Most number-system questions in a preliminary paper are solved in under thirty seconds if you know the standard shortcuts. This piece collects the ones that come up most often.
Unit digit of a power repeats in a cycle of at most four, so 7^103 has the same unit digit as 7^3, which is 3. Divisibility by 11 is the alternating sum of digits. A number is divisible by 8 when its last three digits are.