Question Analysis:
The question provides a series of numbers - 7, 4, 0, -5, and -11 - and asks for a solution. We need to determine what the numbers have in common and find the missing piece or pattern to complete the series.

Solution:
To find the missing piece or pattern in the series, let's analyze the given numbers:

Step 1: Identifying the Pattern:
Looking at the series, we can observe the following pattern:
- The first number is 7.
- The second number is obtained by subtracting 3 from the previous number (7 - 3 = 4).
- The third number is obtained by subtracting 4 from the previous number (4 - 4 = 0).
- The fourth number is obtained by subtracting 5 from the previous number (0 - 5 = -5).
- The fifth number is obtained by subtracting 6 from the previous number (-5 - 6 = -11).

Based on this pattern, it appears that each number in the series is obtained by subtracting an increasing value from the previous number. Therefore, the next number in the series should be obtained by subtracting 7 from the previous number (-11 - 7 = -18).

Step 2: Finding the Missing Piece:
To find the missing piece in the series, we subtract 7 from the last number (-11 - 7 = -18).

Therefore, the missing number in the series is -18.

Conclusion:
The missing piece in the series 7, 4, 0, -5, -11 is -18. The series follows a pattern where each number is obtained by subtracting an increasing value from the previous number. By applying this pattern, we can find the missing number.