This paper discusses one of the arguments that has been advanced against the use of standardized college admissions tests: the notion that their use leads admissions officers to reject non-Asian minority students on the basis of small and insignificant differences in scores. In the aggregate, the disadvantage minority students face as a result of their test scores is not a matter of small differences at the margin. For the purposes of this paper, it is accepted that college admissions tests show fairly typical group differences and that these differences are not biased against minorities as predictors of college grades. The differences are largely relative to the distribution of achievement within each group. The reasons for such differences are not explored; the size and effects are examined in practical terms using simulated data that mimic the typical differences found in large-scale testing programs. Databases were created that had a mean difference of 0.80 standard deviation between blacks and whites, somewhat smaller than those found on the Scholastic Assessment Test but larger than some of the most recent differences found in the National Assessment of Educational Progress. The effects of several simple admissions rules that depended solely on scores were studied, and a number of cut cores were set. Three scenarios, varying the numbers of black and white applicants and the cut scores, were considered. The simulations illustrate that when cut scores count heavily in admissions, the large differences in scores between black and white students have a major impact on the probability that black students will be admitted and on the composition of the accepted student population. These effects become progressively more severe as the selectivity of admissions increases. Results also illustrate the difficulty inherent in reconciling academic selectivity with increased equity of access to postsecondary education for non-Asian minority groups. (SLD)