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CAT 2021 Slot 1 — DILR questions with answers

All 20 questions of the Data Interpretation & Logical Reasoning section (15 MCQs, 5 TITA, 4 sets). Try each one, then open its answer and solution.

CAT 2021 Slot 1, timed like the real exam (120 minutes, 40 a section) and scored the CAT way: +3 right, −1 for a wrong MCQ, 0 for a wrong TITA, with the full post-mock analysis. Older official papers are in CATin Pro, with 80+ mocks and the full planner. The last three years of papers are free.

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Data Interpretation & Logical Reasoning

CAT 2021 Slot 1 · 40 minutes · +3 for a right answer, −1 for a wrong MCQ, 0 for a wrong TITA

Data set

Set for questions 25–30

Instructions [25 - 30 ] A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas — Manufacturing, Automation, and Logistics. Four of the authors were from the Logistics area and two were from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal. The following facts are also known. 1. F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue. 2. A was from the Automation area and did not have a paper scheduled in the October issue. 3. None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area. 4. A and H were from different countries, but had their papers scheduled in exactly the same issues. 5. C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not. 6. B, from the Logistics area, had a paper scheduled in the April issue of the journal. 7. B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal. 8. D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue. 9. C and H belonged to different areas.

Q25MCQTeam Selection & Scheduling

What is the correct sequence of number of papers written by B, C, E and G, respectively?
  1. 1, 2, 2, 3
  2. 1, 3, 3, 1
  3. 3, 1, 1, 3
  4. 1, 2, 2, 1
Answer and solution

Answer: (A) 1, 2, 2, 3

A, D, G and H wrote twice as many papers as B, C, E and F, so they wrote 1212 of the 1818 papers and the other four wrote 66. No author wrote more than 33, so A, D, G and H wrote exactly 33 each. F wrote 11 paper (fact 1), so B+C+E=5B + C + E = 5. E had papers in consecutive issues, so E wrote at least 22, and C wrote the same number as E (fact 5). C=E=3C = E = 3 would exceed 5, so C=E=2C = E = 2 and B=1B = 1. As a check, B's one paper is in April (fact 6) and G shares no issue with B (fact 7), so G's three papers are in January, July and October. The completed table: Solution figure for question 25, CAT 2021 Slot 1 So B, C, E and G wrote 1,2,2,31, 2, 2, 3 papers. Option D (1, 2, 2, 1) fails because G, like A, D and H, must have written 3 papers. Hence, option A (1, 2, 2, 3).

Q26TITATeam Selection & Scheduling

How many papers were written by Indian authors?

Type in your answer (TITA). No negative mark for a wrong answer.

Answer and solution

Answer: 8

A, D, G and H wrote 12 of the 18 papers (twice the other four's 6), so 3 each. F wrote 1 and E at least 2 (consecutive issues), with C=EC = E, so C=E=2C = E = 2 and B=1B = 1. A, in Automation, is Indian (fact 3). H is from another country and C, E are the Chinese, so H is Japanese like D, and B, G are Indian. As B and F are Logistics, G is the other Automation author. C and E, in different areas, are one Manufacturing and one Logistics, so H is Logistics; fact 9 makes C Manufacturing, E Logistics. The completed table: Solution figure for question 26, CAT 2021 Slot 1 Indian authors are A (3), G (3), B (1) and F (1), so they wrote 3+3+1+1=83 + 3 + 1 + 1 = 8 papers. The answer is 8.

Q27MCQTeam Selection & Scheduling

Which of the following statement(s) MUST be true? Statement A: Every issue had at least one paper by author(s) from each country. Statement B: Every issue had at most two papers by author(s) from each area.
  1. Both the statements
  2. Only Statement B
  3. Only Statement A
  4. Neither of the statements
Answer and solution

Answer: (C) Only Statement A

A, D, G and H wrote 12 of the 18 papers (twice the other four's 6), so 3 each. F wrote 1 and E at least 2 (consecutive issues), with C=EC = E, so C=E=2C = E = 2 and B=1B = 1. A, in Automation, is Indian (fact 3). H is from another country and C, E are the Chinese, so H is Japanese like D, and B, G are Indian. As B and F are Logistics, G is the other Automation author. C and E, in different areas, are one Manufacturing and one Logistics, so H is Logistics; fact 9 makes C Manufacturing, E Logistics. A and H have no October paper (facts 2, 4), D none in July and G none in B's April, so A and H take Jan, Apr, Jul; D Jan, Apr, Oct; G Jan, Jul, Oct. One slot is left per issue: E takes consecutive Apr, Jul and C non-consecutive Jan, Oct. Solution figure for question 27, CAT 2021 Slot 1 Statement A: every issue has an Indian (A or G), a Japanese (D or H) and a Chinese author (C or E), so it is true. Statement B: April has three Logistics papers (H, B, E), so it is false, and option A fails. Hence, option C (Only Statement A).

