CAT 2023 Slot 3 DILR Set 4 Q16–Q20

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2023 Slot 3, with 5 questions (Routes & Networks). Answers are CAT's official key.

The set

This set relies on a figure in the original paper, which is not reproduced here. The questions and answers are below.

A, B, C, D, E and F are the six police stations in an area, which are connected by streets as shown below. Four teams – Team 1, Team 2, Team 3 and Team 4 –
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.

[Figure in the original paper]
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.

The following facts are known:
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.

Question 16

Which one among the following stations is visited the largest number of times?
  1. A
    Station D
  2. B
    Station C
  3. C
    Station F
  4. D
    Station E

Answer: (D) Station E Routes & Networks MCQ

Solution

  1. Each team makes 6 moves (one every 30 min) and must keep moving. Team 4 avoids B, D, F, so it only shuttles A-E and A-C. At 11:30 it is at E, so it is at A at 11:00 and 12:00; at 10:30 E holds only Teams 1 and 3, so Team 4 is at C then, and at A at 10:00.
  2. Team 3 is at D at 10:00 without using A-E, so A-C-D; at 10:30 it is at E (D to E). To be back at A by 12:00 without A-E it must go E-D-C-A.
  3. Team 2 is at E at 10:00 via A-F-E. At 10:30 it cannot stay at E, cannot use A-E, and cannot use D-E (Team 3 is on it), so it goes to F.
  4. Team 1 reaches E at 10:30 from A (F-E is occupied by Team 2) and is at B at 11:30, so A at 11:00. At 9:30 A-C (Team 3) and A-F (Team 2) are taken, and Team 4 must be at E at 9:30 (A-C is taken), so Team 1 goes to B.
  5. Routes: T1 A-B-A-E-A-B-A; T2 A-F-E-F-(A or E)-F-A; T3 A-C-D-E-D-C-A; T4 A-E-A-C-A-E-A. For Team 2's 11:00-11:30 leg, going A to C clashes with Team 3 on C-A at 11:30-12:00, and B is excluded at 11:30, hence F.
  6. Visits (excluding start and end): E is visited 5 or 6 times (T1 once, T2 once or twice, T3 once, T4 twice), more than C (3), F (3) or D (2).

Question 17

How many times do the teams pass through Station B in a day?

TITA: type in the answer. There are no options and no negative marking.

Answer: 2 Routes & Networks TITA

Solution

  1. Each team makes 6 moves (one every 30 min) and must keep moving. Team 4 avoids B, D, F, so it only shuttles A-E and A-C. At 11:30 it is at E, so it is at A at 11:00 and 12:00; at 10:30 E holds only Teams 1 and 3, so Team 4 is at C then, and at A at 10:00.
  2. Team 3 is at D at 10:00 without using A-E, so A-C-D; at 10:30 it is at E (D to E). To be back at A by 12:00 without A-E it must go E-D-C-A.
  3. Team 2 is at E at 10:00 via A-F-E. At 10:30 it cannot stay at E, cannot use A-E, and cannot use D-E (Team 3 is on it), so it goes to F.
  4. Team 1 reaches E at 10:30 from A (F-E is occupied by Team 2) and is at B at 11:30, so A at 11:00. At 9:30 A-C (Team 3) and A-F (Team 2) are taken, and Team 4 must be at E at 9:30 (A-C is taken), so Team 1 goes to B.
  5. Routes: T1 A-B-A-E-A-B-A; T2 A-F-E-F-(A or E)-F-A; T3 A-C-D-E-D-C-A; T4 A-E-A-C-A-E-A. For Team 2's 11:00-11:30 leg, going A to C clashes with Team 3 on C-A at 11:30-12:00, and B is excluded at 11:30, hence F.
  6. Only Team 1 goes to B, twice (9:30 and 11:30): 2.

