Seven numbers have an average of 24. The largest of them, 42, is written down once more so that the list now holds 8 entries. What is the average of the 8 entries?

The seven numbers total $7\times 24=168$. Writing 42 again makes the total 210 across 8 entries, so the average is 210/8 = 26.25. 24 assumes that repeating a number already in the list cannot move the average; it moves it whenever the repeated number differs from the average, and 42 is 18 above it. 30 divides the new total of 210 by the old count of 7. 33 is the plain midpoint of 24 and 42, which would hold only if the old average carried the same weight as the single new entry - it carries seven times as much.