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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.

1. Annie prepared the fifth question for both MT and ET. For MT, this question carried 5 marks.
2. Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT.
3. All questions prepared by a faculty member appeared consecutively in MT as well as ET.
4. Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both.
5. 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.

How many $5$ – mark questions were there in MT and ET combined?

1. 12
2. 10
3. 13
4. Cannot be determined