Question 1208821
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Let k be the number of correct answers,  0 <= k <= 10.


Then the number of wrong answers is 10-k.


The formula for the score as the function of "k" is

    S(k) = 4k - (10-k) = 5k - 10.


So, when k =   0,  1, 2, 3,  4,  5,  6,  7,  8,  9, 10,  the values for S(k) are

             -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40 .


Thus, 11 different values of scores are possible.
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Solved.