# CAT Questions | CAT LR DI

###### CAT DILR | CAT Previous year questions
CAT Questions

CAT DI LR section has become increasingly tough beginning from 2015. However, Understanding the basics of Bar graphs, Pie Charts, Multiple graphs, Line Graphs etc forms an integral part of solving tougher CAT level DI LR questions for the CAT Exam. This question is from CAT 2017 Slot 1 CAT DILR.

## CAT DILR : 2017 slot 1 questions

### Airlines Company

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.

Question 1: 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:

1. 45
2. 90
3. 180
4. 135

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##### Method of solving this Question on CAT DILR

General Solution

Consider, the ten cities to be A,B,C,D and so on till City J.

Let us consider Cities A and B.
As per the underlying principle any person should be able to take a round trip between the two cities in the same day.
So, from A to B and vice versa (B to A) one flight should leave from each city in the morning and similarly in the evening, two flight should leave for the person to reutrn.

A total 4 flight are to be operate between any 2 cities.

We can select 2 cities out of 10 cities in 10C2 = 45 ways.

Four flights from a pair of cities, therefore total of 45 * 4 = 180 flights.

The question is "The minimum number of direct flights to be scheduled is:"

##### Hence, the answer is "180 flights".

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