The number $n$ is a prime number between 20 and 30. If you divide $n$ by 8, the remainder is 5. What is the value of $n$?
To find $n$, I need to use the fact that it is a prime number and the remainder when divided by 8. I can write $n$ as $8k + 5$, where $k$ is some positive integer. If $n$ is between 20 and 30, then $k$ must be either 2 or 3, since $8 \times 2 + 5 = 21$ and $8 \times 3 + 5 = 29$. I can check if 21 or 29 are prime numbers by dividing them by some small primes, such as 2, 3, 5, and 7. 21 is not prime, since it is divisible by 3. 29 is prime, since it is not divisible by any of the small primes. Therefore, $n$ must be 29. 