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CAT 2020 Slot 2 DILR · Set 2 of 5Logical ReasoningModerate DifficultyQ5–Q10 · 6 MCQ

CAT 2020 Slot 2 DILR Set 2: Optimization (6 Questions) with Solutions

The Optimization set from the official CAT 2020 Slot 2 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 2020 Slot 2 DILR · Questions 5–10
The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department.
Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be Scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.
The following additional facts are also known.
1
Seminars by students from Economics are scheduled in each of the four slots.
2
A's is the only seminar that is scheduled at 10:00 am. A is guided by R.
3
F is an Anthropology student whose seminar is scheduled at 10:30 am.
4
The seminar of a Sociology student is scheduled at 9:00 am.
5
B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.
6
P, who is guiding both B and C, has students scheduled in the first two slots.
7
A and G are scheduled in two consecutive slots.

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

Q5. Optimization

MCQ · +3 / −1
Which one of the following statements is necessarily true?
  1. A) Three seminars are scheduled in the first slot.
  2. B) Two seminars are scheduled in the first slot.
  3. C) Only one seminar is scheduled in the second slot.
  4. D) Three seminars are scheduled in the last slot.
Correct Answer
B) Two seminars are scheduled in the first slot.
Step-by-step solution
📌 Core Concept
Fix the departments and guides first, then use the slot clues to find how many seminars each slot holds.
🔢 Step-by-Step Solution
1
P guides B and C. B is Sociology, so P is a Sociology guide and C is Sociology too. G is also Sociology, so the three Sociology students are B, C and G. Their third guide is Q or S.
2
F is the Anthropology student and is guided by the other of Q and S. The Economics students are A, D, E and H. Their guides are R (2 students, one of them A) and T (2 students).
3
P's students B and C are in the first two slots, and B shares a slot with G (clue 5). A is alone at 10:00, and G is in a slot next to A (clue 7), so G is at 9:30 or 10:30. 10:30 would put B outside P's first two slots, so G and B are at 9:30. Then C is at 9:00.
4
The 9:30 slot holds B, G and a T-guided Economics student. That is 3 seminars, so the room limit is reached.
5
R's other student must be next to A, so at 9:30 or 10:30. 9:30 is full, so this student is at 10:30.
6
T's two students must be consecutive. One is at 9:30, and 10:00 holds only A, so the other is at 9:00.
7
Slot counts: 9:00 has C and a T student (2). 9:30 has 3. 10:00 has 1. 10:30 has F and R's other student (2).
Why Not the Others
A: the first slot has 2 seminars, not 3.
C: the second slot has 3 seminars.
D: the last slot has 2 seminars.
Correct Answer: B

Q6. Optimization

MCQ · +3 / −1
Who all are NOT guiding any Economics students?
  1. A) P, Q and S
  2. B) P, R and S
  3. C) Q, R and S
  4. D) P, Q and R
Correct Answer
A) P, Q and S
Step-by-step solution
📌 Core Concept
Match each guide to a department. Each student's guide belongs to the student's own department, and the headcounts fix which guides are left for Economics.
🔢 Step-by-Step Solution
1
P guides B and C, and B is a Sociology student. So P guides Sociology, and C is Sociology as well.
2
G is also Sociology, so the three Sociology students are B, C and G. P takes B and C, and G is guided by Q or S, the guides with one student each.
3
F is the Anthropology student. F's guide is the remaining one of Q and S, since the Anthropology guide has exactly one student.
4
A is guided by R and is Economics (A is neither B, C, G nor F). The Economics students are A, D, E and H, and they need two guides with two students each. These are R and T.
5
Economics is therefore guided only by R and T. The guides with no Economics students are P, Q and S.
Correct Answer: A

Q7. Optimization

MCQ · +3 / −1
Which one of the following statements is necessarily true?
  1. A) B is scheduled in the first slot.
  2. B) H is an Economics student.
  3. C) Q is guiding G.
  4. D) S is guiding F.
Correct Answer
B) H is an Economics student.
Step-by-step solution
📌 Core Concept
Sort the students into departments using the guide counts, then test each statement against what is forced.
🔢 Step-by-Step Solution
1
P guides B and C, so P is the Sociology guide and C is Sociology. With B and G (clue 5), the Sociology students are B, C and G.
2
F is Anthropology. The remaining students A, D, E and H are therefore the four Economics students.
3
B must be at 9:30. P's students are in the first two slots, and G shares B's slot. G sits next to A at 10:00, so G is at 9:30 or 10:30. 10:30 would put B outside the first two slots, so B is at 9:30 with G.
4
Check each option: B is at 9:30, not the first slot, so A fails. H is Economics, so B holds. G's guide is Q or S, and either can guide G, so C and D are not forced.
Why Not the Others
A: B is in the second slot (9:30).
C: G may be guided by S instead of Q.
D: F may be guided by Q instead of S.
Correct Answer: B

