The average of 7 consecutive even numbers is 58. Then the difference between the highest even number and the lowest even number is

Explanation:

Let the 7 consecutive even numbers be:

(x - 6), (x - 4), (x - 2), x, (x + 2), (x + 4), (x + 6)

Here, x is the middle number, and the other numbers are spaced evenly around x, increasing or decreasing by 2. Consecutive even numbers are separated by a difference of 2.

Step 2: Calculating the average

The average of these numbers is given as 58. Using the formula for the average, we can calculate x:

Average = Sum of all numbers ÷ Total number of numbers

Sum = (x - 6) + (x - 4) + (x - 2) + x + (x + 2) + (x + 4) + (x + 6)

Sum = 7x (since all other terms cancel out when added)

Average = 58 = 7x ÷ 7

x = 58

So, the middle number of the sequence is 58. The numbers are:

(58 - 6), (58 - 4), (58 - 2), 58, (58 + 2), (58 + 4), (58 + 6)

Which simplifies to:

52, 54, 56, 58, 60, 62, 64

Step 3: Finding the difference between the highest and lowest numbers

The highest number in the sequence is 64, and the lowest number is 52. The difference between them is:

Difference = Highest number - Lowest number

Difference = 64 - 52

Difference = 12

Correct Answer: The difference between the highest even number and the lowest even number is 12