Data Sufficiency

Q: Q: In a certain country have 15 cities and a single road type connects only two cities, How many road types are required to connect the cities so that each city is connected to all other cities with a single road type ?

A: 330 B: 14! C: 105 D: 30 E: 15!


I AM NOT ABLE TO UNDERSTAND WHAT THE QUESTION IS ASKING

O.A 105

Consider the 15 cities to be 15 different points on a paper.

Now a single road means, you connect each of these 15 points in a paper with a line.

Take the 1st point, you gotto draw 14 lines to connect to 14 other points,
From the 2nd point, you draw 13 lines (1 lesser because the 1st and 2nd are already connected)

Similarly go on till you complete all the 15 points;

You get = 14+13+12+11+10+9+8+7+6+5+4+3+2+1=105

[email protected] wrote:Q: Q: In a certain country have 15 cities and a single road type connects only two cities, How many road types are required to connect the cities so that each city is connected to all other cities with a single road type ?

A: 330 B: 14! C: 105 D: 30 E: 15!


I AM NOT ABLE TO UNDERSTAND WHAT THE QUESTION IS ASKING

O.A 105

[email protected] wrote:Q: Q: In a certain country have 15 cities and a single road type connects only two cities, How many road types are required to connect the cities so that each city is connected to all other cities with a single road type ?

A: 330 B: 14! C: 105 D: 30 E: 15!


I AM NOT ABLE TO UNDERSTAND WHAT THE QUESTION IS ASKING

O.A 105

This question is similar to the question asking how many matches took place in a football league of each team played with all other teams.

you simply have to add from 14... to 1.

Reason - City 1 will be connect to rest of the 14 cities via 14 roads.
now city 2 will need only 13 because the case of connection between city 1 and city 2 is already counted above.

Similarly city 3.. 12 road.

go till city 15.. 1 road..

add all of them . Ans = 105


PS: this is a PS question and not a DS question. Post it under the right forum please.

You can treat the 15 cities as 15 non collinear points and the question is asking you to find the number of lines that you can form?

15C2 = 15*14/2 = 105