In the recent years Approximate Computing (AC) has emerged as new paradigm for energy efficient IC design. It addresses the problem of maintaining reliability and thus coping with run-time errors exploiting an acceptable amount of overheads in terms of area, performances and energy consumption. This work starts from the consideration that AC-based systems can intrinsically accept the presence of faulty hardware (i.e., hardware that can produce errors). This paradigm is also called "computing on unreliable hardware". The hardware-induced errors have to be analyzed to determine their propagation through the system layers and eventually determining their impact on the final application. In other words, an AC-based system does not need to be built using defect-free ICs. Under this assumption, we can relax test and reliability constraints of the manufactured ICs. One of the ways to achieve this goal is to test only for a subset of faults instead of targeting all possible faults. In this way, we can reduce the manufacturing cost since we eventually reduce the number test patterns and thus the test time. We call this approach Approximate Test. The main advantage is the fact that we do not need a prior knowledge of the workload (i.e., we are application independent). Therefore, the proposed approach can be applied to any kind of ICs, reducing the test time and increasing the yield. We present preliminary results on some simple case studies. The main goal is to show that by letting some faults undetected we can save test time without having a huge impact on the application quality.