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Directions for Questions: A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.
The underlying principle that they are working on is the following.
Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.
(2017)
Q. Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and /or terminating in one of  the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is.
  • a)
    54
  • b)
    120
  • c)
    96
  • d)
    60
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Directions for Questions: A new airlines company is planning to start ...
Let the ten cities be represented by A through J.
Among these ten cities, consider A, B and C to be hubs and the other seven cities to be non-hub cities.
It is given that any direct flight should originate and terminate at a hub.
Total flight from D = 4 × 3 = 12
[∵ Only for A, B, C]
Non hub city flight = 12 × 7 = 84
[∵ for other then A, B, C]
Total flight = 12 + 84 = 96
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Most Upvoted Answer
Directions for Questions: A new airlines company is planning to start ...
Let the ten cities be represented by A through J.
Among these ten cities, consider A, B and C to be hubs and the other seven cities to be non-hub cities.
It is given that any direct flight should originate and terminate at a hub.
Total flight from D = 4 × 3 = 12
[∵ Only for A, B, C]
Non hub city flight = 12 × 7 = 84
[∵ for other then A, B, C]
Total flight = 12 + 84 = 96
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Community Answer
Directions for Questions: A new airlines company is planning to start ...
Calculation of Minimum Number of Direct Flights
There are 10 cities in total, out of which 3 cities will be developed as hubs. The hubs will have direct flights to all other cities in the morning and evening.

Calculating the number of direct flights from each hub:
- For each hub, there will be direct flights to 7 other cities (since the hub itself is not counted).
- In the morning, there will be 7 direct flights from the hub.
- In the evening, there will be another 7 direct flights from the hub.
- Therefore, the total number of direct flights from each hub will be 14.

Calculating the total number of direct flights:
- As there are 3 hubs, the total number of direct flights will be 3 hubs * 14 direct flights = 42 direct flights.
- However, each direct flight connects two cities, so the total number of direct flights (round trip) needed will be 42 * 2 = 84.

Adjustment for not visiting more than one hub:
- Since the requirement is to ensure that a person does not visit more than one hub during a trip, we need to consider that each city should have direct flights to every other city without visiting more than one hub.
- To achieve this, for each city, there will be direct flights to 9 other cities (excluding itself and the city connected through the hub).
- Therefore, the total number of direct flights required will be 10 cities * 9 direct flights = 90 direct flights.
- However, as we have already calculated the total number of direct flights needed with hubs (84), we need to subtract the overlapping direct flights from hubs, which is 6 (2 for each hub).
- Therefore, the minimum number of direct flights needed to meet the principle without visiting more than one hub during one trip is 90 - 6 = 84.
Therefore, the correct answer is option C) 96.
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Directions for Questions: A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.The underlying principle that they are working on is the following.Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.(2017)Q.Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and /or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is.a)54b)120c)96d)60Correct answer is option 'C'. Can you explain this answer?
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Directions for Questions: A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.The underlying principle that they are working on is the following.Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.(2017)Q.Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and /or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is.a)54b)120c)96d)60Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions for Questions: A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.The underlying principle that they are working on is the following.Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.(2017)Q.Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and /or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is.a)54b)120c)96d)60Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions for Questions: A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.The underlying principle that they are working on is the following.Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.(2017)Q.Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and /or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is.a)54b)120c)96d)60Correct answer is option 'C'. Can you explain this answer?.
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