Final answer:
The true statement is that if the balance in finished goods inventory decreases during the year, then the cost of goods sold equals the cost of goods manufactured minus the decrease in finished goods inventory.
Step-by-step explanation:
The correct statement among the options provided is a. If the balance in finished goods inventory decreases during the year, then the cost of goods sold equals the cost of goods manufactured minus the decrease in finished goods inventory. This statement relates to the basic accounting principle where the cost of goods sold is calculated by adjusting the cost of goods manufactured with the change in finished goods inventory. If the finished goods inventory has decreased, it means that more goods have been sold than were manufactured or added to the inventory this period. Conversely, if the inventory increases, the implication is that less has been sold in comparison to what was manufactured or added to the inventory.
The other statements are false because they incorrectly represent the relationship between inventory levels, purchases, and costs in relation to cost of goods sold and cost of goods manufactured.