Q28MCQTeam Selection & Scheduling

Which of the following statements is FALSE?
  1. Every issue had at least one paper by author(s) from Automation area.
  2. Every issue had exactly one paper by a Chinese author.
  3. Every issue had exactly two papers by authors from Logistics area.
  4. Every issue had exactly two papers by Indian authors.
Answer and solution

Answer: (C) Every issue had exactly two papers by authors from Logistics area.

A, D, G and H wrote 12 of the 18 papers (twice the other four's 6), so 3 each. F wrote 1 and E at least 2 (consecutive issues), with C=EC = E, so C=E=2C = E = 2 and B=1B = 1. A, in Automation, is Indian (fact 3). H is from another country and C, E are the Chinese, so H is Japanese like D, and B, G are Indian. As B and F are Logistics, G is the other Automation author. C and E, in different areas, are one Manufacturing and one Logistics, so H is Logistics; fact 9 makes C Manufacturing, E Logistics. A and H have no October paper (facts 2, 4), D none in July and G none in B's April, so A and H take Jan, Apr, Jul; D Jan, Apr, Oct; G Jan, Jul, Oct. One slot is left per issue: E takes consecutive Apr, Jul and C non-consecutive Jan, Oct. Solution figure for question 28, CAT 2021 Slot 1 Each issue has A or G (Automation), C or E (Chinese) and two Indians, so A, B and D are true. January has one Logistics paper (H) and April three (H, B, E), so C is false. Hence, option C (Every issue had exactly two papers by authors from Logistics area.).

Q29MCQTeam Selection & Scheduling

Which of the following statements is FALSE?
  1. There were exactly two papers by authors from Manufacturing area in the January issue.
  2. There was exactly one paper by an author from Manufacturing area in the April issue.
  3. There was exactly one paper by an author from Logistics area in the October issue.
  4. There were exactly two papers by authors from Manufacturing area in the July issue.
Answer and solution

Answer: (D) There were exactly two papers by authors from Manufacturing area in the July issue.

A, D, G and H wrote 12 of the 18 papers (twice the other four's 6), so 3 each. F wrote 1 and E at least 2 (consecutive issues), with C=EC = E, so C=E=2C = E = 2 and B=1B = 1. A, in Automation, is Indian (fact 3). H is from another country and C, E are the Chinese, so H is Japanese like D, and B, G are Indian. As B and F are Logistics, G is the other Automation author. C and E, in different areas, are one Manufacturing and one Logistics, so H is Logistics; fact 9 makes C Manufacturing, E Logistics. A and H have no October paper (facts 2, 4), D none in July and G none in B's April, so A and H take Jan, Apr, Jul; D Jan, Apr, Oct; G Jan, Jul, Oct. One slot is left per issue: E takes consecutive Apr, Jul and C non-consecutive Jan, Oct. Solution figure for question 29, CAT 2021 Slot 1 Manufacturing (D, C) has two January papers and one April paper, so A and B are true. F has October's only Logistics paper, so C is true. July (A, G, H, E) has no Manufacturing paper, so D is false. Hence, option D (There were exactly two papers by authors from Manufacturing area in the July issue.).

Q30MCQTeam Selection & Scheduling

Which of the following is the correct sequence of number of papers by authors from Automation, Manufacturing and Logistics areas, respectively?
  1. 6, 5, 7
  2. 6, 6, 6
  3. 6, 7, 5
  4. 5, 6, 7
Answer and solution

Answer: (A) 6, 5, 7

A, D, G and H wrote 12 of the 18 papers (twice the other four's 6), so 3 each. F wrote 1 and E at least 2 (consecutive issues), with C=EC = E, so C=E=2C = E = 2 and B=1B = 1. A, in Automation, is Indian (fact 3). H is from another country and C, E are the Chinese, so H is Japanese like D, and B, G are Indian. As B and F are Logistics, G is the other Automation author. C and E, in different areas, are one Manufacturing and one Logistics, so H is Logistics; fact 9 makes C Manufacturing, E Logistics. The completed table: Solution figure for question 30, CAT 2021 Slot 1 Automation (A, G): 3+3=63 + 3 = 6. Manufacturing (D, C): 3+2=53 + 2 = 5. Logistics (H, E, B, F): 3+2+1+1=73 + 2 + 1 + 1 = 7. Option D (5, 6, 7) swaps the first two counts. Hence, option A (6, 5, 7).

Data set

Set for questions 31–34

Instructions [31 - 34 ] Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table. One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit. The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2. The following additional facts are known. 1. No one except possibly Ganga sold any Mango smoothie. 2. Each woman sold either zero or one unit of any single finished product in any hour. 3. Each woman had exactly one unit each of two different raw materials as leftovers. 4. No one had any banana leftover.
Data for questions 31–34, CAT 2021 Slot 1 DILRData for questions 31–34, CAT 2021 Slot 1 DILR

Q31MCQLogical Puzzles

What BEST can be concluded about the number of units of fruit salad sold in the first hour?
  1. Either 1 or 2.
  2. Either 0 or 1 or 2.
  3. Exactly 2.
  4. Exactly 1.
Answer and solution

Answer: (A) Either 1 or 2.

A price is the raw-material cost plus twice the number of raw materials: mango smoothie 8+4=128 + 4 = 12, apple smoothie 7+4=117 + 4 = 11, banana smoothie 6+4=106 + 4 = 10, mixed fruit smoothie 11+8=1911 + 8 = 19, fruit salad 6+6=126 + 6 = 12. Solution figure for question 31, CAT 2021 Slot 1 Leftovers are sold only in the last hour, so hour-1 revenue comes from products alone, at most one of each per woman (fact 2), with mango smoothies only from Ganga (fact 1). Kaveri's 19 can only be one mixed fruit smoothie, so no fruit salad. Narmada's 31 can only be 19+1219 + 12: a mixed fruit smoothie and a fruit salad. Ganga's 23 can only be 11+1211 + 12: an apple smoothie plus a 12, which is a fruit salad or a mango smoothie. Nothing in the data decides which. Solution figure for question 31, CAT 2021 Slot 1 So 1 or 2 fruit salads were sold in hour 1. Option B, which allows 0, fails because Narmada's fruit salad is certain; options C and D each fix one value that the data leaves open. Hence, option A (Either 1 or 2.).

Q32MCQLogical Puzzles

Which of the following is NECESSARILY true?
  1. Ganga did not sell any leftover mangoes.
  2. Ganga did not sell any leftover apples.
  3. Narmada sold one unit of leftover milk.
  4. Kaveri sold one unit of leftover mangoes.
Answer and solution

Answer: (B) Ganga did not sell any leftover apples.

Prices (raw-material cost plus twice the number of raw materials): mango smoothie 12, apple smoothie 11, banana smoothie 10, mixed fruit smoothie 19, fruit salad 12. Leftovers sell at cost minus 1: milk 4, mango 2, apple 1, and no banana is left over. So two leftovers bring 6 (milk, mango), 5 (milk, apple) or 3 (mango, apple), all in hour 4. Ganga's 30: products must make 24, 25 or 27. Only 24=12+1224 = 12 + 12 works (mango smoothie and fruit salad), so her leftovers are milk and mango. Kaveri's 27: 21=10+1121 = 10 + 11 with milk and mango, or 22=10+1222 = 10 + 12 with milk and apple. 24 would need a mango smoothie, which only Ganga sells. Narmada's 22: 16 and 17 cannot be made, so it is 19+319 + 3, with mango and apple left over. Below are Kaveri's two cases (the first table is milk and mango left). Solution figure for question 32, CAT 2021 Slot 1 Ganga sold no leftover apple, so B must be true. A is false, as Ganga sold a leftover mango. C is false, as Narmada had no leftover milk. D holds only in Kaveri's first case, so it is not necessary. Hence, option B (Ganga did not sell any leftover apples.).

Q33MCQLogical Puzzles

What BEST can be concluded about the total number of units of milk the three women had in the beginning?
  1. Either 19 or 20 units.
  2. Either 18 or 19 or 20 units.
  3. Either 18 or 19 units.
  4. Either 17 or 18 or 19 units.
Answer and solution

Answer: (B) Either 18 or 19 or 20 units.

