Number series (primes): 11, 13, 17, 19, 23, 29, 31, 37, 41, (…) Identify the next term that correctly continues this prime-number sequence.
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A43
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B47
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C53
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D51
Answer
Correct Answer: 43
Explanation
Introduction / Context:This question tests recognition of prime-number sequences in quantitative aptitude. Primes are integers greater than 1 with exactly two positive divisors: 1 and the number itself. Spotting primes and continuing a prime sequence is a foundational skill for many number series problems.
Given Data / Assumptions:
- Sequence provided: 11, 13, 17, 19, 23, 29, 31, 37, 41.
- Terms are strictly increasing and appear to be consecutive primes in ascending order.
- We must find the next prime after 41.
Concept / Approach:To extend a prime sequence, test successive integers after the last term for primality (no divisors other than 1 and itself). Typical quick checks include divisibility by small primes (2, 3, 5, 7).
Step-by-Step Solution:
The last given prime is 41.Check 42: divisible by 2 and 3, so not prime.Check 43: not divisible by 2 (odd), by 3 (4+3=7, not multiple of 3), by 5 (does not end in 0 or 5), or by 7 (43 / 7 is not an integer). 43 is prime.Therefore, the next consecutive prime after 41 is 43.Verification / Alternative check:List known consecutive primes around 40: 37, 41, 43, 47. The next after 41 is indeed 43.
Why Other Options Are Wrong:
- 47, 53: These are primes but not the immediate next prime.
- 51: Composite (51 = 3 * 17).
Common Pitfalls:Confusing “any prime” with “next prime.” Always ensure immediacy in ordered prime sequences.
Final Answer:43