The least the student can get is -15 when he answers all wrong.
The next possibility is 14 wrong, so -14.
Thus he can get each of the possible scores in the lower range.

What about upper end?
He can get max of 15*3 or 45 marks.
But he cannot get 43 and 44 as he does not have any more questions for negative marking.
He can get 42 marks by answering 14 right. He is left with one question, it can be left or answered incorrectly, so 42-1 or 41.
But again he cannot score 40 as he does not have any more questions left to answer.
Lesser than that he can get all possible values as his score. For example 13 correct and two not attempted or 13 correct and one not attempted and one wrong or 13 correct and two wrong.

Thus he can get all scores from -15 to 45 except 44, 43 and 40. => (45-(-15)+1)-3=61-3=58


B
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Maximum Score obtainable = 15x3=45
Minimum Score Obtainable = 15x-1=-15

44, 43, 40 are not possible

So, scores possible = {-15,-14,-13,----45} - {40,43,44}
Nos. of score possible = 61-3 = 58