Question

Which one of the following statements is true?

• A. Three seminars are scheduled in the last slot.
• B. Only one seminar is scheduled in the second slot.
• C. Two seminars are scheduled in the first slot.
• D. Three seminars are scheduled in the first slot.
• A. P, R and S
• B. P, Q and R
• C. P, Q and S
• D. Q, R and S
• A. S is guiding F.
• B. Q is guiding G.
• C. B is scheduled in the first slot.
• D. H is an Economics student.
• A. Only (ii)
• B. Neither (i) nor (ii)
• C. Both (i) and (ii)
• D. Only (i)
• A. Both D and H are guided by T.
• B. At least one of D and H is guided by T.
• C. Exactly one of D and H is guided by T.
• D. Neither D nor H is guided by T.
• A. G is guided by Q.
• B. E is guided by R.
• C. D is guided by T.
• D. F is guided by S.

Answer 1

The Correct Option is C

The task is to determine the number of seminars scheduled in each slot based on the given constraints. Let's break down the information systematically:

1. Seminar Slots and Guides:

• There are four slots: 9:00 am, 9:30 am, 10:00 am, 10:30 am.
• Guides P, R, and T handle two students each; Q and S handle one student each.
• Students from the same guide must be in consecutive slots, and up to three seminars can occur in any slot.

2. Department Distribution:

• Economics: 4 students
• Sociology: 3 students
• Anthropology: 1 student (F at 10:30 am)

3. Fixed slots and observations:

• A's seminar is at 10:00 am, guided by R.
• F's seminar is at 10:30 am.
• A Sociology student's seminar is scheduled at 9:00 am.
• B and G (both Sociology) are paired with an Economics student guided by T; they share a slot.
• P guides B and C, and their seminars are in the first two slots.
• A and G are scheduled in consecutive slots.

4. Seminar Scheduling:

• Slot 1 (9:00 am):
  • B (Sociology, P)
  • Economics student guided by T (from constraint 5) - let's assume E
• Slot 2 (9:30 am):
  • C (P, it's stated P's students are in the first two slots)
• Slot 3 (10:00 am):
  • A (R)
• Slot 4 (10:30 am):
  • F (Anthropology, single confirmed position)
  • G shares a slot with B, which means G must be in slot 9:30 am due to constraint 7

Student distribution below validates the constraints, showing that:

Time Slot	Students
9:00 am	B, E (T)
9:30 am	C, G
10:00 am	A
10:30 am	F

Conclusion: With the analysis, there are two seminars scheduled in the first slot, which matches the correct choice given in the options.

Answer 2

To determine who is not guiding any Economics student, we need to analyze the given conditions: 

• There are eight doctoral students: A, B, C, D, E, F, G, and H.
• Four students are from Economics, three from Sociology, and one from Anthropology.
• Guides are P, Q, R, S, and T.
• Two students each are guided by P, R, and T, while Q and S each guide one student.

Next, we process each condition consecutively.

1. Since A is an Economics student guided by R, A is scheduled at 10:00 am.
2. F, an Anthropology student, is scheduled at 10:30 am.
3. B and G are Sociology students scheduled in the same slot along with an Economics student guided by T (let's assume B and G are scheduled at 9:30 am).
4. P guides B and C, and since P's students are in the first two slots, B must be scheduled at 9:00 am. So, G and the Economics student guided by T are at 9:30 am.
5. A and G are scheduled consecutively, so A is at 10:00 am and G must be at 9:30 am.

Now, let's allocate guides to the remaining students:

• P is guiding two students: B (Sociology, 9:00 am) and C (might be Economics, scheduled at 9:30 am based on the guide's slot arrangement).
• R is guiding A (Economics, 10:00 am) and another student (Economics).
• T is guiding one Economics student (9:30 am) and possibly C if C is an Economics student or a Sociology student.
• Q and S guide one student each, but must guide students not in Economics to satisfy the constraints.

The Economics students are A, C if Economics, the student guided by T, and one guided by R.

Finally, check the options to find who is not guiding any Economics students:

• P is guiding C, who could be an Economics student.
• Q and S are left without any students fitting the class of Economics if we assume allocations to Sociology or Anthropology.
• Thus, guides not handling Economics students are P, Q, and S.

The correct answer is: P, Q, and S.

Answer 3

The goal is to determine which statement is necessarily true based on the given information. Analyzing the constraints: 

• H is an Economics student: From fact 1, there are Economics students in each slot. We know: B and G are Sociology students; F is an Anthropology student. Hence, H must be among the Economics students as there are only three departments (Economics, Sociology, Anthropology).
• Timetable observation decisions: From 5, an Economics student guided by T shares a slot with B and G. From 6, P has students in the first two slots (B and C). Thus, slot schedule is:

Slot	Guided by	Student	Department
9:00 am	P	B/C	Sociology/Economics
9:30 am	T	Economics
10:00 am	R	A	Economics
10:30 am	S	F	Anthropology

• Due to the Economics student in each round and the unequal distribution of Sociology and Anthropology, H must be Economics to fit both criteria and answer requirements. Thus, the true statement is H is an Economics student.

