We consider the problem of determining the individual preference rankings that are necessarily implied by a dataset consisting of prices, income distributions and total resources. We show the equivalence between the compatibility with individual preference rankings and the existence of a solution to a set of linear equalities and inequalities. Using this characterization, we give new proofs of the rationalizability of finite data sets where total resources are close to being collinear and the contractibility and pathconnectedness of the set that consists of rationalizable finite datasets.