Prices: mango smoothie 12, apple smoothie 11, banana smoothie 10, mixed fruit smoothie 19, fruit salad 12. Leftovers (hour 4): milk 4, mango 2, apple 1. Every product except fruit salad uses one unit of milk. Ganga: 23=11+1223 = 11 + 12, 21=10+1121 = 10 + 11, 29=10+1929 = 10 + 19, 30=12+12+630 = 12 + 12 + 6 (mango smoothie, fruit salad, leftover milk and mango). Milk: 1 or 2 (her hour-1 12 may be a mango smoothie), then 2, 2, 1, plus 1 left over: 7 or 8. Kaveri: 1919, 22=10+1222 = 10 + 12, 30=11+1930 = 11 + 19, and 27=10+11+627 = 10 + 11 + 6 (leftover milk, mango) or 10+12+510 + 12 + 5 (leftover milk, apple). Milk: 1, 1, 2, then 3 or 2: 7 or 6. Narmada: 31=12+1931 = 12 + 19, 21=10+1121 = 10 + 11, 23=11+1223 = 11 + 12, 22=19+322 = 19 + 3 (leftover mango, apple). Milk: 1, 2, 1, 1: 5. Solution figure for question 33, CAT 2021 Slot 1 The total runs from 7+6+5=187 + 6 + 5 = 18 to 8+7+5=208 + 7 + 5 = 20, with 19 also possible. Option A misses 18: Ganga's hour-1 fruit salad plus Kaveri's milk-and-apple case. Hence, option B (Either 18 or 19 or 20 units.).

Q34TITALogical Puzzles

If it is known that three leftover units of mangoes were sold during the last business hour of the day, how many apple smoothies were sold during the day?

Type in your answer (TITA). No negative mark for a wrong answer.

Answer and solution

Answer: 6

Prices: apple smoothie 11, banana smoothie 10, fruit salad 12, mixed fruit smoothie 19, mango smoothie 12 (Ganga only). Leftovers sell at milk 4, mango 2, apple 1. Last hour: Ganga's 30 is 12+12+612 + 12 + 6, with leftover milk and mango. Narmada's 22 is 19+319 + 3, with leftover mango and apple. Kaveri's 27 is either 10+11+610 + 11 + 6 (banana and apple smoothies; leftover milk and mango) or 10+12+510 + 12 + 5 (banana smoothie and fruit salad; leftover milk and apple). Ganga and Narmada supply two leftover mangoes, so a third means Kaveri's first case: she sold an apple smoothie in hour 4. That is the first table below. Solution figure for question 34, CAT 2021 Slot 1 Apple smoothies, from the only possible splits: Ganga, 23=11+1223 = 11 + 12 and 21=10+1121 = 10 + 11, so 2. Kaveri, 30=11+1930 = 11 + 19 plus hour 4, so 2. Narmada, 21=10+1121 = 10 + 11 and 23=11+1223 = 11 + 12, so 2. In total, 2+2+2=62 + 2 + 2 = 6 apple smoothies were sold. The answer is 6.

Data set

Set for questions 35–40

Instructions [35 - 40 ] Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha. Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below. The following additional facts are also known. 1. Amudha, Bharatan, and Chandran are mutual strangers. 2. Amudha, Dhinesh, and Fani are Ezil's friends. 3. Chandran and Gowtham are friends. 4. Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha. 5. Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.
Data for questions 35–40, CAT 2021 Slot 1 DILR

Q35MCQLogical Puzzles

Who are Gowtham’s acquaintances?
  1. Dhinesh, Ezhil and Fani
  2. Amudha, Dhinesh and Fani
  3. Bharatan, Dhinesh and Ezhil
  4. Amudha, Bharatan and Fani
Answer and solution

Answer: (A) Dhinesh, Ezhil and Fani

From the table, Amudha has 6−1−4=16 - 1 - 4 = 1 friend and Gowtham 6−3−2=16 - 3 - 2 = 1. By facts 2 and 3, Ezhil is the only friend of Amudha and of Fani, and Chandran is Gowtham's only friend. Fact 4 makes Ezhil Bharatan's only acquaintance. Fact 5 makes Amudha's one acquaintance a friend of Bharatan. Bharatan and Chandran are strangers to Amudha (fact 1), so that acquaintance is Dhinesh, Fani or Gowtham. Fani and Gowtham already have their one friend, so it is Dhinesh, who is Bharatan's friend. Fani and Gowtham are then strangers to both Amudha and Bharatan. Gowtham has 2 strangers, Amudha and Bharatan, and one friend, Chandran. His three acquaintances are the rest: Dhinesh, Ezhil and Fani. The completed table: Solution figure for question 35, CAT 2021 Slot 1 Options B, C and D each include Amudha or Bharatan, who are strangers to Gowtham. Hence, option A (Dhinesh, Ezhil and Fani).

