Question

An instructor has graded 25 exam papers submitted by students in a class of 26 students, and the average so far is 70. (The maximum possible score is 100.) How high would the score on the last paper have to be to raise the class average by 1 point?


By 2 points?

Answer 1

Case - 1: Average to be increased by 1 point:

Current average for 25 students = 70

Required average for 26 students = 71

Let the score of 26th exam paper is X. Then:

70*25 + X = 71*26

X = 71*26 - 70*25 = 96

Case - 2: Average to be increased by 2 points:

Current average for 25 students = 70

Required average for 26 students = 72

Let the score of 26th exam paper is X. Then:

70*25 + X = 72*26

X = 72*26 - 70*25 = 122

But this is not possible because maximum marks one can get is 100. Hence, raising average by 2 points is not possible.