CAT 2019 Slot 2 — DILR Question 7
Answer the following questions based on the information given below.
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.
- Annie prepared the fifth question for both MT and ET. For MT, this question carried 5 marks.
- Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT.
- All questions prepared by a faculty member appeared consecutively in MT as well as ET
- Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both.
- 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.
Who prepared 15-mark questions for MT and ET?
Answer & solution
Only Dave, Esha and Fakir
- B
Only Beti, Dave, Esha and Fakir
- C
Only Dave and Fakir
- D
Only Esha and Fakir
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.
Therefore, Each of MT and ET had at least 4 + 3 + 2 = 9 questions. Also, these 9 questions were worth 80 marks. So, remaining 20 marks can be from (one 5-mark and one 15-mark questions OR two 10-mark questions OR two 5-mark questions and one 10-mark question OR four 5-mark questions).
From (ii), Annie prepared exactly one question (i.e., fifth question) for MT and minimum number of questions in MT = 1 + 5 × 5 = 11
From (iv) and (v), Fakir and Chetan prepared the first and the third questions respectively. Now from (ii) and (iii), Fakir and Chetan prepared the second and the fourth questions also.
Similarly it can be concluded that Dave prepared first two questions of ET and Chetan prepared the third and the fourth questions of ET.
Also, as each faculty member prepared the same number of questions and Chetan prepared 4 questions, each prepared 4 questions.
Total number of questions in ET and MT together = 4 × 6 = 24. As ET contained more questions than MT, MT had 11 questions and ET had 13 questions.
Therefore, Beti (6th and 7th), Esha (8th and 9th) and Dave (10th and 11th) prepared exactly two questions for MT. Also, first five questions were of 5 marks, then three 10-mark questions and in the last, three 15- mark questions. As ET has 13 questions and 9 among these contribute to 80 marks, we are left with the possibility that there were four 5-mark questions other than the 9 questions.
Annie prepared 3 questions for ET (i.e., the 5th, 6th and 7th). Esha prepared 8th and 9th questions. And Fakir prepared last two questions. Thus, we have
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Only Esha and Dave prepared 15-mark questions for MT while Fakir prepared 15-mark questions for ET.
Hence, option (a).