since the prime factors need not necessarily be distinct in order to be counted for the length, would start working using 2 and solve for values of x and y which satisfy the given equation

For getting the max of length of x, let's go with 512 for x (2^9).

Then try solving for y, which should be < 488. It works out ~ 2^7 or 128.

Now plugging this back in the equation

512 + 3 x 128 < 1000

512 + 384 < 1000 (which is satisfied)

So max of sums of length of x , y = 9 + 7 = 16. Answer D

_________________

excellence is the gradual result of always striving to do better