Problems And Answers PHIMO MOCK 2020 SECONDARY 2

16. In the system
\(8y – 3x ≤ 16\)
\(3x + 8y ≥ -18\)
for which solution \((x, y)\) is \(x + y\) minimum?

17. If \(x\) and \(y\) are positive numbers such that \(x^2 + y^2 = 8\) and \(xy = 2\), find \(x + y\).

18. How many positive integers less than 2016 are divisible by 28 but not by 12?

19. The sum of two numbers is 9 and their product is 25. What is the sum of their cubes?

20. A ladder is leaning against a house with its lower end 15 feet from the house. When the lower end is pulled 9 feet farther from the house, the upper end slides 13 feet down. How long is the ladder (in feet)?