The negotiations are unsuccessful, and the Boards’ hopes to continuing talks on a future deal seems to be increasingly improbable.

This question tests subject-verb agreement and infinitive construction.

Subject-verb agreement means the verb must match its subject in number (singular/plural). When using infinitives, we pair "to" with the base form of the verb, like "to continue" not "to continuing." Think of it like a dance - the subject and verb need to move in sync, and infinitives follow a strict two-step pattern.

Option 1 → Perfect grammar tango: singular board, plural hopes, correct infinitive.

Option 2 → Wrong verb agreement and mangled infinitive - double grammar fail.

Option 3 → Awkward "hopes on continued" phrasing disrupts the smooth flow.

Option 4 → Triple trouble: wrong possessive, wrong infinitive, wrong verb agreement.