Using python codes is a great way to efficiently solve them but we are focused on problem solving our own minds here.

1. 15 = 5 *3

Since the three digit numbers have a unit digits of 5, we just need the number in the form of AB5, to be divisible by 3. And in order for a number to be divisible by 3, its digits need to add up to a multiple of 3.

A + B + 5 = 0 (mod 3)

A + B = 1 (mod 3)

Can you solve the question from here and find all digits A and B that make the congruence true? (Hint, casework!)

2. One simple way to solve this is by using the loss of generality, plug in any numbers a and b, where their product leaves a remainder of 17 when divided by 20. After finding those numbers, plug it into (a + 10)(b + 10) and see the remainder.