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    Question

    Average of four consecutive prime numbers T1, T2, T3,

    and T4 is (17 + x). If the average of T1 and T2 is (13 + x) and the average of T3 and T4 is (13 + 3x), then find T4.
    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 T1, T2, T3, and T4 = (17 + x) × 4 = 68 + 4x Sum of T1 and T2 = (13 + x) × 2 = 26 + 2x Sum of T3 and T4 = (13 + 3x) × 2 = 26 + 6x Now, setting the equations equal: 26 + 2x + 26 + 6x = 68 + 4x Or, x = 4 Sum of T3 and T4 = 26 + 6 × 4 = 50 T3, T4 = 23, 29 Answer: T4 = 29

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