In a test comprising 50 questions, a student attempts all questions.

The student has to get minimum questions right. That means maximum wrong. So we have to assume he got all of the first 10 and also 11th to 20th questions wrong (since this questions have less negative penalty)

So the negative penalty value becomes: (-0.25)*10 + (-0.50)*10= -2.5 - 5.0= -7.5

now let us assume he solved 'n' out of 30 the remaining questions correctly. That means (30-n) questions wrong.

so equation: n*1 + (-0.75)*(30-n)=0 we get n= 120/7= 17.14 , so least value of n should be 18 to get a non-negative score
>>>My answer 18

To have minimum number of correct questions, he must have maximum number of incorrect questions.

Suppose 1st 10 questions are all incorrect= 2.5 (negative marks)
Suppose 11-20 questions are wrong= 5 (negative marks)

In order to balance negative 7.5 marks, he must have 8 correct questions from Q21 to Q50

Now, he has 22 remaining questions, in which he can have 4 wrong questions (.75*4=3) for every 3 correct questions (3*1=3)
Number of right questions he can have = 22*3/7= 9.___= 10 (approximately)

Hence he can have 10 +8= 18 minimum correct questions.

B is the answer

IMO B.

By poe:

From A you will difference of -0.25

17 X1 - (10 x0.25 + 10x 0.50 + 13 x 0.75)
17 - 17.25 = -0.25

From B the difference is +0.50.

Dear Bunuel

According to the OA, the minimum number should be 18. However, I if the whole wrong answers were in the last category then it should not be the right answer as per my below:

18 right = 18 mark

32 is wrong (30 in last category and 2 wrong answers in second one)

30 * 0.75 + 2 * 0.5 = 23.5 (negative)

the result = 18 - 23.5 = -4.5

Why did we assume the he answered first 10 wrong and then second 10 wrong and 2 from last category? He might answered got the whole wrong answers from the last one as shown above.

Thanks

You assume that each question in the list of 50 questions has some specific negative mark assigned to it if it's answered incorrectly. So, you assume that the questions numbered from 1 through 10 have 0.25 negative mark, from 11 through 20 have 0.5 negative mark and from 21st to 50 have 0.75 negative mark. That's not what the question is saying. The placement of a question in the list of 50 questions does not matter. If say, ONLY one question is answered incorrectly it still gets 0.25 negative mark no matter whether it's Q#1 or Q#50. If say 10 questions are answered incorrectly, all of them will get 0.25 negative mark no matter which questions they are in the list. So, only the number of incorrectly answered questions matter and not their placement in the list of the questions.

Hope it's clear.

Why did we assume the he answered first 10 wrong and then second 10 wrong and 2 from last category? He might answered got the whole wrong answers from the last one as shown above.

We have to assume the last 17 are wrong because the question asked us to find the minimum number of questions.
If the question asked maximum then yes , we have to assume the first 17 are correct.

Hope this helps , if so click a kudos

C - number of correct questions
C + 20 (first 20 incorrect questions) + I (number of incorrect questions after 20) = 50
I = 30 - C
to get non-negative mark
\(C >= 10 * 0.25 + 10 * 0.5 + 0.75 * I\)
\(C >= 2.5 + 5 + 0.75(30 - C)\)
=> rearranging , 1.75C >= 30 => C >= 17.x => 18 (B)

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