A test has 50 questions A student scores 1 mark for a correct answer ndash 1 3 for a wrong answer an...........

Quantitative Aptitude ( CCS) Ratio, Proportion

A test has 50 questions. A student scores 1 mark for a correct answer, –1/3 for a wrong answer, and –1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

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Explanation:

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
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 or the smallest possible number of wrong answers is 3.