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CAT 2019 Slot 2 DILR · Set 7 of 8Logical ReasoningHard DifficultyQ25–Q28 · 4 MCQ

CAT 2019 Slot 2 DILR Set 7: Arrangements (4 Questions) with Solutions

The Arrangements set from the official CAT 2019 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2019 Slot 2 DILR · Questions 25–28
The first year students in a business school are split into six sections. In 20192019 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 100100 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 55 marks, at least three questions that were worth 1010 marks, and at least two questions that were worth 1515 marks. In both MT and ET, all the 55-mark questions preceded the 1010-mark questions, and all the 1515 - mark questions followed the 1010-mark questions.
The following additional facts are known.
i
Annie prepared the fifth question for both MT and ET. For MT, this question carried 55 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.

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q25. Arrangements

MCQ · +3 / −1
The second question in ET was prepared by:
  1. A) Chetan
  2. B) Beti
  3. C) Dave
  4. D) Esha
Correct Answer
C) Dave
Step-by-step solution
📌 Core Concept
Count the questions each person must set, then use the consecutive-block rule to lay out both papers.
🔢 Step-by-Step Solution
1
Clue ii says Annie set 1 MT question and each of the other five set at least 2. So MT has at least 1+5×2=111+5\times2=11 questions.
2
Every faculty member set the same total across MT and ET, so the combined count is a multiple of 6. ET has more questions than MT, so the combined count is at least 23 and therefore at least 24. The smallest fit is MT =11=11, ET =13=13, with 4 questions per person.
3
This forces the MT split: Annie 1 and the others exactly 2 each. In ET, Annie therefore set 3 and the others 2 each.
4
In ET, Dave has Q1 and Fakir has Q13 (clue v). Chetan has Q3 and Annie has Q5 (clues i and iv).
5
Annie's 3 questions form one block containing Q5. Chetan has Q3, so Q4 cannot be Annie's. Q3 is also not Annie's, so the block cannot be Q3-5 or Q4-6, which leaves Q5-7.
6
Dave set 2 questions in a block starting at Q1, so he has Q1-2. The second question of ET is therefore Dave's.
Why Not the Others
Chetan: his block is Q3-4, because Q2 is Dave's.
Beti: her block is Q10-11.
Esha: her block is Q8-9.
Correct Answer: C

Q26. Arrangements

MCQ · +3 / −1
How many 5-mark questions were there in MT and ET combined?
  1. A) 13
  2. B) 10
  3. C) cannot be determined
  4. D) 12
Correct Answer
A) 13
Step-by-step solution
📌 Core Concept
Solve each paper's mark total with the minimum-question conditions, then use the clue that MT Q5 is a 5-mark question.
🔢 Step-by-Step Solution
1
From the earlier deduction, MT has 11 questions and ET has 13. Each paper totals 100 marks.
2
Let aa, bb, cc be the numbers of 5-, 10- and 15-mark questions. For MT, a+b+c=11a+b+c=11 and 5a+10b+15c=1005a+10b+15c=100, so b+2c=9b+2c=9.
3
The minimums are b≥3b\ge3 and c≥2c\ge2, which gives (a,b,c)=(4,5,2)(a,b,c)=(4,5,2) or (5,3,3)(5,3,3).
4
All 5-mark questions come first and Q5 of MT carries 5 marks, so Q1-5 are all 5-mark questions. Hence a≥5a\ge5, and MT has (5,3,3)(5,3,3), i.e. five 5-mark questions.
5
For ET, a+b+c=13a+b+c=13 and a+2b+3c=20a+2b+3c=20, so b+2c=7b+2c=7. With b≥3b\ge3 and c≥2c\ge2, the only solution is c=2c=2, b=3b=3, a=8a=8.
6
Total 5-mark questions: 5+8=135+8=13.
Quick Check
ET: 8×5+3×10+2×15=40+30+30=1008\times5+3\times10+2\times15=40+30+30=100.
Correct Answer: A

Q27. Arrangements

MCQ · +3 / −1
Who prepared 15-mark questions for MT and ET?
  1. A) Only Beti, Dave, Esha and Fakir
  2. B) Only Esha and Fakir
  3. C) Only Dave, Esha and Fakir
  4. D) Only Dave and Fakir
Correct Answer
C) Only Dave, Esha and Fakir
Step-by-step solution
📌 Core Concept
15-mark questions are the last ones in each paper, so find who set the final questions of MT and ET.
🔢 Step-by-Step Solution
1
MT has 11 questions in the order Fakir (1-2), Chetan (3-4), Annie (5), Beti (6-7), Esha (8-9), Dave (10-11). This follows from Chetan having Q3, Annie Q5, Esha Q8, Fakir Q1 and Dave Q11, with each block consecutive.
2
MT has three 15-mark questions, and they come last: Q9-11. These were set by Esha (Q9) and Dave (Q10-11).
3
ET has 13 questions in the order Dave (1-2), Chetan (3-4), Annie (5-7), Esha (8-9), Beti (10-11), Fakir (12-13).
4
ET has two 15-mark questions, which are Q12-13, both set by Fakir.
5
The setters of 15-mark questions are therefore Dave, Esha and Fakir only.
Why Not the Others
Option A: Beti's questions are Q6-7 in MT and Q10-11 in ET, which are 5- or 10-mark questions.
Options B and D: each leaves out a setter who did set a 15-mark question (Dave in B, Esha in D).
Correct Answer: C

Q28. Arrangements

MCQ · +3 / −1
Which of the following questions did Beti prepare in ET?
  1. A) Fourth question
  2. B) Seventh question
  3. C) Tenth question
  4. D) Ninth question
Correct Answer
C) Tenth question
Step-by-step solution
📌 Core Concept
Place the consecutive blocks of ET one by one, and Beti's block is what remains.
🔢 Step-by-Step Solution
1
ET has 13 questions, with Annie setting 3 and the others 2 each.
2
Dave has Q1 and Fakir has Q13 (clue v). Chetan has Q3 and Dave's block is Q1-2, so Chetan's block is Q3-4.
3
Annie has Q5 and a block of 3. Q3-4 are Chetan's, so her block is Q5-7.
4
Esha has Q8 (clue iv). Q7 is Annie's, so Esha's block is Q8-9.
5
Fakir has Q13, so his block is Q12-13.
6
Beti is left with Q10-11, so she set the tenth question.
Why Not the Others
Fourth: Chetan.
Seventh: Annie.
Ninth: Esha.
Correct Answer: C
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CAT 2019 Slot 2 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Kozhikode

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