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CAT 2023 Slot 1 DILR · Set 1 of 4Logical ReasoningEasy DifficultyQ1–Q5 · 5 MCQ

CAT 2023 Slot 1 DILR Set 1: Arrangements (5 Questions) with Solutions

The Arrangements set from the official CAT 2023 Slot 1 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 2023 Slot 1 DILR · Questions 1–5
Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1
There cannot be more than two candidates from a single department.
2
A candidate cannot vote for himself/herself.
3
Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.

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

Q1. Arrangements

MCQ · +3 / −1
Which two candidates can belong to the same department?
  1. A) Prof. Pakrasi and Prof. Samuel
  2. B) Prof. Qureshi and Prof. Ramaswamy
  3. C) Prof. Pakrasi and Prof. Qureshi
  4. D) Prof. Ramaswamy and Prof. Samuel
Correct Answer
C) Prof. Pakrasi and Prof. Qureshi
Step-by-step solution
📌 Core Concept
The four candidate-to-candidate votes plus the block-voting rule fix the department sizes of the non-candidate groups. That fixes where each candidate sits.
🔢 Step-by-Step Solution
1
The candidates' own votes are S→P, P→R, R→Q and Q→S. Each candidate gets exactly 1 vote this way.
2
The non-candidates therefore cast the remaining votes: P 2, Q 13, R 5, S 0. That is 20 votes.
3
Each department's non-candidates vote as one block. O&Q has one candidate, so its block is 4. The other 3 candidates sit in F&A, M&S and B&H, with at most 2 per department.
4
P needs a block of exactly 2. Only B&H can give that, with 1 candidate (3 − 1 = 2). The other two candidates are then in F&A and M&S.
5
The blocks left are O&Q 4 and F&A 9−f9-f and M&S 7−m7-m, where f+m=2f+m=2. Only f=0, m=2f=0,\ m=2 gives blocks 4, 9, 5. Then Q's 13 = 4 + 9, and R's 5 is the M&S block.
6
So F&A has no candidate and M&S has two. The M&S block votes R, so R is not in M&S. The O&Q block votes Q, so Q is not in O&Q. Q is therefore in M&S or B&H.
7
If Q were in B&H, P and S would both be in M&S. But S voted for P, which breaks rule 3. So Q is in M&S.
8
Q's partner in M&S cannot be S, because Q voted for S. It cannot be R either. So it is P, and Prof. Pakrasi and Prof. Qureshi share M&S.
Why Not the Others
A: Samuel voted for Pakrasi, so they cannot share a department.
B: Ramaswamy voted for Qureshi, so they cannot share a department.
D: Ramaswamy and Samuel occupy O&Q and B&H, one each.
Correct Answer: C

Q2. Arrangements

MCQ · +3 / −1
Which of the following can be the number of votes that Prof. Qureshi received from a single department?
  1. A) 77
  2. B) 99
  3. C) 66
  4. D) 88
Correct Answer
B) 99
Step-by-step solution
📌 Core Concept
Qureshi's votes come as whole department blocks plus single votes from candidates. Working out the block sizes shows which single-department count is possible.
🔢 Step-by-Step Solution
1
The candidates' votes are S→P, P→R, R→Q and Q→S. Q gets 1 vote this way, from R.
2
Q's other 13 votes come from non-candidate blocks. P's 2 votes, R's 5 votes and S's 0 votes also come from blocks.
3
Only one candidate is from O&Q, so its block is 4. P's block of 2 can only be B&H, which has 1 candidate.
4
The remaining 2 candidates must then be in M&S, which gives an M&S block of 5. F&A, with no candidate, gives a block of 9. The other splits cannot produce R's 5 or Q's 13.
5
R's 5 votes are the M&S block. Q's 13 votes are the O&Q block (4) plus the F&A block (9).
6
So Q's 14 votes are 1 from R, 4 from O&Q and 9 from F&A. The only count from a single department that Q can receive is 9, from F&A.
Quick Check
1+4+9=141+4+9=14, which matches Qureshi's total.
Correct Answer: B

