Question 10
Mary told John her score on the American High School Mathematics Examination (AHSME), which was over $80.$ From this, John was able to determine the number of problems Mary solved correctly. If Mary’s score had been any lower, but still over $80,$ John could not have determined this. What was Mary’s score? (Recall that the AHSME consists of $30$ multiple-choice problems and that one’s score, $s,$ is computed by the formula $s=30+4c-w,$ where $c$ is the number correct and $w$ is the number wrong; students are not penalized for problems left unanswered.)