Q36MCQLogical Puzzles

Which of these pairs share the same type of relationship?
  1. (Amudha, Gowtham) and (Ezhil, Fani)
  2. (Bharatan, Chandran) and (Dhinesh, Ezhil)
  3. (Chandran, Ezhil) and (Dhinesh, Gowtham)
  4. (Bharatan, Ezhil) and (Fani, Gowtham)
Answer and solution

Answer: (D) (Bharatan, Ezhil) and (Fani, Gowtham)

From the table, Amudha has 6−1−4=16 - 1 - 4 = 1 friend and Gowtham 6−3−2=16 - 3 - 2 = 1. By facts 2 and 3, Ezhil is the only friend of Amudha and of Fani, and Chandran is Gowtham's only friend. Fact 4 makes Ezhil Bharatan's only acquaintance. Fact 5 makes Amudha's one acquaintance a friend of Bharatan. Bharatan and Chandran are strangers to Amudha (fact 1), so that acquaintance is Dhinesh, Fani or Gowtham. Fani and Gowtham already have their one friend, so it is Dhinesh, who is Bharatan's friend. Fani and Gowtham are then strangers to both Amudha and Bharatan. With friend Chandran and strangers Amudha and Bharatan, Gowtham's acquaintances are Dhinesh, Ezhil and Fani. Ezhil has friends Amudha, Dhinesh, Fani and acquaintances Bharatan, Gowtham, so his one stranger is Chandran. The completed table: Solution figure for question 36, CAT 2021 Slot 1 A: Amudha-Gowtham strangers, Ezhil-Fani friends. B: Bharatan-Chandran strangers, Dhinesh-Ezhil friends. C: Chandran-Ezhil strangers, Dhinesh-Gowtham acquaintances. D: Bharatan-Ezhil and Fani-Gowtham are both acquaintances. Hence, option D ((Bharatan, Ezhil) and (Fani, Gowtham)).

Q37MCQLogical Puzzles

Who is an acquaintance of Amudha?
  1. Dhinesh
  2. Fani
  3. Gowtham
  4. Ezhil
Answer and solution

Answer: (A) Dhinesh

From the table, Amudha has 6−1−4=16 - 1 - 4 = 1 friend and Gowtham 6−3−2=16 - 3 - 2 = 1. By facts 2 and 3, Ezhil is the only friend of Amudha and of Fani, and Chandran is Gowtham's only friend. Fact 4 makes Ezhil Bharatan's only acquaintance. Fact 5 makes Amudha's one acquaintance a friend of Bharatan. Bharatan and Chandran are strangers to Amudha (fact 1), so that acquaintance is Dhinesh, Fani or Gowtham. Fani and Gowtham already have their one friend, so it is Dhinesh, who is Bharatan's friend. Fani and Gowtham are then strangers to both Amudha and Bharatan. The completed table: Solution figure for question 37, CAT 2021 Slot 1 So Amudha's acquaintance is Dhinesh. Fani and Gowtham fail because either would have to be Bharatan's friend, and each already has their only friend. Ezhil is Amudha's friend, not an acquaintance. Hence, option A (Dhinesh).

Q38MCQLogical Puzzles

Who is an acquaintance of Chandran?
  1. Dhinesh
  2. Fani
  3. Ezhil
  4. Bharatan
Answer and solution

