CAT 2022 Slot 1 DILR Set 2 Q6–Q10

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2022 Slot 1, 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.

[Figure in the original paper]

Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g. R) and small filled-up circles denoting other stations. Each train runs either in east-west or north-south direction, but not both. All trains stop for 2 minutes at each of the junction stations on the way and for 1 minute at each of the other stations. It takes 2 minutes to reach the next station for trains going in east-west direction and 3 minutes to reach the next station for trains going in north-south direction. From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight. Otherwise, during the service hours, there are metro service every 15 minutes in the north-south lines and every 10 minutes in the east-west lines. A train must rest for at least 15 minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction. (All questions are related to this metro service only. Assume that if someone reaches a station exactly at the time a train is supposed to leave, (s)he can catch that train.)

Question 6

If Hari is ready to board a train at 8:05 am from station M, then when is the earliest that he can reach station N?
  1. A
    9:01 am
  2. B
    9:13 am
  3. C
    9:06 am
  4. D
    9:11 am

Answer: (D) 9:11 am Routes & Networks MCQ

Solution

  1. Line lengths from the map: A-B line is A, 2 stations, R, 3 stations, T, 2 stations, B (C-D is the same with S, V). M-N line is M, 3 stations, R, 9 stations, S, 5 stations, N (P-Q is the same with T, V).
  2. East-west: 2 min per hop; north-south: 3 min per hop; halts 1 min at ordinary stations, 2 min at junctions. Departures from each terminal: N-S at :00/:15/:30/:45, E-W every 10 min, all from 6:00 am.
  3. Trains leave M at 8:00, 8:10, ...; Hari takes the 8:10.
  4. M to N: 20 hops \(\times 2 = 40\) min, 17 ordinary halts \(= 17\) min, junctions R and S \(= 4\) min. Total 61 min.
  5. Arrives N at 9:11 am.

Question 7

If Priya is ready to board a train at 10:25 am from station T, then when is the earliest that she can reach station S?
  1. A
    11:22 am
  2. B
    11:28 am
  3. C
    11:12 am
  4. D
    11:07 am

Answer: (C) 11:12 am Routes & Networks MCQ

Solution

  1. Line lengths from the map: A-B line is A, 2 stations, R, 3 stations, T, 2 stations, B (C-D is the same with S, V). M-N line is M, 3 stations, R, 9 stations, S, 5 stations, N (P-Q is the same with T, V).
  2. East-west: 2 min per hop; north-south: 3 min per hop; halts 1 min at ordinary stations, 2 min at junctions. Departures from each terminal: N-S at :00/:15/:30/:45, E-W every 10 min, all from 6:00 am.
  3. Route via R: a northbound A-B train leaving B at 10:15 reaches T at 10:26 and leaves at 10:28; T to R is 4 hops + 3 halts = 15 min, arriving R at 10:43.
  4. Eastbound M-N train leaving M at 10:30 reaches R at 10:41 and leaves at 10:43, so she just catches it. R to S: 10 hops \(\times 2 = 20\) + 9 halts = 29 min, arriving S at 11:12.
  5. Route via V: P-Q train leaves T at 10:33, reaches V at 11:02, then the next northbound C-D train leaves V at 11:13, reaching S at 11:28. So the earliest is 11:12 am.

Question 8

Haripriya is expected to reach station S late. What is the latest time by which she must be ready to board at station S if she must reach station B before 1 am via station R?
  1. A
    11:35 pm
  2. B
    11:39 pm
  3. C
    11:43 pm
  4. D
    11:49 am

Answer: (B) 11:39 pm Routes & Networks MCQ

Solution

  1. Line lengths from the map: A-B line is A, 2 stations, R, 3 stations, T, 2 stations, B (C-D is the same with S, V). M-N line is M, 3 stations, R, 9 stations, S, 5 stations, N (P-Q is the same with T, V).
  2. East-west: 2 min per hop; north-south: 3 min per hop; halts 1 min at ordinary stations, 2 min at junctions. Departures from each terminal: N-S at :00/:15/:30/:45, E-W every 10 min, all from 6:00 am.
  3. The last southbound train leaves A at midnight, reaches R at 0:11 and leaves R at 0:13 (it reaches B at 0:41). An earlier option is pointless, so she must be at R by 0:13.
  4. Westbound train from N: N to S takes 6 hops (12) + 5 halts = 17 min, then 2 min halt, then S to R takes 29 min. Leaving N at \(t\), it departs S at \(t + 19\) and reaches R at \(t + 48 \le\) 0:13, so \(t \le\) 23:25, i.e. the 23:20 train.
  5. That train leaves S at 23:39 pm, the latest boarding time.

Question 9

What is the minimum number of trains that are required to provide the service on the AB line (considering both north and south directions)?

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

Answer: 8 Routes & Networks TITA

Solution

  1. Line lengths from the map: A-B line is A, 2 stations, R, 3 stations, T, 2 stations, B (C-D is the same with S, V). M-N line is M, 3 stations, R, 9 stations, S, 5 stations, N (P-Q is the same with T, V).
  2. East-west: 2 min per hop; north-south: 3 min per hop; halts 1 min at ordinary stations, 2 min at junctions. Departures from each terminal: N-S at :00/:15/:30/:45, E-W every 10 min, all from 6:00 am.
  3. A to B: 10 hops \(\times 3 = 30\) min, 7 ordinary halts, 2 junction halts \(= 4\): 41 min per trip.
  4. A train leaving A at 0 arrives B at 41, may leave after 15 min rest (56) so takes the 60 departure, returns to A at 101 and takes the 120 departure: a 120-minute cycle.
  5. With a train every 15 minutes, \(\frac{120}{15} = 8\) trains are needed.

Question 10

What is the minimum number of trains that are required to provide the service in this city?

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

Answer: 48 Routes & Networks TITA

Solution

  1. Line lengths from the map: A-B line is A, 2 stations, R, 3 stations, T, 2 stations, B (C-D is the same with S, V). M-N line is M, 3 stations, R, 9 stations, S, 5 stations, N (P-Q is the same with T, V).
  2. East-west: 2 min per hop; north-south: 3 min per hop; halts 1 min at ordinary stations, 2 min at junctions. Departures from each terminal: N-S at :00/:15/:30/:45, E-W every 10 min, all from 6:00 am.
  3. A-B and C-D lines are identical: 41-min trips, 120-min cycle, 15-min headway, so 8 trains each.
  4. M-N and P-Q: 61-min trips; arrive at 61, rest to 76, next departure at 80, so a 160-min cycle with 10-min headway: 16 trains each.
  5. Total \(= 8 + 8 + 16 + 16 = 48\).

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.