How do we know when to provide an exhaustive answer to a wh-question, which mentions all the items that satisfy the property being asked about? We explored the nature of this exhaustivity requirement by investigating whether it is grammatical or based on assessing the information needs of the person asking the question. In Experiment 1 we tested 14 individuals after right hemisphere damage who had Theory of Mind (TOM) impairment (aTOMia), which compromised their ability to assess the information needs of their interlocutor, but whose grammatical abilities were normal. The rationale was that if they provided an exhaustive answer to certain question types, the exhaustivity requirement could not depend on considering the asker's intentions. We assessed their responses to single wh-questions (e.g., Who is painting?) and multiple wh-questions (e.g., Who is painting what?) in a question-about-a-picture task compared to 5 right-hemisphere damaged patients with good TOM, and to healthy controls. The individuals with aTOMia often failed to provide exhaustive responses to the single wh-questions, but consistently produced exhaustive responses to the multiple wh-questions. This finding suggests that the source of exhaustivity in single wh-questions is based on TOM, whereas exhaustivity in multiple wh-questions is grammatically-based. Following up on a further result from Experiment 1, Experiment 2 investigated the effect of the exhaustivity requirement on attention: 6 additional participants with left visuo-spatial neglect after right hemisphere damage were tested with a similar task to assess whether their answers omitted figures on the left. Both experiments – Experiment 1 with eight neglect patients and Experiment 2 with six, revealed that the exhaustivity requirement also triggered attention shift to the left in individuals with left neglect: in their responses to single wh-questions they omitted the left figures, but in paired wh-questions they scanned the entire visual field and responded with exhaustive answers. The results provide clear evidence from neurolinguistics that exhaustivity in single wh-questions requires considerations of the asker's intentions, whereas multiple wh-questions mark the exhaustivity requirement grammatically.