The correct answers are:
where the parent company was not already preparing group accounts; and
where an associate was sold during the year.
A parent company need not prepare group accounts just for the sake of an associate. IAS 28 allows a choice of equity accounting or recording at historic cost in this situation.
The statement of financial position represents a snap shot at the year end. Obviously if there was no investment or significant influence over the associate at the year end, because that investment was sold by the holding company, the now ex-associate would not be equity accounted.
Materiality does not affect the inclusion of an associate within a set of group accounts. If an associate is considered immaterial to the group it might mean that certain detailed disclosures within the accounts relating to the associate can be avoided.
Goodwill represents the excess paid for an investment over its net worth. Full impairment of that excess has no effect on the status of the associate or on the investor's long term interest in it.