Asian Science And Math Olympiad (ASMO) 2019 For Grade 6

11. What is the whole number solution for \(3x + 4y = 23\). if \(x < 5\)?

12. The area of the square is 24 cm² , what is the area of the shaded region? \(π=\frac{22}{7}\)

13. In some water that has a salt content of 15%, the weight of salt in the water is 20kg. To make the salt content 20%, how much salt must be added into the water?

14. 2019 divided by a natural number ‘a’. If the quotient is 51, what is the remainder?

15. Two cars depart from the same place to send some stuff to a factory 165km away. Car A reaches the factory 48 minutes earlier than car B, and car B is 24km away from the destination. How long does it take for car A to reach the factory?

16. One number is deducted from the numerator and denominator of \(\frac{5}{7}\). The new fraction is \(\frac{2}{3}\) after simplification. What is the number deducted?

17. \(a\) and \(b\) are different numbers from the first 50 whole numbers. What is the largest value of
\(\frac{a-b}{a+b}\)

18. In natural numbers 1~100, how many ‘1’s are there?

19. Just like in the diagram, there are three arrangements of cubes labelled with 1，2，3，4， 5，6. In the diagram below, what is the sum of the numbers on the face of the cube that faces left?

20. In a mathematics competition, the average score for the class is 70 marks. \(\frac{3}{5}\) of the students in the class got the passing grade in the competition. The average mark for the students that passed is 80. What is the average mark for the student that failed?

21. There is a job which Ali used 12 hours to finish it alone. If Ali and Abu work on the job together for 4 hours, Abu can finish the remaining in 6 hours. How many hours does it take for Ali and Abu to finish the entire job together?

22. There are four colours of balls, red, white, blue and yellow. There are 20 balls for each colour. All the balls are put into the bag. Each time, one ball is taken out of the bag. What is the minimum amount of balls that must be taken out of the bag so that in the balls taken out, there would be 6 balls of the same colour for sure?

23. Today is Sunday, what day is it after \(99^2\) days?

24. Calculate：

\(\frac{1}{1×5}+\frac{1}{5×9}+\frac{1}{9×13}+…+\frac{1}{53×57}\)

25. A, B and C are three gears that mesh together. When A spins for 4 times, B spins for 7 times and C spins for 3 times. What is the minimum number of teeth for each gear respectively?