Final answer:
The grammatically correct sentence is 'Ellos están impacientes.'
Step-by-step explanation:
The grammatically correct sentence is Ellos están impacientes. The correct form of the verb 'to be' in Spanish for the subject 'ellos' is 'están' which is the third person plural form. The other options 'Ellos estamos impacientes', 'Ellos estoy impacientes', and 'Ellos estáis impacientes' are incorrect because they do not match the subject.
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