Problem Solving

EMPOWERgmat

A student's grade in a college course is determined by the scores of 5 quizzes, a midterm exam and a final exam. The midterm exam and the final exam both count twice as much as a quiz in determining the student's average grade. If the student averages a score of 80 on the quizzes and scored a 90 on the midterm exam, then what would the student have to score on the final exam to have an overall average grade of 85 for the entire course?

A. 85.5
B. 90
C. 92.5
D. 93.5
E. 95

OA C

Here, we have to look at how much weightage each test carries while calculating overall grade.

As per the question, the midterm and the final exam both have double weightage compared to one quiz.
Take weightage of each quiz = X %
So weightage of 5 quizzes = 5X % , that of midterm exam = 2X % and that of final exam = 2X %
Take overall final marks = 100.
So overall wightage = 5X + 2X + 2X = 9X % = 100
So X = 11.11 %

Now, average score of 5 quizzes is 80.
But as collective weightage of 5 quizzes = 5X = 55.55 %
$$contribution\ of\ 5\ quizzes\ in\ overall\ marks\ =\ 80*0.5555\ \approx44$$
Same way contribution of midterm exam = 22.22 % of 90 = 20

Overall marks = 44 + 20 = 64
So we need 21 marks more which must be contribution of end term exam.

21 = 22.22 % of endterm exam
$$and\ end\ term\ exam\ \approx92.5 $$
which is answer option C.