Calculate Test Score: 5 Points Right, -2 Points Wrong in 20-Question Exam

In math class it was decided to give:

5 Points for each correct answer,

(-2) for each incorrect answer,

(-4) for each answer without a solution.

In the exam there were 20 questions.

What is the grade of the student who solved all questions correctly, except 4 questions he/she got wrong?

Let's follow the step-by-step solution:

• Calculate the points from the correct answers:

There are 16 correct answers. For each correct answer, the student gets $5$ points.

$\text{Points from correct answers} = 16 \times 5 = 80$.

• Calculate the points from incorrect answers:

There are 4 incorrect answers. For each incorrect answer, the student loses $2$ points.

$\text{Points from incorrect answers} = 4 \times (-2) = -8$.

• Calculate the total score:

The student answered all questions, so there are no unanswered questions.

The total score is the sum of the points from correct and incorrect answers.

$\text{Total Score} = 80 + (-8) = 72$.

Thus, the total grade of the student is $72$.