MathDB

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?

<span class='latex-bold'>(A) </span>175\qquad<span class='latex-bold'>(B) </span>179.5\qquad<span class='latex-bold'>(C) </span>182\qquad<span class='latex-bold'>(D) </span>188.5\qquad<span class='latex-bold'>(E) </span>201

Problem Statement