SOLUTION: in a test 50 questions are there, students scores 1 mark for correct answer ,-1/3 for wrong answers and -1/6 for not attempt questions, if the net score of the student is 32 then t

Question 918961: in a test 50 questions are there, students scores 1 mark for correct answer ,-1/3 for wrong answers and -1/6 for not attempt questions, if the net score of the student is 32 then the numbef of questions answered wrongly by the student cannot be less than

Answer by Graeme(1) (Show Source): You can put this solution on YOUR website!
Let x be the number of questions answered correctly, and let y be the number of wrong answers. Then 50-x-y is the number of questions not attempted.

The question seeks to find the smallest possible value of y.

The score is x - y/3 - (50-x-y)/6

The score in this case is 32, so we have the equation 32 = x - y/3 - (50-x-y)/6

This simplifies to 32 = (7x-y-50)/6, and then we get
192 = 7x-y-50
242 = 7x-y
y = 7x - 242

242 is more than 7*34, so x has to be at least 35, or else y is negative.
So the smallest value of y occurs when x=35, and in that case, 7x - 242 is 3.

So the smallest value of y -- the smallest possible number of wrong answers -- is 3.

Now, are you curious to know what the largest possible number of wrong answers can be given that the total score is 32?

We already found out that when x=35, y=3, so 50-x-y (the number of questions not attempted) must be 12, because there are 50 questions.

Now, let's see what happens when x=36. We find from y=7x-242 that y has to be 10, and so 50-x-y=4 questions not attempted.

When x is 37, we get y=17, but this can't happen, because that's more than 50 questions.

And it only gets worse with larger x.

You can kinda see why, can't you? With each correct answer in excess of 32, you need some combination of 3 wrong answers or 6 unattempted questions to bring the score down to 32.

So if you get 37 or more correct answers, there just aren't any ways with just 13 wrong or unanswered questions to add up enough 1/3's and 1/6's to make up the difference between correct answers and 32.

So the largest possible number of wrong answers is 7*36 - 242, which is 10. In case you were wondering!

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