Question

How many numbers between 101 and 1400 are not divisible either by 3 or 5?

Answer 1

There are 1400-101-1=1298 numbers between  101 and 1400.

First, we need to find how many numbers are there which are divisible by 3, 5 and 15.  

Numbers divisible by 3 between 101 and 1400=433

Numbers divisible by 5 between 101 and 1400=259

Numbers divisible by 15 between 101 and 1400=87

Now, the total numbers divisible by 3 or 5 =433+259-87=605

And the total numbers not divisible by 3 or 5 =1298-605=693

Therefore, there are 693 numbers which are not divisible either by 3 or 5