In a test the highest mark is 72 and the lowest is 42. Every mark is first increased by 8 and then halved. What is the range of the new marks?

The original range is 72 − 42 = 30. Adding 8 shifts the highest and the lowest by the same amount, so the gap between them is untouched; halving every mark then halves that gap. The new range is 30 ÷ 2 = 15, and indeed the two extreme marks become (72 + 8)/2 = 40 and (42 + 8)/2 = 25. Answering 30 forgets the halving; 38 = 30 + 8 treats a shift as though it widened the spread; and 19 = (30 + 8)/2 makes the same mistake and then halves it.