Across 30 readings the average is 18. One of the readings is then corrected to 42 and the average rises to 19. What was that reading before it was corrected?

The count stays at 30, so a rise of 1 in the average means the total rose by $30\times 1=30$. Only one reading changed, so it went up by 30, and since it ended at 42 it began at 42 - 30 = 12. (Totals: 540 before, 570 after.) 41 subtracts the 1-unit rise once, forgetting that the average of thirty readings moves only when the total moves thirty times as much. 72 adds the 30 to 42 instead of subtracting it, but the average went UP, so the corrected value must be the larger of the two. 30 is the rise in the total, mistaken for the reading itself.