<em>Requisite</em>
Made necessary by particular circumstances or regulations.
"the application will not be processed until the requisite fee is paid"
synonyms: necessary, required, prerequisite, essential, indispensable, vital, needed, needful
This would mean that the correct answer to your uestion would be C. Nikkita didn't get the job because she didn't posses the [Nesscary/Requisite] (exam?).
For number 1, your option is correct (B). "Doggedly" is synonymous with "persistent," so "with great determination" matches that.
For number 2, your option is correct (D). "Stoutly" means "strong" and "sturdy," so "solid" would also work.
For number 3, your option is incorrect. The correct answer is B. "Boisterous" and "rowdy" both mean energetic and noisy. Since the children were bouncing off the walls, they were indeed energetic, boisterous, and rowdy.