Math Olympiad Essay Problems

Instructions:
* Write down your name and country on every page.
* Answer all 13 questions.
* You have 90 minutes to work on this test.
* Write down your answer and the explanation on the space below the  question.
* Use pen to write your answer.
* Use pencil only to draw figures.

1. John gives 1/6 of his marbles to Alex and 20 marbles to Simon. John’s remaining marblesvis now 55. How many marbles does John have originally?

2. The total number of ducks and chickens in the garden is 335. If the number of chickensvis 2/3 of the number of ducks, how many chickens are there in the garden?

3. Mr. Sweet has three kinds of books: 120 mathematics, 144 biology, and 100 physics books. He is going to give all the books to the schools in his village such that each school receives the same number of mathematics, biology and physics books. How many schools, at most, receive books from Mr. Sweet?

4. Jerry is riding a motorbike at 60 km/hour while Tom is riding his motorbike at 45 km/hour in the same direction from the same starting point. Jerry left 1 1/3 hours later than Tom did. How long will it take Jerry to catch up Tom?

5. An ant moves on the surface of a cube from vertex A to vertex B. Draw the shortest path from A to B passed by the ant.

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