What is X in the sequence 132, 129, 124, 117, 106, 93, X ?
- (a) 74
- (b) 75
- (c) 76 ✓ UPSC's answer
- (d) 77
Why the answer is (c)
• Calculate the differences between consecutive terms: 132 - 129 = 3, 129 - 124 = 5, 124 - 117 = 7, 117 - 106 = 11, 106 - 93 = 13.
• Observe that the differences are consecutive prime numbers: 3, 5, 7, 11, 13.
• Identify the next prime number in the sequence, which is 17.
• Subtract this next difference from the last given term: 93 - 17 = 76.
• Therefore, X is 76, which corresponds to option (c).
Why the other options are wrong
- (a) 74
- 74 is incorrect because it would require a difference of 19, skipping the prime number 17.
- (b) 75
- 75 is incorrect because it would require a difference of 18, which is not a prime number.
- (d) 77
- 77 is incorrect because it would require a difference of 16, which is not a prime number.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.