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Problem definition: Traditionally, New York City's top 8 public schools have selected candidates solely based on their scores in the Specialized High School Admissions Test (SHSAT). These scores are known to be impacted by socioeconomic status of students and test preparation received in middle schools, leading to a massive filtering effect in the education pipeline. The classical mechanisms for assigning students to schools do not naturally address problems like school segregation and class diversity, which have worsened over the years. The scientific community, including policymakers, have reacted by incorporating group-specific quotas and proportionality constraints, with mixed results. The problem of finding effective and fair methods for broadening access to top-notch education is still unsolved. Methodology/results: We take an operations approach to the problem different from most established literature, with the goal of increasing opportunities for students with high economic needs. Using data from the Department of Education (DOE) in New York City, we show that there is a shift in the distribution of scores obtained by students that the DOE classifies as "disadvantaged" (following criteria mostly based on economic factors). We model this shift as a "bias" that results from an underestimation of the true potential of disadvantaged students. We analyze the impact this bias has on an assortative matching market. We show that centrally planned interventions can significantly reduce the impact of bias through scholarships or training, when they target the segment of disadvantaged students with average performance.