Answer Happy

(c) The School of Mathematical Sciences is planning an end-of-semester sales promotion of its T-shirts. It is giving away discount coupons of up to 52 percent numbered from 0 to 52. The amount of discount you get depends on your student ID. You will be given a discount using a discount hashing function f(x)= 3x mod 53, where x is the number formed from the first two digits of your student ID. (i) Compute the discount that you will get. (2 marks) (ii) Assuming that 16 ≤ x ≤21, is there a possibility that you get 0% discount? Justify your answer. (3 marks) (iii) The school intends to buy 2 types of T-shirts, long sleeve and short sleeve from a supplier for the sales promotion. Each long sleeve T-shirt costs RM11 and each short sleeve T-shirt costs RM7. The school wants to spend RMa (where a is the number formed from the first 3 digits of your student ID) to buy the T-shirts. Find one possible combination of the number of long sleeve and short sleeve T-shirts that were bought from the supplier. (7 marks)