A father has three daughters named Alice, Betty, and Cathy. Alice is older than Betty, but younger than Cathy. Their ages are consecutive prime numbers. What are their ages?
Alice is 5 years old, Betty is 3 years old, and Cathy is 7 years old.

Here's the reasoning:
1. We know that Alice is older than Betty and younger than Cathy, and their ages are consecutive prime numbers.
2. Prime numbers are numbers greater than 1 that can only be divided by themselves and 1.
3. Starting with the smallest prime number, 2, we look for three consecutive prime numbers.
4. The next prime number is 3, and the one after that is 5.
5. Since Alice is older than Betty but younger than Cathy, their ages must be 3, 5, and 7, respectively.

Therefore, Alice is 5 years old, Betty is 3 years old, and Cathy is 7 years old.