Design an application in Python that accomplishes the following:
1) The application would generate a set of 100 integers in a random manner in the range of 50 to 150 including both the numbers in the range.
2) Save these numbers in the same order as they are generated in memory or further manipulation.
3) Output these numbers as a set for the user.
4) Save these numbers to fa file.
5) Generate another set of 100 integers 5 times the original set.
6) Same as items 2-4 on the new set.