Explanation:

- The average of 52, 71, 43, 22, a, and b is given as 55.

- Add up all numbers: 52 + 71 + 43 + 22 + a + b = 188 + a + b

- For their average to be 55:

$$(188 + a + b) / 6 = 55$$

- Simplifying, you find:

$$a + b = 142$$

- The average of 42, 45, 49, 51, 42, c, and d is given as 53.

- Add up all numbers: 42 + 45 + 49 + 51 + 42 + c + d = 229 + c + d

- For their average to be 53:

$$(229 + c + d) / 7 = 53$$

- Simplifying, you find:

$$c + d = 142$$

- Combined, \(a + b + c + d = 142 + 142 = 284\).

- The average of a, b, c, and d:

$$(a + b + c + d) / 4 = 284 / 4 = 71$$

- Correct Answer: Option 2: 71