Final answer:
The building has 9 stories, and each story has 3 apartments, because 9 is the only divisor of 27 that falls within the specified range of stories for the building.
Step-by-step explanation:
To determine the number of apartments in each story of the building that has more than 4 stories but fewer than 10 stories, with a total of 27 apartments, we need to find a divisor of 27 that is within the range of 5 to 9 (since the building has more than 4 stories but fewer than 10). Divisors of 27 are 1, 3, 9, and 27. The only number in this set that falls into the required range for the number of stories is 9. Therefore, the building must have 9 stories with each story containing 3 apartments.