Answer: (B) Fani

From the table, Amudha has 6−1−4=16 - 1 - 4 = 1 friend and Gowtham 6−3−2=16 - 3 - 2 = 1. By facts 2 and 3, Ezhil is the only friend of Amudha and of Fani, and Chandran is Gowtham's only friend. Fact 4 makes Ezhil Bharatan's only acquaintance. Fact 5 makes Amudha's one acquaintance a friend of Bharatan. Bharatan and Chandran are strangers to Amudha (fact 1), so that acquaintance is Dhinesh, Fani or Gowtham. Fani and Gowtham already have their one friend, so it is Dhinesh, who is Bharatan's friend. Fani and Gowtham are then strangers to both Amudha and Bharatan. Gowtham, with friend Chandran and strangers Amudha and Bharatan, has acquaintances Dhinesh, Ezhil and Fani. Ezhil, with friends Amudha, Dhinesh, Fani and acquaintances Bharatan, Gowtham, has Chandran as his one stranger. Dhinesh has friends Ezhil, Bharatan and acquaintances Amudha, Gowtham, so his two strangers are Chandran and Fani. The completed table: Solution figure for question 38, CAT 2021 Slot 1 Chandran is a stranger to Amudha, Bharatan, Dhinesh and Ezhil, and a friend of Gowtham, so his one acquaintance is Fani. Hence, option B (Fani).

Q39TITALogical Puzzles

How many friends does Ezhil have?

Type in your answer (TITA). No negative mark for a wrong answer.

Answer and solution

Answer: 3

From the table, Amudha has 6−1−4=16 - 1 - 4 = 1 friend and Gowtham 6−3−2=16 - 3 - 2 = 1. By facts 2 and 3, Ezhil is the only friend of Amudha and of Fani, and Chandran is Gowtham's only friend. Fact 4 makes Ezhil Bharatan's only acquaintance. Fact 5 makes Amudha's one acquaintance a friend of Bharatan. Bharatan and Chandran are strangers to Amudha (fact 1), so that acquaintance is Dhinesh, Fani or Gowtham. Fani and Gowtham already have their one friend, so it is Dhinesh, who is Bharatan's friend. Fani and Gowtham are then strangers to both Amudha and Bharatan. Ezhil is a friend of Amudha, Dhinesh and Fani (fact 2). Bharatan is his acquaintance (fact 4). Gowtham, whose friend is Chandran and whose strangers are Amudha and Bharatan, has Ezhil as an acquaintance. Ezhil has exactly one stranger, and only Chandran is left, so he has no other friend. The completed table: Solution figure for question 39, CAT 2021 Slot 1 The answer is 3.

Q40TITALogical Puzzles

How many people are either a friend or a friend-of-a-friend of Ezhil?

Type in your answer (TITA). No negative mark for a wrong answer.

Answer and solution

Answer: 4

From the table, Amudha has 6−1−4=16 - 1 - 4 = 1 friend and Gowtham 6−3−2=16 - 3 - 2 = 1. By facts 2 and 3, Ezhil is the only friend of Amudha and of Fani, and Chandran is Gowtham's only friend. Fact 4 makes Ezhil Bharatan's only acquaintance. Fact 5 makes Amudha's one acquaintance a friend of Bharatan. Bharatan and Chandran are strangers to Amudha (fact 1), so that acquaintance is Dhinesh, Fani or Gowtham. Fani and Gowtham already have their one friend, so it is Dhinesh, who is Bharatan's friend. Fani and Gowtham are then strangers to both Amudha and Bharatan. Gowtham, with friend Chandran and strangers Amudha and Bharatan, has acquaintances Dhinesh, Ezhil and Fani. So Ezhil has friends Amudha, Dhinesh, Fani, acquaintances Bharatan, Gowtham, and his one stranger is Chandran: no other friend. Amudha and Fani have Ezhil as their only friend. Dhinesh has friends Ezhil and Bharatan, acquaintances Amudha and Gowtham, and strangers Chandran and Fani. The completed table: Solution figure for question 40, CAT 2021 Slot 1 Friends or friends-of-friends of Ezhil: Amudha, Dhinesh, Fani and Bharatan. The answer is 4.

Data set

Set for questions 41–44

Instructions [41 - 44 ] The horizontal bars in the above diagram represent 2020 aggregate sales (in ₹ million) of a company for the different subcategories of its products. The top four product subcategories (Bookcases, Chairs, Furnishings, Tables) belong to furniture product category; the bottom four product subcategories (Accessories, Copiers, Machines, Phones) belong to the technology product category while all other product subcategories belong to the office supply product category. For each of the product subcategories, there is a vertical line indicating the sales of the corresponding subcategory in 2019.
Data for questions 41–44, CAT 2021 Slot 1 DILR

Q41MCQBar & Line Charts

The total sales (in ₹ million) in 2019 from products in office supplies category is closest to
  1. 18.0
  2. 16.5
  3. 13.5
  4. 12.5
Answer and solution

