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CAT 2019 Slot 2 DILR · Set 4 of 8Logical ReasoningModerate DifficultyQ13–Q16 · 4 MCQ

CAT 2019 Slot 2 DILR Set 4: 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 13–16
In the table below the check marks indicate all languages spoken by five people: Paula, Quentin, Robert, Sally and Terence. For example, Paula speaks only Chinese and English.
ArabicBasqueChineseDutchEnglishFrench
Paula✓✓
Quentin✓✓
Robert✓✓
Sally✓✓
Terence✓✓
These five people form three teams, Team 1, Team 2 and Team 3. Each team has either 2 or 3 members. A team is said to speak a particular language if at least one of its members speak that language.
The following facts are known.
1
Each team speaks exactly four languages and has the same number of members.
2
English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team.
3
None of the teams include both Quentin and Robert.
4
Paula and Sally are together in exactly two teams.
5
Robert is in Team 1 and Quentin is in Team 3.

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

Q13. Arrangements

MCQ · +3 / −1
Who among the following four is not a member of Team 2?
  1. A) Sally
  2. B) Terence
  3. C) Paula
  4. D) Quentin
Correct Answer
D) Quentin
Step-by-step solution
📌 Core Concept
Count how many team slots each person fills using the language-count facts, then use the size and exclusion conditions to fix the three teams.
🔢 Step-by-Step Solution
1
Each team speaks 4 languages, and the totals are English 3, Chinese 3, Basque 2, French 2, Arabic 1, Dutch 1. That is 12 language-slots, which matches 3 teams × 4.
2
Arabic is spoken only by Robert and Dutch only by Quentin. Each is spoken by exactly one team, so Robert and Quentin are each in exactly one team (Team 1 and Team 3 respectively, by Fact 5).
3
Basque is spoken only by Sally and by exactly two teams, so Sally is in exactly two teams. By Fact 4, Paula is with Sally in both of those teams.
4
Count the slots. Two-member teams give 6 slots, but Robert 1 + Quentin 1 + Sally 2 + Paula at least 2 + Terence at least 1 is already 7. So every team has 3 members (9 slots).
5
Fact 3 keeps Robert and Quentin apart. Team 2 therefore has neither of them, so Team 2 = Paula, Sally, Terence.
6
Sally's second team is Team 1 or Team 3. If it were Team 1 (Robert, Sally, Paula), it would speak Arabic, French, Basque, English and Chinese, which is 5 languages. That is not allowed, so Sally is in Team 3 with Paula and Quentin.
7
Team 1 = Robert, Paula, Terence.
Quick Check
Team 1 speaks Arabic, French, Chinese and English. Team 2 speaks Chinese, English, Basque and French. Team 3 speaks Dutch, English, Basque and Chinese. Each has 4 languages and the totals match Fact 2.
Team 2 is Paula, Sally and Terence, so Quentin is the one who is not in it.
Correct Answer: D

Q14. Arrangements

MCQ · +3 / −1
Who among the following four people is a part of exactly two teams?
  1. A) Quentin
  2. B) Robert
  3. C) Paula
  4. D) Sally
Correct Answer
D) Sally
Step-by-step solution
📌 Core Concept
Count how many team slots each person fills using the language-count facts, then use the size and exclusion conditions to fix the three teams.
🔢 Step-by-Step Solution
1
Each team speaks 4 languages, and the totals are English 3, Chinese 3, Basque 2, French 2, Arabic 1, Dutch 1, which is 12 language-slots.
2
Arabic is spoken only by Robert and Dutch only by Quentin. Each is spoken by exactly one team, so Robert and Quentin are each in exactly one team.
3
Basque is spoken only by Sally and by exactly two teams, so Sally is in exactly two teams. By Fact 4, Paula is with Sally in both of them.
4
Two-member teams would give only 6 slots, but Robert 1 + Quentin 1 + Sally 2 + Paula at least 2 + Terence at least 1 is already 7. So every team has 3 members.
5
Robert (Team 1) and Quentin (Team 3) cannot share a team. Team 2 has neither of them, so Team 2 = Paula, Sally, Terence.
6
Sally in Team 1 would give Robert, Sally, Paula, which speaks 5 languages (Arabic, French, Basque, English, Chinese). That is not allowed, so Sally's second team is Team 3 = Quentin, Sally, Paula.
7
Team 1 = Robert, Paula, Terence.
Quick Check
The teams are T1 = {Robert, Paula, Terence}, T2 = {Paula, Sally, Terence}, T3 = {Quentin, Sally, Paula}. The number of teams each person is in is: Quentin 1, Robert 1, Paula 3, Sally 2.
Among the options, only Sally is in exactly two teams.
Correct Answer: D

