Let n 2 be an integer. Suppose that there are n Metro stations in a city located around a circular path. Each pair of the nearest stations is connected by a straight track only. Further, each pair o

Question

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located around a circular path. Each pair of the nearest stations is connected by a straight track only. Further, each pair of the nearest station is connected by blue line, whereas all remaining pairs of stations are connected by red line. If number of red lines is 99 times the number of blue lines, then the value of n is

TestHub · Accepted Answer

Two consecutive stations = n Two non-consecutive stations = C 2 n - n C 2 n - n = 99 n ⇒ n n - 1 2 - n = 99 n ⇒ n 2 - n 2 = 100 n ⇒ n 2 = 201 n ⇒ n = 0 , 201 n = 0 is not possible. ⇒ n = 201

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