How many whole numbers in between 50 and 150 that are multiples of 7 but not 4? Be quick

Explanation:

What we need to do is first find out how many multiples of 7 are between 50 and 150.

Divide 50 over 7 to get 50/7 = 7.1 approximately. So we can see that 7*7 = 49 and 7*8 = 56. This shows that 56 is the smallest such multiple of 7 between 50 and 150.

We'll do the same for 150. So, 150/7 = 21.4 approximately which means 7*21 = 147 and 7*22 = 154

The multiples of 7 between 50 and 150 are: {56, 63, ..., 147}

We can rewrite that list into {7*8, 7*9, ..., 7*21}

For each multiplication, we have 7 times something. That "something" is in the list {8, 9, ..., 21} in which we see there are 21-8+1 = 14 items here. I used the formula b-a+1 to count the number of whole numbers from 'a' to b, including both endpoints.

In short, there are 14 multiples of 7 between 50 and 150.

That would be the final answer if we weren't worried about ignoring multiples of 4.

However, what we need to do now is look at the list {8, 9, ..., 21} and see which of those are multiples of 4. That sub-list is {8, 12, 16, 20} and those values will be kicked out. So we'll go from 14 multiples of 7 to 14-4 = 10 multiples of 7.

answer: the common difference is -0.10