Question
Average of four consecutive prime numbers Q1, Q2, Q3,
and Q4 is (15 + x). If the average of Q1 and Q2 is (11 + x) and the average of Q3 and Q4 is (11 + 3x), then find Q4.Solution
ATQ, Sum of Q1, Q2, Q3, and Q4 = (15 + x) × 4 = 60 + 4x Sum of Q1 and Q2 = (11 + x) × 2 = 22 + 2x Sum of Q3 and Q4 = (11 + 3x) × 2 = 22 + 6x Now, setting the equations equal: 22 + 2x + 22 + 6x = 60 + 4x Or, x = 4 Sum of Q3 and Q4 = 22 + 6 × 4 = 46 Q3, Q4 = 23, 29 Answer: Q4 = 29
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