Pre RMO Practice question: 2018: How long does it take for a news to go viral in a city? And, a cyclist vs horseman

Problem 1:

Some one arrives in a city with very interesting news and within 10 minutes tells it to two others. Each of these tells the news within 10 minutes to two others(who have not heard it yet), and so on. How long will it take before everyone in the city has heard the news if the city has three million inhabitants?

Problem 2:

A cyclist and a horseman have a race in a stadium. The course is five laps long. They spend the same time on the first lap. The cyclist travels each succeeding lap 1.1 times more slowly than he does the preceding one. On each lap the horseman spends d minutes more than he spent on the preceding lap. They each arrive at the finish line at the same time. Which of them spends the greater amount of time on the fifth lap and how much greater is this amount of time?

I hope you enjoy “mathematizing” every where you see…

Good luck for the Pre RMO in Aug 2018!

Nalin Pithwa.



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