Question

In the set of consecutive integers from 21 to 46 , inclusive, there are 2 integers that are multiples of both 2 and 7. How many integers in the set are mulitples of neither 2 nor 7 ?.

The answer is 11 but
Please show me how to do it

Answer 1

Considering the set:

`A=\{ 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, \\35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46 \}`

In order to find the numbers that are not multiples of 2, eliminate the even.

`B=\{ 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45 \}`

Now eliminate the multiples of 7.

`C=\{ 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45 \}`

So, you got the 11 numbers.

Note: The multiples of both 2 and 7, are 28 and 42.