Four prime numbers are arranged in increasing order. The product of the first three primes is 385, while the product of the last three primes is 1001. What is the value of the fourth prime number?

Explanation

Given that the product of the first three primes is 385 and the product of the last three primes is 1001, we can factor these numbers to find the primes. 385 factors into 5 × 7 × 11, and 1001 factors into 7 × 11 × 13. Since the primes are in ascending order, the four primes are 5, 7, 11, and 13. Therefore, the fourth prime number is 5.