Final answer:
The total assets of a partnership can indeed increase when a new partner purchases interest in the business, as their contribution becomes part of the partnership's total assets.
Step-by-step explanation:
The statement that the total assets of the partnership may increase upon admission of a new partner by purchase of interest is True. When a new partner buys into a partnership, they typically contribute assets—such as cash, property, or other resources—to the partnership in exchange for their share or interest in the business. This injection of additional assets can increase the total assets of the partnership. In return for the contribution, the new partner gains a share in the profits and losses of the business and has an influence on its management, proportional to their interest in the partnership.