2002 AMC 10P Problem 25

Under the new AMC 10, 12 scoring method, 6 points are given for each correct answer, 2.5 points are given for each unanswered question, and no points are given for an incorrect answer. Some of the possible scores between 0 and 150 can be obtained in only one way, for example, the only way to obtain a score of 146.5 is to have 24 correct answers and one unanswered question. Some scores can be obtained in exactly two ways, for example, a score of 104.5 can be obtained with 17 correct answers, 1 unanswered question, and 7 incorrect, and also with 12 correct answers and 13 unanswered questions. There are (three) scores that can be obtained in exactly three ways. What is their sum?

\text{(A) }175 \qquad \text{(B) }179.5 \qquad \text{(C) }182 \qquad \text{(D) }188.5 \qquad \text{(E) }201

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.