Min-Max problem

Mo2men wrote:In a test comprising 50 questions, a student attempts all questions. For every correct answer the student is awarded 1 mark. She will get negative marks for incorrect answers as per the following rule.

1. 0.25 negative mark for each of the first 10 incorrect answer.
2. 0.5 negative mark for each incorrect answer, from the 11th to the 20th.
3. 0.75 negative mark for each incorrect answer, from the 21st.

What is the minimum number of questions that the student should get right to get a non-negative score?

A. 22
B. 18
C. 23
D. 21
E. 17

We can PLUG IN THE ANSWERS, which represent the least number of questions that must be answered correctly to yield a nonnegative score.
Since we need the least number of questions, start with the smallest answer choice.

E: 17
Points earned for 17 correct answers = 17*1 = 17.
Total number of incorrect answers = 50-17 = 33.
Since 0.25 points are lost for each of the first 10 incorrect answers, points lost for the first 10 incorrect answers = 10(0.25) = 2.5
Since 0.5 points are lost for each of the next 10 incorrect answers, points lost for the next 10 incorrect answers = 10(0.5) = 5.
Since 0.75 points are lost for each of the remaining 13 incorrect answers, points lost for the remaining 13 incorrect answers = 13(0.75) = 9.75.
Resulting score:
Points earned - points lost = 17 - (2.5 + 5 + 9.75) = 17 - 17.25 = -0.25.
Since the resulting score is negative, eliminate E.

Since the next biggest answer choice -- 18 -- will include an additional correct answer, the resulting score will be nonnegative.

The correct answer is B.

GMATGuruNY wrote:

Mo2men wrote:In a test comprising 50 questions, a student attempts all questions. For every correct answer the student is awarded 1 mark. She will get negative marks for incorrect answers as per the following rule.

1. 0.25 negative mark for each of the first 10 incorrect answer.
2. 0.5 negative mark for each incorrect answer, from the 11th to the 20th.
3. 0.75 negative mark for each incorrect answer, from the 21st.

What is the minimum number of questions that the student should get right to get a non-negative score?

A. 22
B. 18
C. 23
D. 21
E. 17

We can PLUG IN THE ANSWERS, which represent the least number of questions that must be answered correctly to yield a nonnegative score.
Since we need the least number of questions, start with the smallest answer choice.

E: 17
Points earned for 17 correct answers = 17*1 = 17.
Total number of incorrect answers = 50-17 = 33.
Since 0.25 points are lost for each of the first 10 incorrect answers, points lost for the first 10 incorrect answers = 10(0.25) = 2.5
Since 0.5 points are lost for each of the next 10 incorrect answers, points lost for the next 10 incorrect answers = 10(0.5) = 5.
Since 0.75 points are lost for each of the remaining 13 incorrect answers, points lost for the remaining 13 incorrect answers = 13(0.75) = 9.75.
Resulting score:
Points earned - points lost = 17 - (2.5 + 5 + 9.75) = 17 - 17.25 = -0.25.
Since the resulting score is negative, eliminate E.

Since the next biggest answer choice -- 18 -- will include an additional correct answer, the resulting score will be nonnegative.

The correct answer is B.

Thanks Mitch.

I have a question that confused me.
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.

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

Where is the problem in my thinking??

Mo2men wrote:Thanks Mitch.

I have a question that confused me.
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.

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

Where is the problem in my thinking??

Let's say the following 32 problems are answered incorrectly:
1, 3, 4, 5, 7, 8, 10, 12, 13, 14
15, 16, 17, 19, 20, 21, 22, 24, 25, 26
27, 28, 29, 30, 33, 34, 36, 40, 41, 42
43, 44

The set in red constitutes the first 10 incorrect answers.
Thus, each of these answers receives a mark of -0.25.

The set in blue constitutes the 11th through 20th incorrect answers.
Thus, each of these answers receives a mark of -0.5.

The set in green constitutes incorrect answers from the 21st.
Thus, each of these answers receives a mark of -0.75.