How many numbers between 1 and 100 (inclusive) are divisible by 5 or 3?

Question

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5 and none of the digits is repeated?

Answer 1

Answer is 47.
Numbers divisible by 3 are 3, 6, 9, 12, 15, 18.....99
So, n(3) = 100/3 = 33.33 = 33 whole numbers

Similarly numbers divisible by 5 are 5, 10, 15, 20....100
So, n(5) = 100/5 = 20

Similarly, LCM of 3, 5 = 15 has 15, 30,....90
Which are multiplicands of both 3, 5
=> n(15) = 100/15 = 6 in integer floored

We have n(a U b) +n(a intersection b) = n(a) + n(b)
required + 6 = 33 +20
=> required = 53-6 = 47

So answer is 47