1. Correct Answer: Option B: 2 only
 2. Explanation:
     ● Step 1: Represent the number algebraically  
       Let the two-digit number be represented as \(10x + y\), where \(x\) is the tens digit and \(y\) is the units digit. When the digits are interchanged, the new number is \(10y + x\).
     ● Step 2: Set up the equation  
       According to the problem, the difference between these two numbers is 54:
       \[
       (10x + y) - (10y + x) = 54
       \]
       Simplifying, we get:
       \[
       9x - 9y = 54
       \]
       \[
       x - y = 6
       \]
     ● Step 3: Determine the difference between digits  
       From the equation \(x - y = 6\), we can determine that the difference between the two digits is 6. Therefore, Statement 2 is correct.
     ● Step 4: Evaluate the sum of digits  
       To find the sum of the digits (\(x + y\)), we need another independent linear equation. Knowing the product (\(xy\)) provides a quadratic relationship, which might allow us to solve for \(x\) and \(y\) individually, but the sum cannot be determined from the difference alone. Statement 1 claims the sum can be determined only if the product is known, which is logically incorrect because the sum could also be determined if the original number itself or the ratio of the digits were known. More importantly, knowing the product and the difference can lead to multiple pairs or no integer solutions depending on the value, and does not uniquely define a "sum" rule. Thus, Statement 1 is incorrect.
     ● Conclusion: Statement 2 is correct because the difference between the digits is fixed at 6, while the sum cannot be uniquely determined from the given information. Therefore, the correct answer is Option B: 2 only.