This question tests your understanding of passive voice and verb tenses in English grammar. Let's break it down step-by-step.

Step 1: Identify the Active Voice

The original question is in the active voice: "How old are these houses? When ____ built?" The implied active sentence is: "When did they build these houses?" The subject ("they") performs the action ("build") on the object ("these houses").

Step 2: Convert to Passive Voice

To convert this to the passive voice, the object of the active sentence ("these houses") becomes the subject of the passive sentence. The structure for a passive voice sentence is:

Subject + form of 'be' + Past Participle (V3) + (by + agent)

In this case, the subject is "these houses" (which can be replaced by the pronoun "they"). The past participle of the verb "build" is "built". Therefore, the structure becomes: "they + [form of 'be'] + built".

Step 3: Determine the Correct Tense

The first part of the question, "How old are these houses?", is in the present simple tense. This tells us the houses exist now. The question "When ____ built?" asks about an action (the building) that was completed in the past. Therefore, we need the past simple tense of the verb 'to be'.

The past simple form of 'be' for the plural subject "they" is "were".

Step 4: Choose the Correct Pronoun Case

In the passive structure ("were built"), the word before the verb is the subject of the clause. Subjects must be in the subjective case (I, you, he, she, it, we, they). "They" is the subjective case. "Them" is the objective case (e.g., "I saw them") and is incorrect here.

Conclusion and Final Answer

Combining these points, the correct completion is: "Were they".

The full, correct passive sentence is: "When were they built?"

Why the Other Options are Wrong:

• "Are they": Uses the present tense "are", but the action of building happened in the past.
• "Are them": Uses the wrong tense (present) and the wrong pronoun case ("them" is objective, not subjective).
• "Were them": Uses the correct tense but the wrong pronoun case ("them" is objective, not subjective).

Related Topics & Formulae

Passive Voice Structure: Subject + be + Past Participle (V3)

The form of the verb 'be' changes to reflect the tense (e.g., is/am/are [present], was/were [past], has been/have been [present perfect]).

Pronoun Cases:
Subjective Case (used as subject): I, you, he, she, it, we, they
Objective Case (used as object): me, you, him, her, it, us, them