CAT 2017 Slot 1 — DILR Question 28
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.
Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
- Both cities are in G1
- Between A and any city in G2
- Between B and any city in G3
- Between C and any city in G4
However, due to operational difficulties at A, it was later decided that the only flights that would operate at A would be those to and from B. Cities in G2 would have to be assigned to G3 or to G4.
What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose?
Answer & solution
Answer: 4
Given the above conditions, we know that in G1, A would connect to B and B would connect with C. B would connect with any of the 2 cities in G3 and C would connect with any of the 2 cities in G4.
Now the 2 cities from G2 that were connected to A earlier can now connects to one of the cities in G3 or G4. There is no flight connection possible now between A and C in G1.
So the total number of flight connections as compared to the number of flight connections in the previous question will be less by number of flights connecting A and C i.e., 4.
Answer: 4