ASEAN PRIMARY SCHOOLS MATHEMATICS OLYMPIAS 2003 ESSAYS

1. Now we are in the year 2003. The ratio of ages of my father, my mother and my youngers brother is 12:9:1. Five years from now, my father will be 41 years old. In what year was my younger brother born?

2. Laila’s saving in a bank is $100. Tina’s saving is $40. Every end of week, Laila withdraw $3 from her savings. At the same time, Tina always deposit $2.40 into her savings. After how many weeks will Laila’s savings be $6 than Tina’s savings?

3. The product of two positive integers is even, but not divisible by 4. Is their sum odd or even?

4. On the table, there are 6 coins each of values $5, $10, and $50. Deni takes $75. The number of coins Deni takes is more than 5, but less than 9. Does Deni take all the three types of coins? If not, which type does he not take?

5. The weight of small box, two medium boxes and large box altogether is 10 kg. The weight of small box, two medium boxes and two large boxes altogether is 15 kg. What is the total weight of two small boxes and four medium boxes?

6. Replace the letter A with an modd digit and the letter B with an even digit, so that 12 is a factor of the number A579B. Find the possible values of A579B.

7. Find the missing digits.

8. Find the total area of the shaded regions in the figure.

9. In the following figure, the three squares have equal areas. Determine wheter the areas of the three shared regions in each square are also equal.

10. If the patters below is continued, what is the percentage of the area of the shaded regions in third picture compared to the are of the largest square?

11. Four wheel A, B, C, D are connected by belts, see figure. The wheels B and C are fastened together. The diamters of wheels A, B, C, and D are 12 cm, 36 cm, 9 cm and 27 cm, respectively. The wheel A tursn at a speed of 450 rotations per minute. At what speed does the wheel D turn?

12. Three circular disks of radius 7 cm each are bound tightly with a belt. see figure. What is the length of the belt?

13. The volume of a small balloon is 2 liters and a larger ballon is 5 liters. The larger ballon  is deacreased at the rate of 0.12 liters per second. After how many seconds will the two balloons have the same volume?

14. A train travels between two stations. The train will be on time if it runs at an average speed of 50 km/hour. What is the distance between two stations?

15. Twice the number of marbles in bag A less than the number of marbles in bag B. The sum of the number of marbles in bags A and C is less than hte number
of marbles in bag B. There are more marbles in bag D than in bag B. There are 6 marbles in bag C and 9 marbles in bag D. How many marbles does bag B contain?