In the year 2020, MLK Airlines is headquartered in New York City (NY). They run flights between various pair of cities. Since the recent sharp increase in the number of cities served has made it difficult to keep track on the status of each city, the new logistics manager decides to classify the cities on the basis of how connected they are to NY. He assigns each city a Connectivity Number (CN), with NY itself getting a CN of 0, using the following rules.

- If a city X has a direct flight from NY, then it is awarded a CN of 1.

- If a city Y does not have a direct flight to NY, but has a direct flight to a city such as X with a CN of 1, then city Y is awarded a CN of 2, and so on, with the CN for a city being the number of flights in the shortest chain of direct flights connecting that city with NY.

- Thus, if a new direct flight is introduced between a city with CN of p and another city with CN of q (where p ≥ q) then the CN of the first city remains unchanged (i.e. p) while that of the second becomes p + 1.

- A city with no chain of direct flights connecting it to NY has a CN of infinity.

Over the next few years, the airline is planning to start new flights to seven cities, A, B, C,D, E, F, G. As of 2020, none of these cities has a direct flight to NY; one of the seven citie has a CN of infinity while F has the smallest CN and E the largest CN among the other six cities.

In 2021, MLK introduces three new pairs of flights between B and F, F and E, and B and E. No other flights are introduced during 2021. As a result of this, the average CN of seven cities at the end of 2021 comes to 4. Also, at the end of 2021, four of the seven cities have the same CN while the remaining three have distinct CN values.

In 2022, MLK introduces flights connecting A and F. No other flights are introduced during 2022. This reduces the average CN of the seven cities by 1.

QUESTIONS:

1) If F's CN in 2020 is x, then answer following in terms of x :

- What is the CN of B in 2021?

- What is the CN of E in 2021?

- What is the CN of A in 2022?

- By how much does A's CN decrease in 2022?

- What is the CN of A in 2020?

2) What was the CN of E at the end of 2022?

a. 2 b. 3 c. 4 d. None of these

3) What is the CN of B in 2020?

a. 2 b. 3 c. 4 d. None of these

4) How many cities among the given seven had the same CN in 2020?

a. 2 b. 3 c. 4 d. None of these

5) What was the CN of A in 2021?

a. 2 b. 3 c. 4 d. None of these

6) How many cities did not change their CN between 2020 and 2022?

a. 2 b. 3 c. 4 d. None of these

7) If G had the highest CN among these 7 cities at the end of 2022, what was its CN?

a. 2 b. 3 c. 4 d. None of these