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Q1:

CAT 2023 Slot 3

Routes & Networks

Hard

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.

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.

Which one among the following stations is visited the largest number of times?

Answer options
Option 4
Correct Answer
Explanation for CAT 2023 Slot 3 DILR question 1

Q2:

CAT 2023 Slot 3

Routes & Networks

Hard

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.

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.

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

Q3:

CAT 2023 Slot 3

Routes & Networks

Hard

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.

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.

Which team patrols the street connecting Stations D and E at 10:15 hrs?

Answer options
Option 1
Correct Answer
Explanation for CAT 2023 Slot 3 DILR question 3

Q4:

CAT 2023 Slot 3

Routes & Networks

Hard

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.

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.

How many times does Team 44 pass through Station E in a day?

Q5:

CAT 2023 Slot 3

Routes & Networks

Hard

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.

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.

How many teams pass through Station C in a day?

Answer options
Option 3
Correct Answer
Explanation for CAT 2023 Slot 3 DILR question 5

Q6:

CAT 2022 Slot 2

Routes & Networks

Medium

Every day a widget supplier supplies widgets from the warehouse ( W ) to four locations - Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40%40 \% chance that the demand in Ahmednagar will be 5050 units and a 60% chance that the demand will be 7070 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km ) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km6 \mathrm{~km} long.

Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.

If the last location visited is Ahmednagar, then what is the total distance covered in the route (in km)?

Q7:

CAT 2022 Slot 2

Routes & Networks

Medium

Every day a widget supplier supplies widgets from the warehouse ( W ) to four locations - Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40%40 \% chance that the demand in Ahmednagar will be 5050 units and a 60% chance that the demand will be 7070 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km ) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km6 \mathrm{~km} long.

Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.

If the total number of widgets delivered in a day is 250250 units, then what is the total distance covered in the route (in km )?

Q8:

CAT 2022 Slot 2

Routes & Networks

Medium

Every day a widget supplier supplies widgets from the warehouse ( W ) to four locations - Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40%40 \% chance that the demand in Ahmednagar will be 5050 units and a 60% chance that the demand will be 7070 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km ) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km6 \mathrm{~km} long.

Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.

What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore?

Answer options
Option 4
Correct Answer
Explanation for CAT 2022 Slot 2 DILR question 8

Q9:

CAT 2022 Slot 2

Routes & Networks

Medium

Every day a widget supplier supplies widgets from the warehouse ( W ) to four locations - Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40%40 \% chance that the demand in Ahmednagar will be 5050 units and a 60% chance that the demand will be 7070 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km ) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km6 \mathrm{~km} long.

Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.

If the first location visited from the warehouse is Ahmednagar, then what is the chance that the total distance covered in the route is 4040 km?

Answer options
Option 3
Correct Answer
Explanation for CAT 2022 Slot 2 DILR question 9

Q10:

CAT 2022 Slot 2

Routes & Networks

Medium

Every day a widget supplier supplies widgets from the warehouse ( W ) to four locations - Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40%40 \% chance that the demand in Ahmednagar will be 5050 units and a 60% chance that the demand will be 7070 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km ) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km6 \mathrm{~km} long.

Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.

If Ahmednagar is not the first location to be visited in a route and the total route distance is 2929 km, then which of the following is a possible number of widgets delivered on that day?

Answer options
Option 2
Correct Answer
Explanation for CAT 2022 Slot 2 DILR question 10

Q11:

CAT 2022 Slot 1

Routes & Networks

Easy

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, she can catch that train).

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?

Answer options
Option 3
Correct Answer
Explanation for CAT 2022 Slot 1 DILR question 11

Q12:

CAT 2022 Slot 1

Routes & Networks

Easy

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, she can catch that train).

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?

Answer options
Option 1
Correct Answer
Explanation for CAT 2022 Slot 1 DILR question 12

Q13:

CAT 2022 Slot 1

Routes & Networks

Easy

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, she can catch that train).

Haripriya is expected to reach station SS late. What is the latest time by which she must be ready to board at station SS if she must reach station BB before 11 am via station RR ?

Answer options
Option 1
Correct Answer
Explanation for CAT 2022 Slot 1 DILR question 13

Q14:

CAT 2022 Slot 1

Routes & Networks

Easy

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, she can catch that train).

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

Q15:

CAT 2022 Slot 1

Routes & Networks

Easy

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, she can catch that train).

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

Q16:

CAT 2019 Slot 1

Routes & Networks

Medium

The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.

Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.

The following additional facts are known.

  1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.
  2. X can see only U and Z.
  3. Y can see only U and W.
  4. U sees V standing in the next intersection behind Z.
  5. W cannot see V or Z.
  6. No one among the six is standing at intersection d.

Who is standing at intersection a?

Answer options
Option 1
Correct Answer
Explanation for CAT 2019 Slot 1 DILR question 16

Q17:

CAT 2019 Slot 1

Routes & Networks

Medium

The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.

Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.

The following additional facts are known.

  1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.
  2. X can see only U and Z.
  3. Y can see only U and W.
  4. U sees V standing in the next intersection behind Z.
  5. W cannot see V or Z.
  6. No one among the six is standing at intersection d.

Who can V see?

Answer options
Option 3
Correct Answer
Explanation for CAT 2019 Slot 1 DILR question 17

Q18:

CAT 2019 Slot 1

Routes & Networks

Medium

The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.

Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.

The following additional facts are known.

  1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.
  2. X can see only U and Z.
  3. Y can see only U and W.
  4. U sees V standing in the next intersection behind Z.
  5. W cannot see V or Z.
  6. No one among the six is standing at intersection d.

What is the minimum number of street segments that X must cross to reach Y?

Answer options
Option 4
Correct Answer
Explanation for CAT 2019 Slot 1 DILR question 18

Q19:

CAT 2019 Slot 1

Routes & Networks

Medium

The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.

Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.

The following additional facts are known.

  1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.
  2. X can see only U and Z.
  3. Y can see only U and W.
  4. U sees V standing in the next intersection behind Z.
  5. W cannot see V or Z.
  6. No one among the six is standing at intersection d.

Should a new person stand at intersection d, who among the six would she see?

Answer options
Option 3
Correct Answer
Explanation for CAT 2019 Slot 1 DILR question 19