Question
The average of 8 consecutive even numbers written in
ascending order is 17. What is the average of the last three numbers, 36 and 53 ?Solution
Let sum of 8 consecutive even numbers be (2a - 6) + (2a - 4) + (2a - 2) + 2a + (2a + 2) + (2a + 4) + (2a + 6) and (2a + 8) ⇒ 16a + (-12 + 20) ⇒ 16a + 8 Average sum of 8 consecutive even numbers = (16a + 8)/8 = 17 ⇒ 8(2a + 1)/8 = 17 ⇒ 2a + 1 = 17 ⇒ 2a = (17 – 1) ⇒ 2a = 16 Now, putting the value in last three three numbers ⇒ (2a + 4) = (16 + 4) = 20 ⇒ (2a + 6) = (16 + 6) = 22 ⇒ (2a + 8) = (16 + 8) = 24 Again, Sum of last three numbers, 36 and 53 = (20 + 22 + 24 + 36 + 53) ⇒ 155 Average of sum of last three numbers, 36 and 53 = (155/5) ⇒ 31 ∴ The average of the last three numbers, 36 and 53 is 31.
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