How many positive integers between 200 and 300 (both inclusi

This is a longish one and very unlikely to happen on GMAT in that form.

There are 101 integers total between 200 and 300, inclusive.

Calculate how many are divisible by 2 or 3 or 5. Use the formula

AorBorC = A + B + C -AandB - AandC - BandC + AandBandC

Subtract that number from the total 101 to get the number that are NOT divisible by 2 or 3 or 5.

There must be a trick because I found this problem on the free resources section of one of the GMAT test Prep companies.
I did the long math but I wasn't convinced that it would be an efficient way to approach the problem; this is why I post it here for alternative solutions.

Prep company problems are often not representative of the official GMAT problems so there doesn't have to be a shortcut like on a real GMAT problem. The problem repeats the same element 'how many numbers between a and b are divisible by ....' several times in the solution, so it is a good exercise of that element and the formula for 3 intersecting sets but it is very unlikely that actual GMAT problem will present that laborous combination because it takes too much time to solve it, even if you know how.