In medical diagnosis, as in many cognitive domains, asking the right questions is crucial. Medical tests differ notonly in the type of information they provide, but in their financial costs and physical risks to a patient. We develop a modelthat combines informational and cost constraints, describing specific medical scenarios of a patient with realistic symptoms.We then define a finite number of existing medical tests that are available in this situation. The tests differ in their sensitivityand specificity concerning different possible underlying diseases as well as in their financial costs and the physical risks theypose to a patient. Combining these, we compare the utilities of the different tests if performed alone as well as if performed incombination. We show how purely informational considerations are not adequate for the analysis of such a scenario; test costsand patient outcomes must also be taken into account.