Question

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

Answer 1

Answer:

33 and 19

Step-by-step explanation:

there are 33 numbers between one and one hundred divisible by 3 and 19 numbers divisible by 5

Answer 2

Answer:

47

Step-by-step explanation:

There are 20 numbers divisible by 5 between 1 and 1001, and 33 numbers divisible by 3 between 1 and 100.

So, you might think there are 20 + 33 = 53 numbers divisible by one or the other, but this is overcounting something.

We're counting every number which is divisible by both 5 and 3 twice. So, for example, 15 is counted once as a number divisible by 5, and then again as a number divisible by 3.

So, we need to count how many numbers are divisible by both 5 and 3 and subtract this from what we had before.

Being divisible by both 5 and 3 is the same thing as being divisible by 15, so there are 6 numbers between 1 and 100 divisible by both.

Subtracting, there are 53 - 6 = 47 numbers divisible by 5 or 3.