Tài liệu Toán học quốc tế SASMO 2014 Vòng 1 Khối 5 - Problems

 Tài liệu Toán Olympic 5 
 SASMO 2014 Round 1 Primary 5 Problems 
 24
1. If n is a whole number, for what values of n is also a whole number? 
 n
2. A textbook is opened at random. To what pages is it opened if the product of the
facing pages is 600?
3. The diagram shows a quadrant OAB of a circle with centre O. OPQR is a
rectangle. Given that PR = 7 cm, find the length of OA.
4. Find an even number between 300 and 400 that is divisible by 5 and by 7.
 Tài liệu Toán Olympic 5 
10. A frog fell into a drain that was 50 cm deep. After one hour, it mastered enough
energy to make a jump of 6 cm but it then slid down 4 cm. If it continued in this
manner after every one hour, how many hours will it take to get out of the drain?
11. A farmer’s chickens produced 4028 eggs one day. Was he able to pack all the
eggs in full cartons of one dozen eggs each?
12. A farmer wants to find out the number of sheep and ducks that he has. He counted
a total of 40 heads and 124 legs. How many sheep and how many ducks does he
have?
13. Jaime puts some blue and red cubes in a box. The ratio of the number of blue
cubes to the number of red cubes is 2 : 1. She adds 12 more red cubes in the box and
the ratio becomes 4 : 5. How many blue cubes are there in the box? Tài liệu Toán Olympic 5 
16. Amy had 3 times as much money as Betty. After they had spent $60 each, Amy
had 4 times as much money as Betty. How much money did Amy have at first?
17. Billy uses identical square tiles to make the following figures. If he continues
using the same pattern, in which figure will there be 6044 tiles?
18. What is the least number of cuts required to cut 12 identical sausages so that they
can be shared equally among 20 people?
 Tài liệu Toán Olympic 5 
 1 1 1 1 1
22. Find the value of ... .
 2 6 12 20 9900
23. The diagram shows a square being divided into four rectangles. If the sum of the
perimeter of the four rectangles is 40 cm, find the area of the square.
24. Given that 5! means 5×4×3×2×1, find the last digit of 2014!.