CAT Quantitative Ability Questions | CAT Algebra questions
CAT/2000
Question . 169
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 roots. There are 33 routes direct & 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 ?
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Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Algebra question
(b) Let the no. 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 no. of routes from A to C are = xy + z = 33. Since the no. 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
Hence, 10 routes are direct from A to C.