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CAT 2017 Slot 1 — DILR Question 25

Routes & NetworkEasy
Passage / Data

Answer the following question based on the information given below.

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.

If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is:

Answer & solution

Correct answer: 180

  • A

    45

  • B

    90

  • 180

  • D

    135

Solution

Since there are a total of 10 cities we can have a combination of 2 cities in 10C2 or 45 ways. Now, if for example we have 2 cities City 1 and City 2, then the cities can be connected in the following 4 ways:

Morning flight from city 1 to city 2

Morning flight from city 2 to city 1

Evening flight from city 1 to city 2

Evening flight from city 2 to city 1

So the minimum number of direct flights to connect all cities is 45 × 4 or 180 ways.

Hence, option (c).

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CAT 2017 Slot 1 DILR Q25: If the underlying principle is to be satisfied in such a way that the journey between any two cities can be pe — Solution | TheCATExam