The first year students in a business school are split into six sections. In 2019 the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common midterm (MT) and a common endterm (ET) worth 100 marks each. ET contained more questions than MT. Questions for MT and ET were prepared collectively by the six faculty members. Considering MT and ET together, each faculty member prepared the same number of questions.

Each of MT and ET had at least four questions that were worth 5 marks, at least three questions that were worth 10 marks, and at least two questions that were worth 15 marks. In both MT and ET, all the 5-mark questions preceded the 10-mark questions, and all the 15-mark questions followed the 10-mark questions.

The following additional facts are known.
i. Annie prepared the fifth question for both MT and ET. For MT, this question carried 5 marks.
ii. Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT.
iii. All questions prepared by a faculty member appeared consecutively in MT as well as ET.
iv. Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both.
v. Fakir prepared the first question of MT and the last one in ET. Dave prepared the last question of MT and the first one in ET.

Q. 1 The second question in ET was prepared by:
1) Chetan 2) Dave 3) Beti 4) Esha
Q. 2 How many 5-mark questions were there in MT and ET combined?
1) 12 2) 10 3) 13 4) Cannot be determined
Q. 3 Who prepared 15-mark questions for MT and ET?
1) Only Dave, Esha and Fakir 2) Only Dave and Fakir 3) Only Esha and Fakir 4) Only Beti, Dave, Esha and Fakir
Q. 4 Which of the following questions did Beti prepare in ET?
1) Tenth question 2) Seventh question 3) Fourth question 4) Ninth question

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🎯 Given Facts Recap

We have:

• 6 faculty members: Annie, Beti, Chetan, Dave, Esha, Fakir
• MT (Midterm) and ET (Endterm) have a combined total of 24 questions
  • MT: 11 questions
  • ET: 13 questions
• Each faculty prepared exactly 4 questions (⇒ 6 × 4 = 24)
• Questions prepared by each faculty appear consecutively in MT and ET
• Each of MT and ET had:
  • At least 4 questions of 5 marks
  • At least 3 questions of 10 marks
  • At least 2 questions of 15 marks
• All 5-mark questions come first, then 10, then 15

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🧩 Step-by-Step Construction of the Table

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✅ Step 1: Use direct placement clues

From the question:

1. Annie prepared Q5 in both MT and ET → MT Q5 = Annie
2. Annie made only 1 question in MT, so must make 3 questions in ET
3. Chetan made Q3 in both MT and ET → Chetan = Q3 in both
4. Esha made Q8 in both MT and ET → Esha = Q8 in both
5. Fakir made Q1 in MT and last Q in ET
6. Dave made last Q in MT and Q1 in ET

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✅ Step 2: Start filling MT with knowns

Start placing known people:

Midterm (MT)

Q#	Prepared By	Marks
1	Fakir	5
2	Fakir	5
3	Chetan	5
4	Chetan	5
5	Annie	5
6	Beti	10
7	Beti	10
8	Esha	10
9	Esha	15
10	Dave	15
11	Dave	15

➡️ Why two questions for Fakir? Because he must prepare 4 total, and we know he gets 2 in ET at the end (Q12–13), so 2 in MT (Q1–2)

➡️ Beti fills Q6–7, to get 2 in MT and 2 in ET later (Q10–11)

➡️ Esha fills Q8–9 — total 2 in MT. She will get Q8–9 in ET (2 more) → 4 total

➡️ Dave fills Q10–11 in MT → 2 here, and 2 in ET (Q1–2) → 4 total

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✅ Step 3: Fill ET based on faculty counts and continuity

We know:

• Annie did only 1 in MT → needs 3 in ET
  → Already has Q5 → assign Q6–7 to her too
• Chetan did 2 in MT (Q3–4) → needs 2 in ET
  → Already has Q3 → give him Q4 too
• Dave needs 2 in ET → already known: Q1–2
• Esha did Q8–9 in MT → now also Q8–9 in ET (as per clues)
• Fakir did Q1–2 in MT → needs 2 in ET
  → Assigned Q12–13
• Beti did Q6–7 in MT → now needs Q10–11 in ET

✅ This satisfies 4 questions per faculty and consecutive blocks

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✅ Final Table:

Midterm (MT)

Q#	Prepared By	Marks
1	Fakir	5
2	Fakir	5
3	Chetan	5
4	Chetan	5
5	Annie	5
6	Beti	10
7	Beti	10
8	Esha	10
9	Esha	15
10	Dave	15
11	Dave	15

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Endterm (ET)

Q#	Prepared By	Marks
1	Dave	5
2	Dave	5
3	Chetan	5
4	Chetan	5
5	Annie	5
6	Annie	5
7	Annie	5
8	Esha	10
9	Esha	10
10	Beti	10
11	Beti	10
12	Fakir	15
13	Fakir	15

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🔒 All Constraints Checked:

Constraint	Satisfied?	Explanation
Each faculty 4 questions	✅	6×4 = 24 total
Consecutive block per faculty	✅	All assignments are grouped
5-mark questions first	✅	Q1–5 (MT) and Q1–7 (ET)
10-mark next	✅	MT Q6–8; ET Q8–11
15-mark at end	✅	MT Q9–11; ET Q12–13

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Midterm (MT)

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Q 1. Who prepared the second question in ET?

✅ Answer: 2) Dave

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🔍 Q2: How many 5-mark questions were there in MT and ET combined?

MT:

• Q1 (Fakir) → 5
• Q2 (Fakir) → 5
• Q3 (Chetan) → 5
• Q4 (Chetan) → 5
• Q5 (Annie) → 5
  ✅ Total = 5

ET:

• Q1, Q2 (Dave) → 5
• Q3, Q4 (Chetan) → 5
• Q5, Q6, Q7 (Annie) → 5
  ✅ Total = 7

👉 Combined = 5 (MT) + 7 (ET) = 12

✅ Answer: 1) 12

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🔍 Q3: Who prepared 15-mark questions for MT and ET?

Let’s extract from the table:

MT:

• Q9 → Esha (15)
• Q10–11 → Dave (15)

ET:

• Q12–13 → Fakir (15)

So:
✅ Esha, Dave, and Fakir only.

✅ Answer: 1) Only Dave, Esha and Fakir

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🔍 Q4: Which of the following questions did Beti prepare in ET?

From the ET table:

• Beti prepared Q10 and Q11

✅ Answer: 1) Tenth question