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 9:00 am, 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.
- Seminars by students from Economics are scheduled in each of the four slots.
- A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
- F is an Anthropology student whose seminar is scheduled at 10:30 am.
- The seminar of a Sociology student is scheduled at 9:00 am.
- 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.
- P, who is guiding both B and C, has students scheduled in the first two slots.
- A and G are scheduled in two consecutive slots.
Q. 9 Which one of the following statements is true?
1) Two seminars are scheduled in the first slot.2) Three seminars are scheduled in the last slot.3) Only one seminar is scheduled in the second slot.4) Three seminars are scheduled in the first slot.
Q. 10 Who all are NOT guiding any Economics students?
1) P, Q and R 2) P, Q and S 3) Q, R and S 4) P, R and S
Q. 11 Which of the following statements is necessarily true?
1) S is guiding F. 2) H is an Economics student. 3) Q is guiding G. 4) B is scheduled in the first slot.
Q. 12 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) Both (i) and (ii) 2) Neither (i) nor (ii) 3) Only (i) 4) Only (ii)
Q. 13 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) Both D and H are guided by T. 2) Neither D nor H is guided by T. 3) At least one of D and H is guided by T. 4) Exactly one of D and H is guided by T.
Q. 14 If D is scheduled in the slot immediately before Q’s, then which of the following is NOT necessarily true?
Let’s go step-by-step to explain how the two final tables were constructed using the clues from the puzzle.
🎯 Objective:
You have 8 students (A–H), 3 subjects (Economics, Sociology, Anthropology), and 5 guides (P, Q, R, S, T). You’re assigning students to 4 time slots (9:00, 9:30, 10:00, 10:30 AM), with constraints based on subject, guide, and slot.
🧩 Step-by-step Construction of Table 1 (Seminar Slot Table):
### 🔹 Step 1: Subject Distribution
- Economics: 4 students
- Sociology: 3 students
- Anthropology: 1 student
🔹 Step 2: Clue Analysis
Clue 1: “Seminars by Economics students are scheduled in each of the four slots.”
✅ Place at least one Economics student in each slot.
Clue 2: “A is in 10:00 AM slot and is guided by R.”
✅ So slot 3 (10:00 AM) = A (Economics)
Clue 3: “F (Anthro) is in 10:30 AM slot”
✅ So slot 4 (10:30 AM) = F (Anthro)
Clue 4: “A Sociology student’s seminar is in 9:00 AM”
✅ Place any Sociology student in slot 1
Clue 5: “B and G (both Sociology) are scheduled in the same slot with an Economics student guided by T”
✅ One slot must have: B + G + Econ (guided by T) — this can only be slot 2 (9:30 AM) to satisfy all constraints
Now build two cases based on how B, G, and Econ(T) are placed.
✅ Case 1: Put B, G, Econ(T) in 9:00
→ Results in conflict with clue 7 (A and G must be in consecutive slots)
⛔ Rejected
✅ Case 2: B, G, Econ(T) in 9:30
- 9:00 AM: Econ + Sociology (C)
- 9:30 AM: B + G (Sociology) + Econ (guided by T)
- 10:00 AM: A (Econ, R)
- 10:30 AM: F (Anthro) + Econ (remaining)
✔ Matches all clues.
🔹 Step 3: Apply Clue 6
P guides B and C and has seminars in first two slots
So:
- B → 9:30
- C → 9:00
Update table accordingly.
✅ Final Table 1:
| Time | Seminars |
|---|---|
| 9:00 AM | D (Econ), C (Soc), B (Soc) |
| 9:30 AM | G (Soc), E/H (Econ) |
| 10:00 AM | A (Econ) |
| 10:30 AM | F (Anthro), E/H (Econ) |
(Where E/H refers to the two remaining Economics students)
🧩 Step-by-step Construction of Table 2 (Guide-Student Table):
Given:
- P, R, T each guide 2 students
- Q, S guide 1 each
- Guide-student pairing must match subject area
🔹 Step 1: Assign known guide-student pairs
- P → B and C (both Sociology)
- R → A (Econ) + E/H (Econ)
- T → D (Econ, in 9:00) + E/H (Econ)
- Q → G (Sociology)
- S → F (Anthropology)
✅ Now all guides have been assigned students.
✅ Final Table 2:
| Guide | Students |
|---|---|
| P | B (Sociology), C (Sociology) |
| Q | G (Sociology) |
| R | A (Econ at 10:00), E/H (Econ at 10:30) |
| S | F (Anthropology) |
| T | D (Econ at 9:00), E/H (Econ at 9:30) |
(Again, E and H’s identities are flexible between R and T)
✅ Summary:
Table 1:
Constructed using all clues 1–7, fixing slots and subjects based on constraints like:
- A at 10:00 AM
- F at 10:30 AM
- B and G together with Econ(T)
- P’s students in first two slots
Table 2:
Created by matching guides with students while following:
- Department consistency (e.g., P with Sociology students)
- Number of students per guide (2 for P/R/T, 1 for Q/S)
Let me know if you want this redrawn visually as a full grid or guide-student chart.
