Of of an integer then minimum possible positive integer value

Step 1: Convert percentages to fractions. 1% = 1/100 and 9.6% = 9.6/100 = 12/125.

Step 2: Multiply the fractions. (1/100)·(12/125) = 12/12500 = 3/3125.

Step 3: Use the integer condition. For (3/3125)·x to be an integer, x must be divisible by 3125 (gcd(3,3125)=1).

Conclusion: The smallest positive integer x that makes 1% of 9.6% of x an integer is 3125.

Note: Among the provided choices, 31250 is divisible by 3125 so it yields an integer, but it is not the minimal possible value (3125 is smaller).