Inquiry and its relation to knowledge have recently gained significant philosophical attention. Some theorists argue for a close connection between knowledge and inquiry, while others think that they are more distinct. The existing discussions, however, ignore the question of whether knowledge and inquiry are co-extensive, that is whether everything that we can know we can also successfully inquire into and vice versa. In this paper, I will argue that they are not co-extensive, discussing several kinds of propositions that, even though they can be known, we cannot properly inquire into whether they are true. I will introduce rationality requirements for suspension of judgment that limit the possibilities of rational inquiry but not of other potential procedures of knowledge acquisition. As I will show, we cannot rationally inquire in cases where new and independent information is required that is not available. This limitations concern inquiry via bootstrapping and inquiry into the truth of indications that can only be delivered by a single source at a single occasion. However, we can clearly know in this latter case and, arguably, we can also know via bootstrapping. Hence, there are propositions that we can know but into which we cannot rationally inquire.