Problems And Answers PHIMO MOCK 2020 SECONDARY 3

11. There are \(n\) people in a room. They shake hands with each other once. If they shake hands \(120\) times, find \(n\).

12. Carl and Bob can demolish a building in 6 days, Anne and Bob can do it in 3, Anne and Carl can do it in 5. How many days does it take all of them working together if Carl gets injured at the end of the first day and can’t come back? Express your answer as a fraction in lowest terms.

13. The average of some numbers is 90. After adding 6 numbers, 125, 216, 343, 512, 729, 1000, the average of these numbers went high to 105. Find the sum of original numbers.

14. Jethro goes northeast for \(10\sqrt 2\) km, then goes east for 12 km, goes west for 8km and goes southwest for \(15\sqrt 2\) km. How far is he now from the original position?

15. Given that r and s are relatively prime positive integers such that

\(\frac{r}{s}=\frac{2(\sqrt 2 +\sqrt{10})}{5(\sqrt 3 +\sqrt 5)}\),

find \(r + s\).