Explanation:

- Option 1: 169 : 55

- 169 is a perfect square (13^2).

- If you add the digits of 169 (1 + 6 + 9), you get 16, and 16 divided by 3 is approximately 5.33, not related to 55 directly.

- Option 2: 289 : 70

- 289 is a perfect square (17^2).

- The sum of digits of 289 is 19, divided by 3 gives approximately 6.33.

- Option 3: 256 : 61

- 256 is a perfect square (16^2).

- The sum of digits of 256 is 13, divided by 3 gives approximately 4.33.

- Option 4: 324 : 64

- 324 is a perfect square (18^2).

- If you take the digital root of 64, it doesn’t simplify in the same pattern noted in the other pairs.

All pairs seem to relate a perfect square with additional properties not matching a uniform pattern directly. However, the pairs generally pair a perfect square with an unrelated number. All, except Option 4, don't show a clear, uniform mathematical pattern.

The correct answer is Option 4, as it stands out, but not due to a clear mathematical pattern similar to others.