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# There are three cities: A, B and C. Each of these cities is connected

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Senior Manager
Joined: 12 Jan 2019
Posts: 263
There are three cities: A, B and C. Each of these cities is connected  [#permalink]

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12 Jan 2019, 09:57
1
00:00

Difficulty:

(N/A)

Question Stats:

33% (04:36) correct 67% (03:52) wrong based on 3 sessions

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There are three cities: A, B and C. Each of these cities is connected with the other two cities by at least one direct road. If a traveller wants to go from one city (origin) to another city (destination), she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B (including those via C). Similarly, there are 23 routes from B to C (including those via A). How many roads are there from A to C directly?
a. 6
b. 3
c. 5
d. 10
e. 12

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Senior Manager
Joined: 12 Jan 2019
Posts: 263
Re: There are three cities: A, B and C. Each of these cities is connected  [#permalink]

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12 Jan 2019, 09:59
Let the number of direct roads from A to B, B to C, and C to A be x, y and z respectively.
Then x + yz = 33, y + xz = 23.
Hence, by solving, we get z = 6.
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Re: There are three cities: A, B and C. Each of these cities is connected   [#permalink] 12 Jan 2019, 09:59
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