Math Olympiade 2014 (Part 1)

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Below I show the problems the Olympics for elementary school.

1. Find a two digit number such that if it is reduced by 5 it is a multiple of 4, if it is reduced by it is a multiple of 5 and if it is reduced by 7 it is a multiple 6.

2. A certain even number has exactly seven positive factor, including 1 and the number it self. What is this number?

3. A number p yields a remainder of 3 when divided by 5, a remainder of 5 when divided by 8 and remainder of 11 when divided by 13. If p is less than 1,000, find the maximum value of p.

4. A six digits number aba,bab is formed by repeating a two digit number ab three times, e.g 525,252. If all such numbers are divisible by p, find maximum value of p.

5. A pair of positive integers a and b is such that the greatest common divisor is 5 and the least common multiple is 1,155. Find the smallest value of (a + b).

6. A positive integer that satisfies all the conditions below is called a Po leung number.
•    the number consist of four digits,
•    each digit is divisor of 48,
•    each digit can appear more that once,
•    the sum of the digit is 20,
•    the number is a multiple of 4.
Find the smallest Po leung number.

7. If 2,009 is divided by a two digit number, the remainder is 9. How many such two digit number are there?
8. John has a rectangular paved area in his yard. He increases both the length and the breath of his paved area by 20%. What is the percentage increases in the paved area?

9. There are 300 girls who represent a certain school in both summer and winter sports. In summer 60% of these girls play cricket and the other 40% play squash. In writer the girls play hockey or netball but not both. 56% of the hockey players take cricket in summer and 30% of the cricket players take netball in winter. The number of girls who play netball and squash is …

10. The population of village is 5.000 and it increases at the rate of 20% every year. After 2 years, the population will be ….

Those are some of the Mathematics can I show this time. May be useful.


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