Explanation

To make sense of this question, we are going to need the prime factorization of 485,100.







Both of these two steps were made possible by seeing the digits summed to 3, so the number had to be divisible by 3. It's the first thing to check after checking whether a number is even.

Working up, for 539, 3 doesn't work, 5 doesn't work, but







This result is the original number expressed in its prime factorization. We are looking for a number x such that is twice the square of some integer. We can construct twice the square of an integer from these factors as . The number is a square, so the number is twice a square. Moreover, it's the largest possible double of a square out of the factors . We are using as many of the factors as possible, so x can be as small as possible, per the question. And x has to cancel the rest, so . We've found that 22 is the smallest number that we can put in the denominator and get 2 times the square of an integer up top.

The correct answer is (C).