Question

Consider the set Sn = {n, n + 2. n + 4. n + 6, n + 8), where n is a natural number between 101 and 200 (both inclusive). How many of the 100 possible sets contain a multiple of 7?​

Answer 1

There are total of  even numbers in the range  (check this: totally-basic-94862.html?hilit=multiple%20range );

There are total of  even multiple of 9 (so multiple of 18) in the range ;

There are total of  even multiple of 7 (so multiple of 14) in the range ;

As there is 1 even multiple of 7 AND 9 (overlap) in the range , which is  then there are total of  even multiples of 7 OR 9 in the range ;

So there are  even numbers which are not divisible neither by 7 nor by 9.

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