A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?

The correct option is 38.

Step-by-Step Explanation:

Let us analyze the relationship between the numbers in the given sequence: 14, 18, 20, 24, 30, 32, ... and prime numbers.

Subtracting 1 from each term in the sequence gives:
14 - 1 = 13
18 - 1 = 17
20 - 1 = 19
24 - 1 = 23
30 - 1 = 29
32 - 1 = 31

We observe that the transformed numbers form a sequence of consecutive prime numbers: 13, 17, 19, 23, 29, 31.

The prime number immediately following 31 is 37.

Therefore, the next number in the original sequence is obtained by performing the reverse operation (adding 1):
$37+1=38$