The question is about finding out the count of numbers from 0 to 999 that are divisible by either 5 or 7.

Option 1 suggests there are 313 numbers divisible by either 5 or 7, which is not high enough to include all these numbers.

Option 2 suggests 341 numbers, but this is also too low to include all requisite numbers.

Option 3 suggests there are 686 such numbers. This is the correct answer as it correctly accounts for all the numbers divisible by 5 (there are 200, from 5, 10, ..., 995), all the numbers divisible by 7 (there are 143, from 7, 14, ..., 994), and crux of the matter, it subtracts those numbers counted twice because they`re divisible by both 5 and 7 (i.e., multiples of 35 - there are 28, from 35, 70, ..., 980). So, 200+143-28=315 is the accurate count of the numbers.

Option 4 suggests 786 numbers divisible by 5 or 7, but this number exceeds the possible magnitude within the 0 to 999 range.