ROUTES AND NETWORKS || Data Interpretation || CAT 2021 || 24 September for CAT & MBA Exams

Question 1

Direction: Read the information given below and answer the question that follows.

Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute.

The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.

How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department?

Question 2

Direction: Read the information given below and answer the question that follows.

Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute.

The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.

If all the cars follow the police order, what is the difference in travel time (in minutes) between a car which takes the route A-N- B and a car that takes the route A-M-B?

Question 3

Direction: Read the information given below and answer the question that follows.

Four cars need to travel from Akala (A. to Bakala (B.. Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute.

The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.

A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M- N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route.

How many cars would the police department order to take the A-M-N-B route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.)

Question 4

Direction: Read the information given below and answer the question that follows.

Four cars need to travel from Akala (A. to Bakala (B.. Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute.

The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.

A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route.

If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.)

Question 5

Directions: 5 cities P, Q, R, S, T are connected by different modes of transports as follows –
â P and Q are connected by boat as well as by rail
â S and R are connected by bus and boat
â Q and T are connected only by air
â P and R are connected only by boat
â T and R are connected by rail and bus

Which of the following pair of cities are connected directly? (Without going to any other city)

Question 6

Directions: 5 cities P, Q, R, S, T are connected by different modes of transports as follows –
â P and Q are connected by boat as well as by rail
â S and R are connected by bus and boat
â Q and T are connected only by air
â P and R are connected only by boat
â T and R are connected by rail and bus

If a person visits each of the places starting from P and gets back to P, which of the following places must he visit twice?

Question 7

Directions: 5 cities P, Q, R, S, T are connected by different modes of transports as follows –
â P and Q are connected by boat as well as by rail
â S and R are connected by bus and boat
â Q and T are connected only by air
â P and R are connected only by boat
â T and R are connected by rail and bus

Between two cities, among the pairs of cities given below, are maximum travel options available? (if there is more than one route possible between two cities, consider the one with lease number of cities enroute)

Question 8

Direction: Read the following passage and answer the given question.
A significant amount of traffic flows from point S to point T in the one-way street network shown below. Point A, B, C and D are junctions in the network and the arrows mark the direction of traffic flow. The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street. Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum. If two or more routes have the same least travel cost. Then motorists are indifferent between them. Hence the traffic gets evenly distributed among all the least cost routes. The government can control the flow of traffic only be levying appropriate toll at each junction. For example, if a motorist takes the rout S-A-T (using junction A alone), then the total cost of travel would be Rs. 14 (i.e., Rs 9 + Rs 5) plus the toll charged at junction A

If the government wants to ensure that all motorists traveling from S to T pay the same amount (fuel costs and toll combined) regardless of the route they choose and the Street from B to C is under repairs (and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

Question 9

Direction: Read the following passage and answer the given question.
A significant amount of traffic flows from point S to point T in the one-way street network shown below. Point A, B, C and D are junctions in the network and the arrows mark the direction of traffic flow. The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street. Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum. If two or more routes have the same least travel cost. Then motorists are indifferent between them. Hence the traffic gets evenly distributed among all the least cost routes. The government can control the flow of traffic only be levying appropriate toll at each junction. For example, if a motorist takes the rout S-A-T (using junction A alone), then the total cost of travel would be Rs. 14 (i.e., Rs 9 + Rs 5) plus the toll charged at junction A

If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

Question 10

Direction: Read the following passage and answer the given question.
A significant amount of traffic flows from point S to point T in the one-way street network shown below. Point A, B, C and D are junctions in the network and the arrows mark the direction of traffic flow. The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street. Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum. If two or more routes have the same least travel cost. Then motorists are indifferent between them. Hence the traffic gets evenly distributed among all the least cost routes. The government can control the flow of traffic only be levying appropriate toll at each junction. For example, if a motorist takes the rout S-A-T (using junction A alone), then the total cost of travel would be Rs. 14 (i.e., Rs 9 + Rs 5) plus the toll charged at junction A

The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. the cost incurred by the commuter traveling from point S to point T under this policy will be: