The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is

There are 9000 four digit integers.

Now if the integers are divisible by 2 and 3, then they must be divisible by 6 also.

Number of four digit integers divisible by 6 =$$\dfrac{9000}{6}=1500$$

But, we also need to eliminate the integers which are divisible by 5

Now, integers divisible by 6 and 5, means it is divisible by 30 also

So, number of four digit integers divisible by 30 =$$\dfrac{9000}{30}=300$$

So, required number of integers =$$1500-300=1200$$