The average of six consecutive odd numbers is 68. What is the cube of the difference between the highest and the lowest numbers?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 1000.
Let, the six consecutive numbers be x, (x + 2), (x + 4), (x + 6), (x + 8), (x + 10)
We know that,
Average = Sum of observations/Number of observations
⇒ (x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10))/6 = 68
⇒ 6x + 30 = 68 × 6
⇒ 6x = 408 - 30
⇒ 6x = 378
⇒ x = 63
Lowest number = x = 63 and, Highest number = (x + 10) = 73
Difference = 10
Cube of the difference = 103 = 1000