Q15. Arrangements

MCQ · +3 / −1
Who among the five people is a member of all teams?
  1. A) Paula
  2. B) No one
  3. C) Sally
  4. D) Terence
Correct Answer
A) Paula
Step-by-step solution
📌 Core Concept
Count how many team slots each person fills using the language-count facts, then use the size and exclusion conditions to fix the three teams.
🔢 Step-by-Step Solution
1
Each team speaks 4 languages, and the totals are English 3, Chinese 3, Basque 2, French 2, Arabic 1, Dutch 1, which is 12 language-slots.
2
Arabic is only Robert and Dutch is only Quentin, each spoken by one team. So Robert and Quentin are each in exactly one team.
3
Basque is only Sally and is spoken by two teams, so Sally is in exactly two teams. By Fact 4, Paula is with Sally in both of them.
4
The minimum slot count is Robert 1 + Quentin 1 + Sally 2 + Paula 2 + Terence 1 = 7, which is more than 6. So each team has 3 members.
5
Fact 3 keeps Robert (Team 1) and Quentin (Team 3) apart. Team 2 has neither, so Team 2 = Paula, Sally, Terence.
6
Putting Sally in Team 1 gives Robert, Sally, Paula, which speaks 5 languages. So Sally's other team is Team 3, which is Quentin, Sally, Paula.
7
Team 1 must then be Robert, Paula, Terence. Its languages are Arabic, French, Chinese and English, which is 4 as required.
Quick Check
The teams are T1 = {Robert, Paula, Terence}, T2 = {Paula, Sally, Terence}, T3 = {Quentin, Sally, Paula}. Paula appears in all three. Terence is in two, Sally in two, and Robert and Quentin in one each.
Correct Answer: A

Q16. Arrangements

MCQ · +3 / −1
Apart from Chinese and English, which languages are spoken by Team 1?
  1. A) Basque and Dutch
  2. B) Arabic and French
  3. C) Basque and French
  4. D) Arabic and Basque
Correct Answer
B) Arabic and French
Step-by-step solution
📌 Core Concept
Count how many team slots each person fills using the language-count facts, then use the size and exclusion conditions to fix the three teams.
🔢 Step-by-Step Solution
1
Each team speaks 4 languages, and the totals are English 3, Chinese 3, Basque 2, French 2, Arabic 1, Dutch 1, which is 12 language-slots.
2
Arabic is only Robert and Dutch is only Quentin, each spoken by one team. So Robert and Quentin are each in exactly one team.
3
Basque is only Sally and is spoken by two teams, so Sally is in exactly two teams. By Fact 4, Paula is with Sally in both of them.
4
Two-member teams would need only 6 slots, but the minimum is Robert 1 + Quentin 1 + Sally 2 + Paula 2 + Terence 1 = 7. So each team has 3 members.
5
Team 2 cannot hold Robert or Quentin (they are in Teams 1 and 3), so Team 2 = Paula, Sally, Terence.
6
Sally's second team cannot be Team 1. Robert, Sally and Paula would speak Arabic, French, Basque, English and Chinese, which is 5 languages. So Sally is in Team 3 with Quentin and Paula.
7
Team 1 is therefore Robert, Paula, Terence. Paula and Terence give Chinese and English, and Robert adds Arabic and French (Terence also speaks French).
Quick Check
Team 1 speaks exactly Arabic, French, Chinese and English, which is 4 languages. French is then spoken in Teams 1 and 2, and Arabic only in Team 1, matching Fact 2.
Apart from Chinese and English, Team 1 speaks Arabic and French.
Correct Answer: B
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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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