Final answer:
An investor who owns 30% of the common stock of an investee is most likely to exercise significant influence requiring use of the equity method when they have the ability to participate in financial and operating policy decisions.
Step-by-step explanation:
When an investor owns 30% of the common stock of an investee, they are most likely to exercise significant influence requiring the use of the equity method when they have the ability to participate in the financial and operating policy decisions of the investee. This means that the investor has the power to affect the investee's strategic decisions and has access to information about the investee's operations. For example, the investor may have a seat on the investee's board of directors or may have a contractual agreement that grants them the right to veto certain decisions.