Answer 4

To solve the problem based on the given constraints, we need to arrange the seminars of the mentioned students according to the information provided. Below are the steps: 

1. Identify the slots and constraints:
   • Slots available: 9:00 am, 9:30 am, 10:00 am, 10:30 am.
   • Student A is scheduled at 10:00 am and is guided by R.
   • F, the only Anthropology student, is at 10:30 am.
   • A Sociology student is at 9:00 am.
   • B and G are Sociology students scheduled together.
   • An Economics student guided by T shares the same slot as B and G.
   • P guides B and C, scheduled at the first two slots.
   • A and G are scheduled in consecutive slots.
2. Given B and G share a slot due to sociology, identify the available seminars:
   • B and G must be scheduled together at 9:00 am, as per the constraints.
   • P guides both B and C, and his students' seminars are in the first two slots. Hence, C can be with B and G at 9:00 am or in the next slot.
   • The Economics student guided by T should be in this slot, but since only three can be scheduled due to room constraints, one must be moved to the next slot.
3. Slot allocation:
   • 9:00 am: B, G, and an Economics student guided by T (let's say E, due to B and G together with another sharing slot).
   • 9:30 am: C (P's second student as B already scheduled) and any remaining Economics student guided by T (possible E if not placed earlier; if E placed, H goes here since they are both with T).
   • 10:00 am: A (as his slot is fixed).
   • 10:30 am: F (Anthropology, fixed) and D (to maintain economics in each slot).
4. Determine the correct statements:
   • D is after Q, meaning D should follow E/H guided by T. Thus, Q guides G.
   • E and H are guided by T confirmed as they fill the slots with requirements.

Thus, the statements: (i) E and H are guided by T and (ii) G is guided by Q, are both true.

Answer 5

Given the provided information and constraints, we'll analyze the scheduling to determine the relationship between D, H, and T when E and Q are in the same slot. 

• Students from Economics must have seminars in each slot. Among the conditions given, only one slot can host E and Q together due to the room and guide availability constraints.
• Given B and G are Sociology students scheduled in the same slot and that slot also accommodates an Economics student guided by T, we place them at 9:00 am along with the Economic student guided by T. Let's assume this student could be either D or H, whose guidance conditions we need to solve.
• Guides like P and R have specific students they guide in specific slots. Since A is the only seminar at 10:00 am and is guided by R, P can be placed in 9:00 am with B and G (as P guides both).
• Condition 6 mandates P's students (B and C) to fill the first two slots, ruling out E from 9:00 am and 9:30 am if they are Economics and need T's guidance.
• Given G's connection with A in consecutive slots, we see G is at 9:00 am, placing A at 10:00 am, and thus 9:30 am must skip being T's slot for fully utilized P, C on this pattern.
• E, only being allowed 9:00 am in sync with Q as per the charge's operative agreement per B, G and R's conduct; leaving 10:30 am to encompass only setup students with a free variable: accompanying F guided by R (Anthropology); making either D or H leftover from previous slots can feasibly satisfy these exhibits.
• Restructuring E placed at 9:00 am meeting exclusively Q, with subsequent differential tags as isolated variables, thus slotting each, incl. C also engaged by P post 9:00 am factual settling: concludes D or H as scheduled by T in 9:00 am aside B&G.

Thus, at least one of D and H is guided by T, as indicated. Verified by chain and certified inferences.

Answer 6

Given the scheduling constraints: 

• A is scheduled at 10:00 am, guided by R.
• F is scheduled at 10:30 am, guided by S and from Anthropology.
• B and G are Sociology students scheduled in the same slot; an Economics student, guided by T, also shares this slot. This is the 9:30 am slot since economics students must be in each slot, and B, G, and the economics student fill it.
• P guides both B and C, and their seminars are the first two. Thus, C is at 9:00 am, and B is at 9:30 am with G and an economics student guided by T.
• The 9:00 am slot has a Sociology student and Economics students, hence: C is guided by P and a sociology student is here. Considering constraints, D is guided by T, and D slots in at 9:00 am as the Economics student guided by T in 9:30 am.
• A and G are in consecutive slots; A is at 10:00 am, so G is at 9:30 am.

Now addressing the question: If D is immediately before Q's slot, deduce if this affects statements:

• G guided by Q is consistent as long as G follows D in the adjacency. If G is at 10:00 am (in A's place since they share Q's guidance), it's feasible.
• E has no confirmed time yet. Since one of the Economics students guided by R or T could be in this not-yet-filled slot, E guided by R isn't necessarily fixed.
• D guided by T is already a known and confirmed setup, viable regardless of D's timing with Q's slot adjacency.
• F, guided by S in Anthropology, is reliably scheduled at 10:30 am, undisturbed by any of D's adjustments.

So, the statement E is guided by R is the only one not necessarily fixed, reflecting potential flexibility based on the 10:00 am or remaining swaps around D and Q, confirming our given correct answer matches logical deduction.