Q8. Optimization

MCQ · +3 / −1
If D is scheduled in a slot later than Q's, then which of the following two statement(s) is (are) true?
i
E and H are guided by T.
ii
G is guided by Q.
  1. A) Only (i)
  2. B) Both (i) and (ii)
  3. C) Only (ii)
  4. D) Neither (i) nor (ii)
Correct Answer
B) Both (i) and (ii)
Step-by-step solution
📌 Core Concept
Q guides either G (at 9:30) or F (at 10:30). Requiring D to be later than Q's student fixes which.
🔢 Step-by-Step Solution
1
The base arrangement is as follows. C is at 9:00 with a T-guided Economics student. B, G and another T-guided Economics student are at 9:30. A is alone at 10:00. F and R's other Economics student are at 10:30.
2
D is Economics, so D is at 9:00, 9:30 or 10:30. For D to be later than Q's student, Q's student must be earlier than D.
3
If Q guided F (10:30), no seminar would be later, so that is impossible. Hence Q guides G at 9:30, which makes (ii) true.
4
D is later than 9:30, and 10:00 is A alone, so D is at 10:30. That slot holds R's other student, so D is guided by R.
5
E and H are the remaining Economics students. They are guided by T, one at 9:00 and one at 9:30, which makes (i) true.
Correct Answer: B

Q9. Optimization

MCQ · +3 / −1
If E and Q are both scheduled in the same slot, then which of the following statements BEST describes the relationship between D, H, and T?
  1. A) At least one of D and H is guided by T.
  2. B) Neither D nor H is guided by T.
  3. C) Both D and H are guided by T.
  4. D) Exactly one of D and H is guided by T.
Correct Answer
A) At least one of D and H is guided by T.
Step-by-step solution
📌 Core Concept
Q is at 9:30 (guiding G) or 10:30 (guiding F). Take each case for E's slot.
🔢 Step-by-Step Solution
1
The Economics seminars are as follows. A is at 10:00 with R. R's other student is at 10:30. T's two students are at 9:00 and 9:30.
2.
Case 1
Q guides G at 9:30. Then E is the T student at 9:30. D and H are the T student at 9:00 and R's student at 10:30. Exactly one of D and H is guided by T.
3.
Case 2
Q guides F at 10:30. Then E is R's other student at 10:30. D and H are then both T's students, so both are guided by T.
4
In both cases at least one of D and H is guided by T.
Why Not the Others
B: in both cases at least one of D and H is T's.
C: both are T's only in case 2.
D: in case 2 both are T's, not exactly one.
Correct Answer: A

Q10. Optimization

MCQ · +3 / −1
If D is scheduled in the slot immediately before Q's, then which of the following is NOT necessarily true?
  1. A) D is guided by T.
  2. B) G is guided by Q.
  3. C) F is guided by S.
  4. D) E is guided by R.
Correct Answer
D) E is guided by R.
Step-by-step solution
📌 Core Concept
Q's student is G (9:30) or F (10:30). The condition that D is immediately before Q's student decides which.
🔢 Step-by-Step Solution
1
If Q guided F at 10:30, D would be at 10:00. But 10:00 holds only A, so this fails.
2
So Q guides G at 9:30, and D is at 9:00. The only Economics student at 9:00 is T's, so D is guided by T.
3
Q guides G, so S guides F.
4
E is Economics, and the remaining Economics slots are T's student at 9:30 and R's student at 10:30. E could be either, so E is guided by R in one case and by T in the other.
Why Not the Others
A: D at 9:00 is T's student, so it is forced.
B: forced, as shown in step 2.
C: forced, since Q guides G.
D: E may be T's student at 9:30, so this is not forced.
Correct Answer: D
Timed Practice

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CAT 2020 Slot 2 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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