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CAT 2017 Slot 1 — DILR Question 27

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.

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:

  1. Both cities are in G1
  2. Between A and any city in G2
  3. Between B and any city in G3
  4. Between C and any city in G4

Then the minimum number of direct fights that satisfies the underlying principle of the airline is:

Answer & solution

Answer: 40

Solution

Now A, B and C are in G1. As there is no restriction of flights that can connect with each other in G1, the total number of flights connecting 2 cities in G1 is 3C2 × 4
= 12

A can connect with any of the 3 cities in G1 in 3C1 × 4 = 12 ways

B can connect with any of the 2 cities in G2 in 2C1 × 4 = 8 ways

C can connect with any of the 3 cities in G3 in 2C1 × 4 = 8 ways

Total minimum number of direct flights that satisfy the underlying principle is 12 + 12 + 8 + 8 = 40

Answer: 40

CAT 2017 Slot 1 DILR Q27: Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respective — Solution | TheCATExam