By 1985, nearly half of the nation's public school students will be required to pass a minimum competency test (MCT) for high school graduation. Supporters of objectives underlying the MCTs suggest that the tests will force school systems to take their responsibilities to all children more seriously. Critics argue that students who fail will become scapegoats for school system failure, with few, if any, new efforts made to meet their needs. The purpose of this study was to examine the validity of the critics' argument. For students who fail MCTs, are remedial services provided to help them pass the tests on later attempts and, if so, who is paying for these services? Analysis of data collected from thirteen states chosen for having an MCT program statewide, underway at survey time, and MCT results determining high school graduation eligibility, revealed that most students failing the MCT the first time and remain in school eventually meet the competency requirements. Nevertheless, not all students pass, and failure rates are higher among minority students than among nonminority students. Potential problems were identified relating to the "required by law,""proportionate share," and "comparability" provisions of Title I in a section on funding remedial activities. (Author/CE)