The sum of six consecutive odd numbers is 168. Average of the highest and…
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The sum of six consecutive odd numbers is 168. Average of the highest and lowest number is:
- A.
26
- B.
25
- C.
28
- D.
27
Attempted by 3 students.
Show answer & explanation
Correct answer: C
For any arithmetic progression, the average (mean) of the first and last terms always equals the mean of the whole progression. Six consecutive odd numbers form an arithmetic progression with common difference 2, so the average of the lowest and highest number equals the mean of all six numbers.
Let the six consecutive odd numbers be x, x+2, x+4, x+6, x+8 and x+10.
Their sum is x + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) = 6x + 30, and this equals 168, so 6x = 138 and x = 23.
The lowest number is x = 23 and the highest number is x + 10 = 33.
The average of the lowest and highest number is (23 + 33) / 2 = 56 / 2 = 28.
Cross-check: the six numbers are 23, 25, 27, 29, 31 and 33; their sum is 23 + 25 + 27 + 29 + 31 + 33 = 168, which matches the given total, confirming the average of 28.
