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

1. 6 2. 12 3. 3 4. 9

Soln. (3) — Let the number of correct answers be ‘x’, number of wrong answers be ‘y’ and

number of questions not attempted be ‘z’.

Thus, x + y + z = 50 … (i)

And x – y – z 32

3 6

The second equation can be written as,

6x – 2y – z = 192 … (ii)

Adding the two equations we get,

7x – y = 242 or x = 242 + y

7

Since, x and y are both integers, y cannot be 1 or 2. The minimum value that y can

have is 3.

can u explain why Y can not be 1 or 2....i tried to make 242/7+Y integer but even 3 is not enough

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