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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

Cars Travel Route

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 2: 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:

CAT DI LR 2017 Slot 1

  1. 54
  2. 120
  3. 96
  4. 60

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Explanatory Answer

Method of solving this Question on CAT DILR

General Solution

Consider 3 cities A,B and C to be the hub cities. So, any flight from hub city and towards hub city are direct flights.
Also, it has to satifsy the underlying principle of the airline.
For the moment, let us forget about the underlying principle.
CAT DI LR 2017 Slot 1

In the first step, forget about the flights between the three hub cities.
Consider only one hub city, say A. So, it will have direct flights with 7 other non hub cities D,E,F,G,H,I and J.
As observed in the previous question, in order to satisfy the underlying principle, 4 flights should be connected to each of the 7 seven cities. So, a total of 7 * 4 = 28 flights are to be operated per hub city.
Similarly, the other two hub cities B and C will have 28 flights each to the other 7 non-hub cities.
Therefore, the total no. of flight will be 28 + 28 + 28 = 84.
But, we still have to account for the flights between the hub cities.
The three cities can be connected by direct flights.
Similarly, if we account for the flights between any two hub cities, a total of 4 flights will have to be operated between the cities such that they satisfy the underlying principle.

For 3 such parirs (AB, BC and AC), we have 4 * 3 = 12 flights.
Total number of flights to be operated = 84 + 12 = 96 flights.

The question is "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:"

Hence, the answer is "96".

Choice C is the correct answer.

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