The Committee let her go because they considered her explanation …

Analyze the question: The sentence says the Committee let her go because of how they viewed her explanation. We need a word that explains why they would be satisfied enough to release her.

Explain the concept: This is a vocabulary-in-context question. Check each word for meaning and for collocation, meaning how naturally it pairs with "explanation."

• Permissible means allowed or permitted. We say an action is permissible, not usually an explanation.
• Clear means easy to understand. A clear explanation is not necessarily believable or acceptable. Someone can explain something clearly and still not be believed.
• Plausible means reasonable, believable, and likely to be true. This fits when someone has to justify themselves and the listeners accept it.
• Necessary means needed or required. It does not suit "explanation" in this context.

Solution:

1. The Committee released her after hearing her explanation.
2. That means they found it believable or acceptable.
3. "Plausible" describes exactly this: an explanation that seems reasonable and credible.
4. "Considered her explanation plausible" is also a natural, common phrase.

Answer: The correct option is C. plausible.

Tip: Words that go with "explanation" or "excuse" include plausible, convincing, reasonable, satisfactory, and acceptable. When a person is let off after explaining, look for a word about believability. Do not confuse plausible (believable) with plausable (a common misspelling) or with permissible (allowed).