While high resolution images contain semantically more useful information than their lower resolution counterparts, processing them is computationally more expensive, and in some applications, e.g. remote sensing, they can be much more expensive to acquire. For these reasons, it is desirable to develop an automatic method to selectively use high resolution data when necessary while maintaining accuracy and reducing acquisition/run-time cost. In this direction, we propose PatchDrop a reinforcement learning approach to dynamically identify when and where to use/acquire high resolution data conditioned on the paired, cheap, low resolution images. We conduct experiments on CIFAR10, CIFAR100, ImageNet and fMoW datasets where we use significantly less high resolution data while maintaining similar accuracy to models which use full high resolution images.