Question 18

Which team patrols the street connecting Stations D and E at 10:15 hrs?
  1. A
    Team 2
  2. B
    Team 1
  3. C
    Team 4
  4. D
    Team 3

Answer: (D) Team 3 Routes & Networks MCQ

Solution

  1. Each team makes 6 moves (one every 30 min) and must keep moving. Team 4 avoids B, D, F, so it only shuttles A-E and A-C. At 11:30 it is at E, so it is at A at 11:00 and 12:00; at 10:30 E holds only Teams 1 and 3, so Team 4 is at C then, and at A at 10:00.
  2. Team 3 is at D at 10:00 without using A-E, so A-C-D; at 10:30 it is at E (D to E). To be back at A by 12:00 without A-E it must go E-D-C-A.
  3. Team 2 is at E at 10:00 via A-F-E. At 10:30 it cannot stay at E, cannot use A-E, and cannot use D-E (Team 3 is on it), so it goes to F.
  4. Team 1 reaches E at 10:30 from A (F-E is occupied by Team 2) and is at B at 11:30, so A at 11:00. At 9:30 A-C (Team 3) and A-F (Team 2) are taken, and Team 4 must be at E at 9:30 (A-C is taken), so Team 1 goes to B.
  5. Routes: T1 A-B-A-E-A-B-A; T2 A-F-E-F-(A or E)-F-A; T3 A-C-D-E-D-C-A; T4 A-E-A-C-A-E-A. For Team 2's 11:00-11:30 leg, going A to C clashes with Team 3 on C-A at 11:30-12:00, and B is excluded at 11:30, hence F.
  6. At 10:15 Team 3 is on its way from D (10:00) to E (10:30).

Question 19

How many times does Team 4 pass through Station E in a day?

TITA: type in the answer. There are no options and no negative marking.

Answer: 2 Routes & Networks TITA

Solution

  1. Each team makes 6 moves (one every 30 min) and must keep moving. Team 4 avoids B, D, F, so it only shuttles A-E and A-C. At 11:30 it is at E, so it is at A at 11:00 and 12:00; at 10:30 E holds only Teams 1 and 3, so Team 4 is at C then, and at A at 10:00.
  2. Team 3 is at D at 10:00 without using A-E, so A-C-D; at 10:30 it is at E (D to E). To be back at A by 12:00 without A-E it must go E-D-C-A.
  3. Team 2 is at E at 10:00 via A-F-E. At 10:30 it cannot stay at E, cannot use A-E, and cannot use D-E (Team 3 is on it), so it goes to F.
  4. Team 1 reaches E at 10:30 from A (F-E is occupied by Team 2) and is at B at 11:30, so A at 11:00. At 9:30 A-C (Team 3) and A-F (Team 2) are taken, and Team 4 must be at E at 9:30 (A-C is taken), so Team 1 goes to B.
  5. Routes: T1 A-B-A-E-A-B-A; T2 A-F-E-F-(A or E)-F-A; T3 A-C-D-E-D-C-A; T4 A-E-A-C-A-E-A. For Team 2's 11:00-11:30 leg, going A to C clashes with Team 3 on C-A at 11:30-12:00, and B is excluded at 11:30, hence F.
  6. Team 4 is at E at 9:30 and 11:30: 2 times.

Question 20

How many teams pass through Station C in a day?
  1. A
    2
  2. B
    1
  3. C
    3
  4. D
    4

Answer: (A) 2 Routes & Networks MCQ

Solution

  1. Each team makes 6 moves (one every 30 min) and must keep moving. Team 4 avoids B, D, F, so it only shuttles A-E and A-C. At 11:30 it is at E, so it is at A at 11:00 and 12:00; at 10:30 E holds only Teams 1 and 3, so Team 4 is at C then, and at A at 10:00.
  2. Team 3 is at D at 10:00 without using A-E, so A-C-D; at 10:30 it is at E (D to E). To be back at A by 12:00 without A-E it must go E-D-C-A.
  3. Team 2 is at E at 10:00 via A-F-E. At 10:30 it cannot stay at E, cannot use A-E, and cannot use D-E (Team 3 is on it), so it goes to F.
  4. Team 1 reaches E at 10:30 from A (F-E is occupied by Team 2) and is at B at 11:30, so A at 11:00. At 9:30 A-C (Team 3) and A-F (Team 2) are taken, and Team 4 must be at E at 9:30 (A-C is taken), so Team 1 goes to B.
  5. Routes: T1 A-B-A-E-A-B-A; T2 A-F-E-F-(A or E)-F-A; T3 A-C-D-E-D-C-A; T4 A-E-A-C-A-E-A. For Team 2's 11:00-11:30 leg, going A to C clashes with Team 3 on C-A at 11:30-12:00, and B is excluded at 11:30, hence F.
  6. C is visited by Team 3 (9:30, 11:30) and Team 4 (10:30) only: 2 teams.

Same concept in other years

See every question on Network of roads/lines with travel times or distances; routes and schedules.

More Routes & Networks questions from CAT

All 41 Routes & Networks questions asked since 2017.