I have e_______ the problem, and here are some solutions that I've found.

• A. Examine
• B. Examinable
• C. Examined
• D. Examining

Answer: (C)

The sentence is using the present perfect pattern with have + past participle to show a completed action with relevance now. For the verb examine, the correct past participle is examined, so the natural completion is “I have examined the problem, and here are some solutions that I've found.” This keeps the action of looking into the problem finished, while the second clause uses found to present the results of that examination.

The other forms don’t fit because examine is not in its past participle form after have, which is needed here. Examinable is an adjective meaning capable of being examined, not a verb. Examining is the present participle, which would require a different construction (like I am examining or I have been examining) to be grammatical.