When recruiting job candidates, employers rarely observe their underlying\nskill level directly. Instead, they must administer a series of interviews\nand/or collate other noisy signals in order to estimate the worker's skill.\nTraditional economics papers address screening models where employers access\nworker skill via a single noisy signal. In this paper, we extend this\ntheoretical analysis to a multi-test setting, considering both Bernoulli and\nGaussian models. We analyze the optimal employer policy both when the employer\nsets a fixed number of tests per candidate and when the employer can set a\ndynamic policy, assigning further tests adaptively based on results from the\nprevious tests. To start, we characterize the optimal policy when employees\nconstitute a single group, demonstrating some interesting trade-offs.\nSubsequently, we address the multi-group setting, demonstrating that when the\nnoise levels vary across groups, a fundamental impossibility emerges whereby we\ncannot administer the same number of tests, subject candidates to the same\ndecision rule, and yet realize the same outcomes in both groups.\n