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Question

A, B and C are 3 cities that form a triangle and where every city is connected to every other one by at least one direct route. There are 33 routes direct and indirect from A to C and there are 23 direct routes from B to A. How many direct routes are there from A to C ?(CAT 2000)

A
15
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B
10
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C
20
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D
25
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Solution

The correct option is B 10

Option (b)

Let the number of direct routes from A to B be x, from A to C be z and that from C to B be y. Then the total number of routes from A to C are = xy + z = 33. Since the number of direct routes from A to B are 23, x = 23. Therefore 23y + z = 33. Then y must take value 1 and then z = 10, thus answer = (b).


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