A test has 160 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?	Select
A) 23
B) 25
C) 27
D) 29
E) 31
A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points.   Let C be the number of correct answers and let I be the number of incorrect answers.   To get 40 points, a test taker must have at least 40 correct answers. Then C=&gt; 40.   For every correct question above 40, the test taker has 4 incorrect answers.   Then, the I = 4*(C - 40).   Also, I + C &lt;= 160. Thus 5C &lt;= 320 and so C &lt;= 64.   Then 40 &lt;= C &lt;= 64 and C can have 25 possible values.   The answer is 25.
<result>B</result>
A test has 160 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?