Question
Average of four consecutive prime numbers R1, R2, R3,
and R4 is (14 + x). If the average of R1 and R2 is (11 + x) and the average of R3 and R4 is (11 + 2x), then find R4.Solution
ATQ, Sum of R1, R2, R3, and R4 = (14 + x) × 4 = 56 + 4x Sum of R1 and R2 = (11 + x) × 2 = 22 + 2x Sum of R3 and R4 = (11 + 2x) × 2 = 22 + 4x Now, setting the equations equal: 22 + 2x + 22 + 4x = 56 + 4x Or, x = 6 Sum of R3 and R4 = 22 + 4 × 6 = 46 R3, R4 = 17, 23 Answer: R4 = 23
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