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?

EXPLANATION

Correct Option (C)

The given sequence is 14, 18, 20, 24, 30, 32. An analysis of the numbers reveals a pattern where each term is one greater than a consecutive prime number:

14 = 13 + 1 (13 is a prime number)
18 = 17 + 1 (17 is a prime number)
20 = 19 + 1 (19 is a prime number)
24 = 23 + 1 (23 is a prime number)
30 = 29 + 1 (29 is a prime number)
32 = 31 + 1 (31 is a prime number)

Following this established pattern, the next prime number after 31 is 37. Therefore, the next number in the sequence would be 37 + 1 = 38.

Incorrect Options:

Option A (34): If 34 were the next number, it would imply 34 = 33 + 1. However, 33 is not a prime number (33 = 3 × 11), which violates the established pattern.
Option B (36): If 36 were the next number, it would imply 36 = 35 + 1. However, 35 is not a prime number (35 = 5 × 7), which violates the established pattern.
Option D (40): If 40 were the next number, it would imply 40 = 39 + 1. However, 39 is not a prime number (39 = 3 × 13), which violates the established pattern.