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sequence A, A1 = 43, A2 = 47,...., Ak = k2 + k + 41

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Source: — Data Sufficiency |

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by Ian Stewart » Wed Sep 19, 2012 11:15 pm
CSASHISHPANDAY wrote:In the sequence A, A1 = 43, A2 = 47,...., Ak = k2 + k + 41. Is every term in sequence A a prime number?

1.There are fewer than 100 terms in sequence A.
2.There are more than 50 terms in sequence A.
If k = 41, then k^2 + k + 41 = 41^2 + 41 + 41, which is a sum of multiples of 41, and is thus certainly divisible by 41 (if you factor out the 41, you can see this term is equal to 41*43). So the 41st term of the sequence will certainly not be prime. Thus Statement 2 is sufficient alone.

Statement 1 is not sufficient. If the sequence only has, say, 3 terms, then all of them are prime, whereas if the sequence has more than 41 terms, we know that at least one of them is not prime (the 41st term). So the answer is B.
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