The mean of five numbers is 18. When one number is removed, the mean of the remaining numbers becomes 16. The number removed is

The total of five numbers is $5\times18=90$ and the total of the remaining four is $4\times16=64$. The removed number is $90-64=26$. Shortcut: the four remaining numbers lost $2$ each from the old mean, so the removed number exceeds $18$ by $4\times2=8$. Trap: 34 comes from computing $90-56$, and 24 from $18+6$; 18 assumes the removed number equals the old mean, which would leave the mean unchanged.