Answer: (C) 13.5

Office supplies are the nine subcategories between Tables and Accessories. Reading each 2019 vertical line from the chart (in ₹ million): Binders 3.6, Art 0.45, Appliances 1.85, Envelopes 0.35, Fasteners 0.05, Labels 0.2, Paper 1.5, Storage 4.3, Supplies 1.05. Total =3.6+0.45+1.85+0.35+0.05+0.2+1.5+4.3+1.05≈13.4= 3.6 + 0.45 + 1.85 + 0.35 + 0.05 + 0.2 + 1.5 + 4.3 + 1.05 \approx 13.4, closest to 13.5. Option A (18.0) is the trap: it is roughly the 2020 total, read from the bars instead of the lines (5.3+0.6+3.1+0.2+0.1+0.3+2.0+5.1+1.2=17.95.3 + 0.6 + 3.1 + 0.2 + 0.1 + 0.3 + 2.0 + 5.1 + 1.2 = 17.9). Option D (12.5) is almost a full million away. Hence, option C (13.5).

Q42MCQBar & Line Charts

The percentage increase in sales in Furniture category from 2019 to 2020 is closest to
  1. 20%
  2. 8%
  3. 25%
  4. 1%
Answer and solution

Answer: (B) 8%

Furniture subcategories, 2019 (vertical line) and 2020 (bar), in ₹ million: Bookcases 1.9 and 2.2; Chairs 6.2 and 7.0; Furnishings 2.05 and 2.1; Tables 4.4 and 4.5. 2019 total =1.9+6.2+2.05+4.4=14.55= 1.9 + 6.2 + 2.05 + 4.4 = 14.55. 2020 total =2.2+7.0+2.1+4.5=15.8= 2.2 + 7.0 + 2.1 + 4.5 = 15.8. Percentage increase =15.8−14.5514.55×100=1.2514.55×100≈8.6%= \frac{15.8 - 14.55}{14.55} \times 100 = \frac{1.25}{14.55} \times 100 \approx 8.6\%, closest to 8%. Options A and C (20% and 25%) would need a rise of about 3 million or more, but the rise is only 1.25 million. Option D (1%) would mean a rise of about 0.15 million, yet Chairs alone rose by about 0.8 million. Hence, option B (8%).

Q43TITABar & Line Charts

How many subcategories had sales of ₹ 4 million or more in 2019 and registered an increase in sales in excess of 25% in 2020?

Type in your answer (TITA). No negative mark for a wrong answer.

Answer and solution

Answer: 1

From the chart, the subcategories with 2019 sales (vertical line) of ₹4 million or more are Chairs, Tables, Storage, Machines and Phones. An increase of more than 25% needs 2020 sales above 1.25 times the 2019 value. Chairs: 6.2 to 7.0; needs more than 7.75. Fails. Tables: 4.4 to 4.5; needs more than 5.5. Fails. Storage: 4.3 to 5.1; needs more than about 5.4. Fails. Machines: about 4.1 to 3.2, a fall. Fails. Phones: about 5.75 to 7.7, a rise of 1.955.75≈34%\frac{1.95}{5.75} \approx 34\%. Passes. Only Phones meets both conditions. The answer is 1.

Q44MCQBar & Line Charts

The improvement index for a category is the maximum percentage increase in sales from 2019 to 2020 among any of its subcategories. The correct order of categories in increasing order of this improvement index is
  1. furniture, technology, office supply
  2. technology, furniture, office supply
  3. office supply, technology, furniture
  4. office supply, furniture, technology
Answer and solution

Answer: (A) furniture, technology, office supply

A category's improvement index is the largest percentage rise among its subcategories. Reading 2019 (line) and 2020 (bar) values from the chart, in ₹ million: Furniture: Bookcases 1.9 to 2.2 (≈16%\approx 16\%) is the best; Chairs rose about 13%, Furnishings and Tables under 3%. Index about 16%. Technology: Accessories 3.1 to 4.4 (≈42%\approx 42\%) is the best; Phones rose about 34%, Copiers about 26%, and Machines fell. Index about 42%. Office supply: Appliances 1.85 to 3.1 (≈68%\approx 68\%) alone beats the other two categories; Binders 3.6 to 5.3 is about 47%. Index at least 68%. So the order is furniture, technology, office supply. Option B fails because furniture's best rise (about 16%) is well below technology's (about 42%). Hence, option A (furniture, technology, office supply).