {B, K}
Bimal	Komal; Amal only if Komal disapproves	{K} or {K, A}
Komal	Amal; Bimal only if Amal disapproves	{A} or {A, B}

Step 2 – Match each question's reviewer set (facts 2–4) with these paths and its result (fact 1).

Question	Reviewed by	Result	Creator	Decisions
Q01	Komal	Accepted	Bimal	K approved
Q02	Amal, Bimal, Komal	Rejected	SME	A/B split, K disapproved
Q03	Amal, Komal	Accepted	Bimal	K disapproved, A approved
Q04	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q05	Komal	Accepted	Bimal	K approved
Q06	Amal, Bimal	Rejected	SME or Komal	A and B disapproved
Q07	Bimal, Komal	Accepted	Amal	B disapproved, K approved
Q08	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q09	Bimal, Komal	Rejected	Amal	B and K disapproved
Q10	Amal	Accepted	Komal	A approved
Q11	Amal, Komal	Rejected	Bimal	K and A disapproved
Q12	Bimal, Komal	Rejected	Amal	B and K disapproved
Q13	Amal, Bimal	Accepted	SME or Komal	SME: both approved; Komal: A disapproved, B approved

This question

Questions reviewed by all three (Q02, Q04, Q08) can only be SME questions. Q06 and Q13 may or may not be. So 3 definitely.

Hence, the answer is 3.

Question 18 · Caselet DI

How many questions were DEFINITELY disapproved by Bimal?

Pick an option, then check.

Answer & solution

Answer: Option B

Solving the set

Step 1 – Possible review paths for each type of creator:

Creator	Who reviews, in order	Possible reviewer sets
SME	Amal, Bimal; Komal only if they split	{A, B} or {A, B, K}
Amal	Bimal; Komal only if Bimal disapproves	{B} or {B, K}
Bimal	Komal; Amal only if Komal disapproves	{K} or {K, A}
Komal	Amal; Bimal only if Amal disapproves	{A} or {A, B}

Step 2 – Match each question's reviewer set (facts 2–4) with these paths and its result (fact 1).

Question	Reviewed by	Result	Creator	Decisions
Q01	Komal	Accepted	Bimal	K approved
Q02	Amal, Bimal, Komal	Rejected	SME	A/B split, K disapproved
Q03	Amal, Komal	Accepted	Bimal	K disapproved, A approved
Q04	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q05	Komal	Accepted	Bimal	K approved
Q06	Amal, Bimal	Rejected	SME or Komal	A and B disapproved
Q07	Bimal, Komal	Accepted	Amal	B disapproved, K approved
Q08	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q09	Bimal, Komal	Rejected	Amal	B and K disapproved
Q10	Amal	Accepted	Komal	A approved
Q11	Amal, Komal	Rejected	Bimal	K and A disapproved
Q12	Bimal, Komal	Rejected	Amal	B and K disapproved
Q13	Amal, Bimal	Accepted	SME or Komal	SME: both approved; Komal: A disapproved, B approved

This question

Bimal reviewed Q02, Q04, Q06, Q07, Q08, Q09, Q12, Q13. Definite disapprovals: Q06 (rejected with only A and B reviewing ⇒ both disapproved), Q07, Q09, Q12 (Amal's questions where Komal was consulted). Q02, Q04, Q08 – Amal and Bimal split, unknown who disapproved. Q13 – Bimal approved. So 4.

Hence, the answer is option 2.

Question 19 · Caselet DI

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?

A
either 0.25 or 0.75
B
0.25
C
lies between 0.25 and 0.50
D
lies between 0.25 and 0.75

Pick an option, then check.

Answer & solution

Answer: Option D

Solving the set

Step 1 – Possible review paths for each type of creator:

Creator	Who reviews, in order	Possible reviewer sets
SME	Amal, Bimal; Komal only if they split	{A, B} or {A, B, K}
Amal	Bimal; Komal only if Bimal disapproves	{B} or {B, K}
Bimal	Komal; Amal only if Komal disapproves	{K} or {K, A}
Komal	Amal; Bimal only if Amal disapproves	{A} or {A, B}

Step 2 – Match each question's reviewer set (facts 2–4) with these paths and its result (fact 1).

Question	Reviewed by	Result	Creator	Decisions
Q01	Komal	Accepted	Bimal	K approved
Q02	Amal, Bimal, Komal	Rejected	SME	A/B split, K disapproved
Q03	Amal, Komal	Accepted	Bimal	K disapproved, A approved
Q04	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q05	Komal	Accepted	Bimal	K approved
Q06	Amal, Bimal	Rejected	SME or Komal	A and B disapproved
Q07	Bimal, Komal	Accepted	Amal	B disapproved, K approved
Q08	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q09	Bimal, Komal	Rejected	Amal	B and K disapproved
Q10	Amal	Accepted	Komal	A approved
Q11	Amal, Komal	Rejected	Bimal	K and A disapproved
Q12	Bimal, Komal	Rejected	Amal	B and K disapproved
Q13	Amal, Bimal	Accepted	SME or Komal	SME: both approved; Komal: A disapproved, B approved

This question

Amal's 8 reviews: approved Q03 and Q10 for sure; disapproved Q06 and Q11 for sure; Q02, Q04, Q08 (one of A/B approved) and Q13 (approved if SME, disapproved if Komal's) are open. Approvals can be anything from 2 to 6: ratio from 2/8 = 0.25 to 6/8 = 0.75.

Hence, the answer is option 4.

Question 20 · Caselet DI

How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?

Pick an option, then check.

Answer & solution

Answer: Option C

Solving the set

Step 1 – Possible review paths for each type of creator:

Creator	Who reviews, in order	Possible reviewer sets
SME	Amal, Bimal; Komal only if they split	{A, B} or {A, B, K}
Amal	Bimal; Komal only if Bimal disapproves	{B} or {B, K}
Bimal	Komal; Amal only if Komal disapproves	{K} or {K, A}
Komal	Amal; Bimal only if Amal disapproves	{A} or {A, B}

Step 2 – Match each question's reviewer set (facts 2–4) with these paths and its result (fact 1).

Question	Reviewed by	Result	Creator	Decisions
Q01	Komal	Accepted	Bimal	K approved
Q02	Amal, Bimal, Komal	Rejected	SME	A/B split, K disapproved
Q03	Amal, Komal	Accepted	Bimal	K disapproved, A approved
Q04	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q05	Komal	Accepted	Bimal	K approved
Q06	Amal, Bimal	Rejected	SME or Komal	A and B disapproved
Q07	Bimal, Komal	Accepted	Amal	B disapproved, K approved
Q08	Amal, Bimal, Komal	Accepted	SME	A/B split, K approved
Q09	Bimal, Komal	Rejected	Amal	B and K disapproved
Q10	Amal	Accepted	Komal	A approved
Q11	Amal, Komal	Rejected	Bimal	K and A disapproved
Q12	Bimal, Komal	Rejected	Amal	B and K disapproved
Q13	Amal, Bimal	Accepted	SME or Komal	SME: both approved; Komal: A disapproved, B approved

This question

Amal's questions: Q07, Q09, Q12 – all disapproved by Bimal (3). Bimal's questions: Q01, Q05 approved by Komal; Q03 and Q11 disapproved by Komal (2). Total 5.

Hence, the answer is option 3.

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