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Seven consecutive number starting from x which is an even number. Out of these seven if the difference between the sum of four consecutive odd numbers and the sum of three consecutive even numbers is 12. Find the average of next five consecutive odd numbers.

Seven consecutive number starting from x which is an even number. Out of these seven if the difference between the sum of four consecutive odd numbers and the sum of three consecutive even numbers is 12. Find the average of next five consecutive odd numbers. Correct Answer 15

Given:

The difference between the sum of four consecutive odd numbers and the sum of three consecutive even numbers is 12

The smallest even number is x

Formula used:

Average = Sum of observations/Number of observations

Calculation:

Let the smallest odd number be x + 1

⇒ Four consecutive odd number = x + 1, x + 3, x + 5, x + 7

⇒ Three consecutive even number = x, x + 2, x + 4

The sum of three consecutive even numbers is = x + (x + 2) + (x + 4)

⇒ 3x + 6

The sum of four consecutive odd numbers is = (x + 1) + (x + 3) + (x + 5) + (x + 7)

⇒ 4x + 16

According to question, we have

⇒ (4x + 16) – (3x + 6) = 12

⇒ (4x – 3x) – (16 – 6) = 12

⇒ x + 10 = 12

⇒ x = 12 – 10

⇒ x = 2

⇒ Five consecutive odd numbers = 3, 5, 7, 9

⇒ Next Five consecutive odd numbers = 11, 13, 15, 17, 19

We know that,

Average = Sum of observations/Number of observations

⇒ Average = (11 + 13 + 15 + 17 + 19)/5

⇒ Average = 75/5

⇒ Average = 15

∴ The average of the next five consecutive odd numbers is 15.

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The average of odd number of consecutive number is the middle number of the series.

11, 13, 15, 17, 19

∴ The average is 15 because it is in the middle position.

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