Problem Solving - Equations

GMAT Problem Solving Question

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

Correct Answer : Choice B. Minimum of 18 questions correct. 

Explanatory Answer

The student has to get a non-negative mark. 

The quickest way to solve this question is to back substitute answers.

Let us start with the smallest number in the given set. 17 questions correct and 33 incorrect.

If she had got 17 questions correct, she will get 17 * 1 - (10 * 0.25 + 10 * 0.5 + 13 * 0.75)
i.e., she will get 17 - (2.5 + 5 + 9.75) = 17 - 17.25 = -0.25 marks.

So, if she got only 17 questions correct she will end up with a negative mark.

If she had got 18 questions correct, then she will get -0.25 + 1.75 = 1.5 mark, a non-negative mark.

Correct answer is choice B.