The average of 4 consecutive odd numbers is half that of the

The average of 4 consecutive odd numbers is half that of the average of 5 consecutive even numbers. If the sum of these two average is 18, then the difference between the largest and smallest of these numbers is
A. 10
B. 21
C. 7
D. 13
E. 5

Some notes:
The average of evenly spaced set with even number of terms (4 in our case) is the average of two middle terms.
The average of evenly spaced set with odd number of terms (5 i our case) is the middle term.

Say the average of 4 consecutive odd numbers is \(x\) and the average of 5 consecutive even numbers is \(y\).

Given: \(x=\frac{y}{2}\) and \(x+y=18\) --> solve for \(x\) and \(y\): \(x=6\)and \(y=12\).

So, we have that the average of 4 consecutive odd numbers is 6, which means that those numbers are: {3, 5, 7, 9} (6 is the average of two middle terms);

Similarly we have that the average of 5 consecutive even numbers is 12, which means that those numbers are: {8, 10, 12, 14, 16} (12 is the middle term);

The difference between the largest and smallest of these numbers is 16-3=13.

Answer: D.

Hope it's clear.