Q3. Arrangements

MCQ · +3 / −1
If Prof. Samuel belongs to B&H, which of the following statements is/are true?
Statement A: Prof. Pakrasi belongs to M&S. Statement B: Prof. Ramaswamy belongs to O&Q.
  1. A) Only statement A
  2. B) Only statement B
  3. C) Neither statement A nor statement B
  4. D) Both statements A and B
Correct Answer
D) Both statements A and B
Step-by-step solution
📌 Core Concept
Once the block structure is worked out, P and Q are forced into M&S. The location of S then fixes R.
🔢 Step-by-Step Solution
1
The candidates' votes are S→P, P→R, R→Q and Q→S. The non-candidate votes left are P 2, Q 13, R 5, S 0.
2
The O&Q block is 4, since one of the five is a candidate. P's block of 2 must be B&H with 1 candidate. R's block of 5 and Q's block of 13 (4 + 9) then force F&A to have no candidate and M&S to have two.
3
So the candidates are placed as follows: two in M&S, one in O&Q and one in B&H.
4
The M&S block votes R, so R is not in M&S. The O&Q and F&A blocks vote Q, so Q is not in O&Q or F&A.
5
Q is in M&S. Its M&S partner cannot be S, because Q voted for S. It cannot be R either. So it is P, and P and Q are both in M&S.
6
Given S is in B&H, R must take the remaining place, O&Q.
7
Statement A is true because Pakrasi is in M&S. Statement B is true because Ramaswamy is in O&Q.
Correct Answer: D

Q4. Arrangements

MCQ · +3 / −1
What best can be concluded about the candidate from O&Q\mathrm{O} \& \mathrm{Q} ?
  1. A) It was Prof. Ramaswamy.
  2. B) It was Prof. Samuel.
  3. C) It was either Prof. Pakrasi or Prof. Qureshi.
  4. D) It was either Prot. Ramaswamy or Prot. Samuel.
Correct Answer
D) It was either Prot. Ramaswamy or Prot. Samuel.
Step-by-step solution
📌 Core Concept
Block voting and the no-self-vote rules determine each candidate's department. This leaves only two candidates who could be the O&Q one.
🔢 Step-by-Step Solution
1
The candidates' votes are S→P, P→R, R→Q and Q→S. The non-candidate votes left are P 2, Q 13, R 5, S 0.
2
The O&Q block is 4. P's 2 votes need a block of 2, which is B&H with 1 candidate.
3
Then F&A has no candidate and M&S has two, giving blocks 4, 9 and 5. Q's 13 = 4 + 9 (O&Q and F&A) and R's 5 is the M&S block.
4
R receives the M&S block, so R is not in M&S. Q receives the O&Q and F&A blocks, so Q is not in O&Q.
5
If Q were in B&H, then P and S would both be in M&S. But S voted for P, so that is not allowed. So Q is in M&S.
6
Q's M&S partner cannot be S (Q voted for S) or R. So it is P, and P and Q are both in M&S.
7
R and S fill O&Q and B&H, one each. Either assignment satisfies every vote, so the O&Q candidate is R or S, and Pakrasi and Qureshi are both ruled out.
Why Not the Others
A and B: each names one of R or S, but both are possible.
C: P and Q are both in M&S, so neither is the O&Q candidate.
Correct Answer: D

Q5. Arrangements

MCQ · +3 / −1
Which of the following statements is/are true?
Statement A: Non-candidates from M&S voted for Prof. Qureshi. Statement B: Non-candidates from F&A voted for Prof. Qureshi.
  1. A) Both statements A and B
  2. B) Only statement B
  3. C) Neither statement A nor statement B
  4. D) Only statement A
Correct Answer
B) Only statement B
Step-by-step solution
📌 Core Concept
Work out which department block voted for which candidate. Then test each statement against those blocks.
🔢 Step-by-Step Solution
1
The candidates' votes are S→P, P→R, R→Q and Q→S. The non-candidate votes left are P 2, Q 13, R 5, S 0.
2
The O&Q block is 4. P's block of 2 can only be B&H with 1 candidate.
3
The other two candidates must be in F&A or M&S. Only F&A with 0 candidates and M&S with 2 gives blocks that sum to R = 5 and Q = 13. The blocks are then O&Q 4, F&A 9 and M&S 5.
4
R's 5 is the M&S block. Q's 13 is the O&Q block (4) plus the F&A block (9). B&H non-candidates (2) vote P.
5
Statement A says the M&S non-candidates voted for Qureshi. They voted for Ramaswamy, so A is false.
6
Statement B says the F&A non-candidates voted for Qureshi. They are the 9-vote block that goes to Qureshi, so B is true.
Quick Check
4+9=134+9=13 non-candidate votes plus 1 from Ramaswamy gives Qureshi's 14.
Correct Answer: B
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CAT 2023 Slot 1 DILR at a Glance

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

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