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 given sequence is 14, 18, 20, 24, 30, 32.

The problem states that a simple mathematical operation on each number results in a sequence with respect to prime numbers.

Let's try subtracting 1 from each number in the given sequence: 14 - 1 = 13 18 - 1 = 17 20 - 1 = 19 24 - 1 = 23 30 - 1 = 29 32 - 1 = 31

The resulting sequence is 13, 17, 19, 23, 29, 31. These are consecutive prime numbers. 13 is the 6th prime number. 17 is the 7th prime number. 19 is the 8th prime number. 23 is the 9th prime number. 29 is the 10th prime number. 31 is the 11th prime number.

Following this pattern, the next prime number in this sequence would be the 12th prime number. The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ... The 12th prime number is 37.

Since the operation was to subtract 1 from the original sequence number to get the prime, to find the next number in the original sequence, we add 1 to the next prime number (37). Next number = 37 + 1 = 38.

Therefore, the next number in the sequence is 38.

Analyzing the options: A) 34: If 34 were the next number, 34-1 = 33, which is not prime. B) 36: If 36 were the next number, 36-1 = 35, which is not prime. C) 38: If 38 were the next number, 38-1 = 37, which is the next prime number in the series. This fits the pattern. D) 40: If 40 were the next number, 40-1 = 39, which is not prime.

The final answer is C) 38.