The average of 11 numbers is 50. The average of the first six is 48 and the average of the last six is 53. What is the sixth number?

Explanation

1. 01

   Total of all $11 = 11 \times 50 = 550$.

2. 02

   First six total = $6 \times 48 = 288$; last six total = $6 \times 53 = 318$.

3. 03

   $288 + 318 = 606$ counts the sixth number twice.

4. 04

   Sixth number = $606 - 550 = 56$.