Question

The average of 11 numbers is 50. If the average of the first six numbers is 49 and that of the last six numbers is 52, then the sixth number is

• A. 54
• B. 56
• C. 58
• D. 52

Hint:

The first-six and last-six groups both include the sixth number, so it is the excess over the total.

Answer 1

The Correct Option is B

Step 1: Use the overlap idea.
The first six and last six together cover all eleven numbers plus the middle one once extra.
Step 2: Difference of sums.
So sixth $=(294+312)-550=56$.
\[\boxed{56}\]