CHICAGO—Gabby Toro Rosa was a strong student in high school but she was lousy at standardized tests, killing her chances at some colleges. Then she heard that DePaul University here was willing to accept a series of short essays in lieu of test scores.

The questions were designed to elicit responses that would gauge traits such as perseverance, adaptability and discipline. They rely on the premise that certain personality types are more likely to succeed at college than others.

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