Query about question "Given an uniformly-distributed random variable..." [5902]

https://www.gregmat.com/problems/quant?problem=given-an-uniform-random-variable


this is a cool question, however, isn’t there a fundamental flaw with this question. Using the first equation we assume that total numbers is 105. However, could be the case that the 3-7 that we considered initially isn’t entirely in the range. how are we sure that total number is 105, could there not be any other combination which leads to another Total N