Here's how I thought of it (quite similar to already mentioned solutions):

The number of values in an arithmetic series is the same as the number of multiples of whatever number you are using. So, for 1-100, if looking at 2, the number of multiples is 100/2 = 50 (2,4,6...100) There are 50 of these multiples.

For 1-100 exclusive, and looking at 5, we can say 100/5 = 20 (5, 10, 15...100) There are 20 of these multiples, BUT we can't include 100 because we were told it's an exclusive range, so we can't include 100. That leaves 95 as the last possible multiple in the range. So there are only 20 - 1 multiples, or 19.

Then we can look for lowest common multiple of the numbers in both of these sets


2 4 6 8 10...
5 10 20...


We can see 10 is the lowest common multiple. Once you have the LCM you can find the rest of the common numbers by incrementing in that unit. So we have common multiples of

10,20,30,40,50,60,70,80,90

We have 9 numbers in common between the two sets.

So, to find the number of values in set X not in Y, we take the total for number of multiples of 2 from 1-100 inclusive, which was 50
and then subtract the number of multiples in the two sets that were in common

So, we get 50 - 9 = 41

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