Multiple-choice examinations play a critical role in university admissions across the world. A key question is whether imposing penalties for wrong answers on these examinations deters guessing from women more than men, disadvantaging female test-takers. We consider data from a large-scale, high-stakes policy change that removed penalties for wrong answers on the national college entry examination in Chile. The policy change reduced a large gender gap in questions skipped. It also narrowed gender gaps in performance, primarily among high-performing test-takers, and in the fields of math, social science, and chemistry.