Choose the preposition that correctly completes the sentence.

During the budget meeting, the committee chair balked ________ approving the proposal until the missing figures were supplied.

The correct option is at.

Explanation:
The verb "balk" (or baulk), when used to express reluctance, hesitation, or refusal to accept or perform an action, is idiomatically followed by the preposition "at".

Phrasal Usage:
• Balk at [something / doing something]: This means to hesitate or refuse to proceed with an idea or task.
Example: "She balked at the high cost of the tour package."

Contextual Analysis:
In the given sentence, the committee chair hesitated and refused to approve the proposal until missing figures were provided. Thus, the verb balked correctly links with the gerund phrase using the preposition "at": "balked at approving..."

Incorrect Options:
• by: "Balk by" is grammatically incorrect in this context.
• with: "Balk with" does not form a standard phrasal expression for showing hesitation.
• for: "Balk for" is not the correct preposition associated with the verb "balk".