How many such numbers are there from 500 to 750 (including both) which are neither divisible by 3 nor by 11?
151
The correct answer is 151.
$A \cap B$ is numbers divisible by both 3 and 11 (i.e., by 33) in the range. The numbers we want to find are those in the total set of numbers in the range that are NOT in the union $A \cup B$. So, the final count is Total - $|A \cup B|$. This fundamental principle is very useful in counting problems involving overlapping sets.
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Which of the following numbers is divisible by 12?
