# How many positive integers H between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?

How many positive integers H between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?

## Answer/Solution

26

### Steps/Work

1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.

2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).

3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.

4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!

6) Answer choice E.

2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).

3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.

4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!

6) Answer choice E.