Question

How many numbers between 1 and 100 (inclusive) are divisible by 3 or 2?

Answer 1

33

Explanation:

There are 100 numbers between 1 and 100, inclusive. Dividing 100 by 2 will give how many even numbers, divide by 2; 50 even numbers, however we know some of them will also be divisible by 3. Dividing 100 by 3 will give how many numbers can be divided by 3; = 33 + 1 remainder.

Hope this helped :)

Answer 2

67

Explanation:

There are 33 numbers divisible by 3 between 1 and 100, and 50 numbers divisible by 2 between 1 and 100.

So, you might think there are 33 + 50 = 83, plus, 50, equals, 83 numbers divisible by one or the other, but this is overcounting something.

We're counting every number which is divisible by both 3 and 2 twice. So, for example, 6 is counted once as a number divisible by 3, and then again as a number divisible by 2.

So, we need to count how many numbers are divisible by both 3 and 2 and subtract this from what we had before.

Being divisible by both 3 and 2 is the same thing as being divisible by 6, so there are 16 numbers between 1 and 100 divisible by both.

Subtracting, there are 83 - 16 = 67, minus, 16, equals, 67 numbers divisible by 3 or 2.