There are 89 numbers between 101 and 999 that are divisible by both 2 and 5.
Explanation
A number divisible by both 2 and 5 must be divisible by their least common multiple (LCM). The LCM of 2 and 5 is 10. Therefore, we are looking for multiples of 10 between 101 and 999.
The first multiple of 10 greater than 101 is 110.
The last multiple of 10 less than 999 is 990.
So, we want to find the number of terms in the arithmetic sequence: 110, 120, 130, ..., 990.
We can write this sequence as 10 11, 10 12, 10 13, ..., 10 99.
Therefore, we want to count the number of integers from 11 to 99, inclusive.
The number of integers is 99 - 11 + 1 = 89.
Therefore, there are 89 numbers between 101 and 999 that are divisible by both 2 and 5.
