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Difficulty: Very hardModal Auxiliaries and Expressing Modality

Complete the sentence by supplying the correct past modal verb phrase to express logical impossibility in the past.

Answer:Since the vault's biometric scanner records every entry timestamped to the millisecond and registered zero activity after midnight, the intruder 【could not have gained】 access through the main security door during the blackout.

Answer

could not have gained (or couldn't have gained / cannot have gained)
The correct answer 'could not have gained' uses the modal structure 'could not + have + past participle' to express a deduction of complete impossibility regarding a past event, which directly aligns with the contextual proof that no biometric entry was logged.

Step-by-Step Solution

1
Analyze the temporal frame and evidence provided in the sentence context.
The event occurred in the past ('registered zero activity after midnight'), establishing a past timeframe.
Modal auxiliaries must agree with the past temporal reference of the main clause.
2
Determine the specific modal function required by the context.
The premises (biometric scanner records and zero activity after midnight) provide conclusive proof that an entry was impossible.
Expressing strong logical deduction of impossibility in the past requires the structure 'could not / cannot + have + past participle'.
3
Formulate the correct modal auxiliary phrase using the verb 'gain'.
'could not have gained' perfectly matches both the past time reference and the negative deduction meaning.
'Must not have gained' expresses past negative conclusion about probability rather than logical impossibility driven by objective constraints, whereas 'could not have gained' strictly denotes impossibility.

Key Concept

Expressing logical impossibility in the past using perfect modal auxiliaries
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Topics

Modal Auxiliaries and Expressing Modality

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