The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then which one is correct?

Question: The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then which one is correct?

Solution:
Total sum of six numbers = 6x
Total sum of three numbers = 3y
Total sum of the other numbers = 3z

Now,
6x = 3y + 3z
⇒ x = 3(y + z)/6
⇒ x = (y + z)/2
∴ 2x = y + z