Ashley Koski, ranked third in the senior class at Thomas Dale High School in Chester, Va., has wanted to attend Duke University since she was 12.

Late last month, she learned that Duke had neither accepted nor rejected her. It had offered her a spot on the waiting list — along with 3,382 other applicants. That is almost twice the size of the incoming freshman class.

“I kind of just went quiet the rest of the day,” Ms. Koski said. “I’d rather have a yes or no. I can’t make plans and be excited like the rest of my friends.”

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