Explanation:

Let's analyze the relationships:

- Option 1: 24 : 142

- No obvious square or power relationship. 142 is not a square number.

- Option 2: 14 : 49

- 49 is the square of 7 (the approximate half of 14). This has a square relationship.

- Option 3: 16 : 64

- 64 is the square of 8 (half of 16). This is another square relationship.

- Option 4: 34 : 289

- 289 is the square of 17 (half of 34). This fits the same pattern.

- Correct Answer: Option 1, 24 : 142

- It does not follow the square pattern where the second number is the square of half of the first.