# 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?

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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?
1. 31
2. 29.8
3. 31.6
4. 32.2

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Correct Answer - Option 1 : 31

Given:

The average of 8 consecutive even numbers in ascending order = 17

Formula used:

Sum of the observations/Number of observations

Calculation:

Let the 8 consecutive even numbers be (2a – 6), (2a – 4), (2a – 2), 2a, (2a +2), (2a + 4), (2a + 6) and (2a + 8)

Sum of 8 consecutive even numbers = (2a – 6) + (2a – 4) + (2a – 2) + 2a, (2a +2) + (2a + 4) + (2a + 6) + (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