Question

The average of any 5 consecutive odd natural numbers is k. If two more such numbers, just next to the previous 5 numbers are added, the new average becomes:

• A. $\frac{2}{7}(k+1)$
• B. 2k - 3
• C. 2k + 1
• D. k + 2

Answer 1

The correct option is D k + 2

Average of 5 consecutive odd natural number will be the third odd number in the series.
When next two odd numbers are added to the series, there will be 7 consecutive odd natural numbers and their average will be the fourth term.If the third term is k, then the fourth term will be k + 2.

Alternatively:
Consider some appropriate numbers.
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Conventional Approach:
The 5 consecutive odd numbers whose average is k are (k - 4), (k - 2), k, (k + 2)(k + 4)
Again the average of (k - 4), (k - 2), (k), (k + 2), (k + 4), (k + 6), (k + 8) is (k + 2)