CAT 2019 LRDI Questions with Answers 12

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.

Question 1:
The second question in ET was prepared by:

  1. Dave
  2. Beti
  3. Chetan
  4. Esha
Show Answer
OPTION: 1

Question 2:
How many 5-mark questions were there in MT and ET combined?

  1. 12
  2. 10
  3. 13
  4. Cannot be determined
Show Answer
OPTION: 3

Question 3:
Who prepared 15-mark questions for MT and ET?

  1. Only Dave and Fakir
  2. Only Beti, Dave, Esha and Fakir
  3. Only Esha and Fakir
  4. Only Dave, Esha and Fakir
Show Answer
OPTION: 4

Question 4:
Which of the following questions did Beti prepare in ET?

  1. Seventh question
  2. Fourth question
  3. Ninth question
  4. Tenth question
Show Answer
OPTION: 4

In the following the names of the faculties are referred by first letter of their names.

Given that each of MT and ET carries 100 marks. Each of MT and ET has at least four questions of 5 marks (4 x 5 = 20), at least three questions of 10 marks (3 x 10 =30) and at least two questions of 15 marks (2 x 15 = 30). These together add up to 80 marks. The remaining 20 marks can be of the following possible combinations. (Four questions of 5 marks) or (two questions of 10 marks) or (one question of 5 marks and 1question of 15 marks)or (two questions of five marks and one question of ten marks). Hence, the total number of questions in MT or ET can be 11 or 12 or 13. It is given that ET has more number of questions than in MT. Hence, MT has 11 or 12 questions.

It is given that the number of questions given by any faculty in both MT and ET together is the same. If MT has 12 questions and ET has 13 questions, or if MT has 11 questions and ET has 12 questions, this condition cannot be satisfied. Hence, MT has 11 (Five 5 marks, three 10 marks and three 15 marks) questions and ET has 13 questions (eight 5 marks, three ten marks and two 15 marks). This implies, each faculty has given four questions in MT and ET together. Since it is given that faculty A has given only one question in MT and each of the other faculties has given more than one question, each of the faculties B, C, D, E and F has given two questions in MT. This implies faculty A has given three questions in ET and all other faculties have given two questions each in ET. From the given data we get the following.

Except A, every other faculty gave at least two questions for MT and all the questions of a faculty appeared consecutively. Hence, 2nd question in MT is given by F, 4th by C, 10th by D. B also has given two questions and both appeared consecutively. Hence, 6th and 7th questions are given by B and the 9th question is given by E. In each test first all 5 marks questions appeared followed by 10 marks questions and then 15 marks questions. It can be understood that MT has five 5 marks, three 10 marks and three 15 marks. Hence, in MT questions 1 to 5 carry 5 marks each, 6 to 8 carry 10 marks each and 9 to 11 carry 15 marks each.

It can be understood that A has given three questions for ET and each of the others has given two questions. Hence, the 2nd question of ET is given by D, the 4th question by C, 6th and 7th questions by A, 9th by E, 10th and 11th by B and 12th by F. Since ET has eight 5 marks questions, three ten marks questions and two 15 marks questions, questions 1 to 8 of ET carry 8 marks each, 9 to 11 carry ten marks each, 12 and 13 carry 15 marks each. Thus, we get the following:

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