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?

(a) 34
(b) 36
(c) 38 ✓ UPSC's answer
(d) 40

Why the answer is (c)

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

• Subtracting 1 from each term yields: 13, 17, 19, 23, 29, 31, ...

• These resulting numbers (13, 17, 19, 23, 29, 31) are consecutive prime numbers.

• The next prime number after 31 is 37.

• Adding 1 back to this prime gives the next term in the original sequence: 37 + 1 = 38.

• Therefore, the next number in the sequence is 38.

Why the other options are wrong

(a) 34: 34 minus 1 is 33, which is not a prime number.
(b) 36: 36 minus 1 is 35, which is not a prime number.
(d) 40: 40 minus 1 is 39, which is not a prime number.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.