The clock will be repaired . . . . . . . . a week.

Answer: Option C

* The Question: The sentence needs a preposition to show *when* the clock repair will happen.

* Why 'in' is correct: "In a week" means the repair will be completed sometime *during* the span of the next week, but not necessarily at the end of the week.
It indicates a period of time *within which* something will occur.

* Why the other options are not:
* A: on: "On" is usually used for specific days or dates (e.g., "on Monday," "on July 4th"). It doesn't fit with a general timeframe like "a week."
* B: within: "Within a week" is grammatically correct and very close in meaning to "in a week", but 'in' is a more common and natural choice in this sentence.
* D: at: "At" is generally used for a specific point in time (e.g., "at 3 PM") or a place. It doesn't work with a duration of time like "a week."

Therefore, 'in' is the best option because it indicates that the repair will be finished sometime during the next week.