TCS Company Numerical Ability Permutation and Combination

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 on 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?

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TCS Other Question

Look at the series
8,43,11,41,____,39,17.

What number should fill in the blank?
what is the highest power of 15 which will divide 90! exactly?