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CAT 2020 Slot 1 DILR · Set 3 of 5Logical ReasoningModerate DifficultyQ11–Q16 · 4 MCQ + 2 TITA

CAT 2020 Slot 1 DILR Set 3: Arrangements (6 Questions) with Solutions

The Arrangements set from the official CAT 2020 Slot 1 DILR paper: the caselet, all 6 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 2020 Slot 1 DILR · Questions 11–16
In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations.
The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations.
If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for.
If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for.
The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.
EnglishHindiMathematicsScienceSocial Science
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883
The following facts are also known.
1
Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.
2
The student who missed the Mathematics examination did not miss any other examination.
3
One of the students who missed the Hindi examination did not miss any other examination.
4
The other student who missed the Hindi examination also missed the Science examination.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q11. Arrangements

MCQ · +3 / −1
Who among the following did not appear for the Mathematics examination?
  1. A) Carl
  2. B) Alva
  3. C) Foni
  4. D) Esha
Correct Answer
A) Carl
Step-by-step solution
📌 Core Concept
A missed exam carries the average of the best three (or best two) of the other scores. So for each student, only certain exams can be the missed ones. Combine that with the facts.
🔢 Step-by-Step Solution
1
Test each student's possible misses. If one exam is missed, its mark must equal the average of the best three of the other four. If two are missed, both marks must be equal, and equal to the average of the best two of the other three.
2
Carl (75, 80, 90, 100, 90): missing Mathematics gives the best three of 75, 80, 100, 90 as 100, 90, 80, average 90, which matches. Missing Social Science also works. Missing English, Hindi or Science does not.
3
Alva: only Hindi and Science (both 75) work. Bithi: only Science and Social Science (both 85). Deep: only Hindi and Science (both 90). Esha: only English. Foni: only English and Social Science (both 83).
4
Only Carl can have missed Mathematics. Esha's Mathematics score is 95, which is not the average of the best three of her other scores (85, 80, 60 gives 75). Foni's 78 also fails.
5
Fact 2 says the Mathematics misser missed nothing else, so Carl missed only Mathematics.
Why Not the Others
Alva: Mathematics 70 is not the average of her best three of the other four, which is 76.67.
Foni: Mathematics 78 does not match the 84.67 that the rule would give.
Esha: Mathematics 95 is far above the 75 that the rule would give.
Correct Answer: A

Q12. Arrangements

MCQ · +3 / −1
Which students did not appear for the English examination?
  1. A) Carl and Deep
  2. B) Esha and Foni
  3. C) Alva and Bithi
  4. D) Cannot be determined
Correct Answer
B) Esha and Foni
Step-by-step solution
📌 Core Concept
Fact 1 means each of English, Hindi, Science and Social Science was missed by exactly two of the six students. The averaging rule narrows who could have missed each.
🔢 Step-by-Step Solution
1
Applying the averaging rule to every student, English can be missed only by Esha (80 is the average of 85, 95, 60) or Foni (83 equals the average of 88, 83, 78, or the average of the best two of 72, 78, 88).
2
Alva, Bithi, Carl and Deep cannot have missed English, because their English marks fail the rule. For Carl the rule would give 93.33, not 75.
3
Fact 1 says exactly two students missed English, so those two must be Esha and Foni.
Why Not the Others
Carl and Deep: neither English mark (75, 70) matches the averaging rule.
Alva and Bithi: their English marks (80, 90) fail the rule too.
Cannot be determined: the two candidates are forced, so it can be determined.
Correct Answer: B

