Explanation:

- We're looking for the greatest number in the form 234a5b, divisible by 22 but not by 5.

- A number is divisible by 5 if it ends in 0 or 5. So, b cannot be 0 or 5.

- Divisibility by 22 means it must be divisible by both 2 and 11.

- A number is divisible by 2 if its last digit is even.

- To be divisible by 11, the difference between the sum of its digits in odd and even places should be a multiple of 11.

- Let's analyze the options:

- Option 1: 234058 - Divisible by 5, so it's out.

- Option 2: 234850 - Ends in 0 (even and it's not in your list to check for divisibility by 22)

- Option 3: 234652 - Ends in 2 (even), and we'll check divisibility by 22.

- Option 4: 234751 - Ends in 1 (not divisible by 2).

- Check option 3, 234652, for divisibility:

- Sum of odd-positioned digits: 2 + 4 + 5 = 11

- Sum of even-positioned digits: 3 + 6 + 2 = 11

- The difference is 0 (a multiple of 11).

- And it ends with 2 (even), divisible by 2.

- Thus, option 3 is divisible by 22, not by 5.

- Check option 2, 234850, for divisibility:

- Sum of odd-positioned digits: 2 + 4 + 5 = 11

- Sum of even-positioned digits: 3 + 8 + 0 = 11

- The difference is 0 (a multiple of 11).

- And it ends with 0 (even), divisible by 2.

- But it's divisible by 5 (as it ends in 0).

- Option 3: 234652 is the correct choice, as it meets all the criteria.