The average of 6 numbers is 7. when a 7th number is addedthe average of all numbers is 0. what is the seventh number?

-- The average of 6 numbers is 7.
    So those 6 numbers must add up to 42.

-- If one more number results in an average of zero,
   the new number must be  -42 .
   Then all 7 numbers add up to zero.