a test has 12 problems and each problem is worth 5 marks. Full marks are given for a correct answer, 2 marks are given if there is no answer, and no marks given for an incorrect answer. Some scores between 1 and 60, are impossible to get on this test. What is the sum of these impossible-to-get scores
I don't have a mathematical proof,
but I think the only impossible-to-get scores are 1 and 3.
If I'm correct, the sum of these impossible-to-get scores would be 4.
Let x be the number of correct answers,
let y be the number of no answers.
score = 5x+2y
Here I have just written the possible scores in a way that is easier to see.
You can add them together yourself.