Q13. Arrangements

MCQ · +3 / −1
What BEST can be concluded about the students who did not appear for the Hindi examination?
  1. A) Alva and Esha
  2. B) Alva and Deep
  3. C) Deep and Esha
  4. D) Two among Alva, Deep and Esha
Correct Answer
B) Alva and Deep
Step-by-step solution
📌 Core Concept
Hindi can be missed only by students whose Hindi mark fits the averaging rule. Facts 3 and 4 then fix how many exams each of them missed.
🔢 Step-by-Step Solution
1
Checking the rule, the Hindi mark fits only for Alva (75) and Deep (90). For Bithi, Carl, Esha and Foni it does not.
2
Fact 1 says exactly two students missed Hindi, so these are Alva and Deep.
3
Facts 3 and 4: one of them missed only Hindi, and the other missed Hindi and Science. Which is which cannot be settled, but the pair is certain.
Why Not the Others
Alva and Esha, and Deep and Esha: Esha's only possible miss is English.
Two among Alva, Deep and Esha: this is weaker than the exact pair, which is Alva and Deep.
Correct Answer: B

Q14. Arrangements

MCQ · +3 / −1
What BEST can be concluded about the students who missed the Science examination?
  1. A) Alva and Bithi
  2. B) Deep and Bithi
  3. C) Alva and Deep
  4. D) Bithi and one out of Alva and Deep
Correct Answer
D) Bithi and one out of Alva and Deep
Step-by-step solution
📌 Core Concept
Science was missed by exactly two students. Find who can miss it and use the Hindi facts to place them.
🔢 Step-by-Step Solution
1
Science fits the averaging rule only for Alva (75), Bithi (85) and Deep (90).
2
Fact 4 says one of the two Hindi missers (Alva and Deep) also missed Science. So exactly one of Alva and Deep missed Science.
3
Science needs two missers in all, so the second must be Bithi, the only other candidate.
4
Which of Alva or Deep missed Science cannot be fixed. Both fit Facts 3 and 4 equally.
Why Not the Others
Alva and Bithi, Deep and Bithi, or Alva and Deep: each names a definite pair, but only one of Alva or Deep missed Science.
Correct Answer: D

Q15. Arrangements

TITA · +3 / 0
How many out of these six students missed exactly one examination?
Correct Answer
3
Step-by-step solution
📌 Core Concept
Work out each student's exact set of missed exams from the rule and the four facts. Then count those who missed exactly one.
🔢 Step-by-Step Solution
1
Carl missed only Mathematics (Fact 2 and the averaging rule). That is one exam.
2
Esha missed only English, because no two of her marks are equal and so two misses are impossible.
3
English was missed by exactly two students, Esha and Foni. Social Science was missed by exactly two, and the only candidates are Bithi and Foni, since Carl missed only Mathematics. So Foni missed English and Social Science, which is two exams.
4
Science was missed by Bithi and one of Alva or Deep. Bithi's Social Science miss makes his set Science and Social Science, which is two exams.
5
Of Alva and Deep, one missed Hindi and Science (two exams) and the other missed only Hindi (one exam).
6
Students who missed exactly one exam: Carl, Esha, and one of Alva or Deep, which makes 3.
Quick Check
Total misses are 1 (Mathematics) + 2 × 4 (English, Hindi, Science, Social Science) = 9. Students with one miss:
3
Students with two misses:
3
Then 3 × 1 + 3 × 2 = 9, which matches.
Correct Answer: 3

Q16. Arrangements

TITA · +3 / 0
For how many students can we be definite about which examinations they missed?
Correct Answer
4
Step-by-step solution
📌 Core Concept
A student's missed set is definite when the facts leave only one possibility for them.
🔢 Step-by-Step Solution
1
Carl: only Mathematics (Fact 2). Definite.
2
Esha: only English, because her marks have no equal pair and so only one miss is possible. Definite.
3
Foni: English was missed by exactly two students, Esha and Foni. Social Science was missed by exactly two, Bithi and Foni, since Carl missed only Mathematics. So Foni missed English and Social Science. Definite.
4
Bithi: Social Science needs Bithi as one of its two missers. Science needs Bithi as well, since only one of Alva or Deep missed it. So Bithi missed Science and Social Science. Definite.
5
Alva and Deep: one missed only Hindi and the other missed Hindi and Science, and nothing decides which is which. Not definite.
6
Definite students: Carl, Esha, Foni, Bithi, which makes 4.
Correct Answer: 4
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CAT 2020 Slot 1 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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