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    Question

    Average of four consecutive prime numbers S1, S2, S3,

    and S4 is (16 + x). If the average of S1 and S2 is (12 + x) and the average of S3 and S4 is (12 + 3x), then find S4.
    A 35 Correct Answer Incorrect Answer
    B 29 Correct Answer Incorrect Answer
    C 30 Correct Answer Incorrect Answer
    D 15 Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    ATQ, Sum of S1, S2, S3, and S4 = (16 + x) × 4 = 64 + 4x Sum of S1 and S2 = (12 + x) × 2 = 24 + 2x Sum of S3 and S4 = (12 + 3x) × 2 = 24 + 6x Now, setting the equations equal: 24 + 2x + 24 + 6x = 64 + 4x Or, x = 4 Sum of S3 and S4 = 24 + 6 × 4 = 48 S3, S4 = 23, 29 Hence, None of these pairs sum to 48. Therefore, there is no pair of consecutive primes summing to 48 in the standard set of known primes.

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