In a class test 5 marks are given for every correct answer and ( - 2 ) marks are given for every incorrect answer and no marks for not attempting any question. C scores ( - 5 ) marks by attempting 13 questions. How many questions has C attempted correctly and how many has C attempted incorrectly?

Answer 1

number correct --- x , where 0 ≤ x ≤ 13
number incorrect --- y
number not answered 13-x-y

5x - 2y + 0(13-x-y) = -5

5x - 2y = -5
we need integer solutions for this equation
y = (5x + 5)/2
the numerator must be even, so x must be odd
if x=1, y=5
if x = 3, y = 10
if x = 5, y = 15 , not possible from here on

So two cases:
1 correct, 5 wrong, 7 not attempted
check: 1(5) + 5(-2) = -5

3 correct, 10 wrong, all attempted
check: 3(5) + 10(-2) = -5