Jareau Hall breezed through high school in Syracuse, N.Y. Graduating in the top 20% of his class, he had been class president and a successful athlete, and he sang in gospel choir. He was actively recruited by Colgate University in rural New York, one of the nation's top liberal-arts colleges.

None of Colgate's recruiters mentioned to Mr. Hall that his combined math and verbal SAT scores were some 250 points below the class median—let alone that this would put him at great risk of academic difficulty.

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