Singapore Mathematical Olympiad for Primary Schools 2004

1. A student multiplies the month and the day in which he was born by 31 and 12 respectively. The sum of the two resulting products is 170. Find the month and the date in which he was born.

2. Given that five whole numbers a, b, c, d and e are the ages of 5 people and that a is 2 times of b, 3 times of c, 4 times of d and 6 times of e, find the smallest possible value of a + b + c + d + e .

First Round

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Singapore Mathematical Olympiad for Primary Schools 2004

3. Lines AC and BD meet at point O. Given that OA = 40 cm, OB = 50 cm, OC = 60 cm and OD = 75 cm , find the ratio of the area of triangle AOD to the area of triangle BOC.

B A

O C D

4. 1000 kg of a chemical is stored in a container. The chemical is made up of 99 % water and 1 % oil. Some water is evaporated from the chemical until the water content is reduced to 96 %. How much does the chemical weigh now?

First Round

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Singapore Mathematical Olympiad for Primary Schools 2004

5. A student arranges 385 identical squares to form a large rectangle without overlapping. How many ways can he make the arrangement? [Note: The arrangements as shown in figure (1) and figure (2) are considered the same arrangement.

Figure (1)

Figure (2) ]

6. A bag contains identical sized balls of different colours : 10 red, 9 white, 7 yellow, 2 blue and 1 black. Without looking into the bag, Peter takes out the balls one by one from it. What is the least number of balls Peter must take out to ensure that at least 3 balls have the same colour?

First Round

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Singapore Mathematical Olympiad for Primary Schools 2004

7. Find the value of

1× 5 ×18 + 2 ×10 × 36 + 3 ×15 × 54 . 1× 3 × 9 + 2 × 6 × 18 + 3 × 9 × 27

8. If the base of a triangle is increased by 10% while its height decreased by 10%, find the area of the new triangle as a percentage of the original one.

First Round

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Singapore Mathematical Olympiad for...