Problems And Answers PHIMO MOCK 2020 JUNIOR SECONDARY

11. What is the smallest prime divisor of \(5^{{20}^{20}} + 1\).

12. A bowl contains 100 piece of colored candy: 28 green, 20 red, 12 yellow, 10 blue, 20 brown, and 10 orange. If you are blind olded as you pick and eat candy from this bowl, then how many pieces must you eat in order to guarantee that you have eaten at least 15 of the same color?

13. Nine nonnegative numbers have average 10. What is the greatest possible value for their median?

14. Given that the mean, median, range and the only mode of 80 integers are also 80. If A is the largest integer among those 80 integers, find the maximum value of A.

15. There are 100 students who want to sign up for the class Introduction to Acting. There are three class sections for Introduction to Acting, each of which will fit exactly 20 students. The 10 students including Dendi and Nico, are put in a lottery, and 60 of them are randomly selected to fill up the classes. What is the probability that Dendi and Nico end up getting into the same section for the class?