The mean of four consecutive even numbers is 2017. What is the difference between the highest and the lowest digits of the highest even number?
2 Answers
The answer is 2.
Don't panic, the process is simpler than it looks.
Explanation:
If the average of 4 numbers is 2017, then their sum must be 4 times that (because the last step of finding the average is dividing by the number of data points, we can to this backward to find the sum, the step of finding the mean before that).
Now, we can represent 8068 as the sum of four even numbers. We could set
Because they are consecutive even numbers, we know that each one is 2 greater than the last one, and so we can represent them with
Now, just solve this equation algebraically to find
Next, add 12 to both sides.
Finally, divide by 4.
If you want to check your work on this part, write out the set of consecutive even numbers with the highest number of 2020. Sure enough, the average of 2014, 2016, 2018, and 2020 is 2017.
And now, the part you've all been waiting for:
The difference between the highest and lowest digits of the highest number is...
Explanation:
Let the four consecutive even numbers be
Given that mean of these four numbers is
Solving for
Highest even number is
Its highest and lowest digits are
Difference between the two digits