A group of students scored 448 marks between them in a test, and their average worked out to an exact whole number of marks. If there were more than 20 but fewer than 30 students in the group, how many students were there?

For the average to be a whole number, the count must divide 448 exactly. Since $448=2\times 2\times 2\times 2\times 2\times 2\times$ 7, its divisors are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, ... and the only one strictly between 20 and 30 is 28, giving an average of 448/28 = 16 marks. The other options all leave a remainder: 448/24 = 18.67, 448/22 = 20.36 and 448/25 = 17.92, so none of them can be the size of the group.