Question

Prof Liu gave the same quiz to the students in her morning class and in her afternoon class. the average score for the two classes combined was 84. which class had more students ?

(1) The average score for the students in the morning class was 80
(2) the average score for the students in the afternoon class was 86

Answer 1

Explanation:

Given that Prof Liu gave the same quiz to the students in her morning class and in her afternoon class. the average score for the two classes combined was 84.

(1) The average score for the students in the morning class was 80

(2) the average score for the students in the afternoon class was 86

Let m be the no of students in I class and n in II class

Total of I class = 80m and

Total of II class = 86n

Total of both classes = 80m +86n

Average =
`(80m+86n)/(m+n) = 84`

m cannot be equal to n because in that case average would have been 83

If m >n, then say n =m+a

then average =
`(80m+86m+86a)/(2m+a) =84`

Because 86 is more times added, average score would decrease hence we would not get 84.

So I class is getting less score of 80 to get a score average of more than 83 (the average) the class II should have more students.