C is corrent. Unanimous consent is needed in the partnership for actions that are not part of the implied authority of individual partners. Purchasing goods are actions that third parties can expect individual partners to do. These actions are binding on the partnership whether that partner had actual authority or not. Admission of a new partner is not based on implied authority and needs the approval of all partners. A is incorrect because admission of a new partner is a major event and requires approval of all partners. B is incorrect because purchasing goods for the partnership is part of the implied authority of each partner. Admission of a new partner requires unanimous approval. D is incorrect because this is an implied authority of each partner to enter into contracts related to the partnership business.
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