On a ten question math test, each correct answer is worth 5 points, each unanswered question is worth 1 point, and each incorrect answer is worth 0 points. What scores greater than 40 are not possible to achieve?

the score is 5x+y where x is correct answers y is unanswered questions,

5x+y >40

x+y <=10

5x+y +10>40+x+y

4x> 30

x>=8

x = 8, y = 0, 1 or 2, score = 40, 41, 42

x = 9, y = 0, 1 score = 45, 46

x = 10, y=0 score = 50

obvious score > 50 are impossible,

43, 44, 47,48,49 are also not possible

thank you! that was really helpful!

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