Question 89

How many integers between 1 and 100 (inclusive) are neither divisible by 2 nor 3 ?

Solution

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The odd numbers are not divisible by 2. There are 50 odd numbers.

There are 33 numbers between 1 and 100 that are divisible by 3. Of them, 17 are odd and 16 are even.

So, of the 50 odd numbers, we subtract the 17 that are divisible by 3. So, we get 33 numbers.  

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