Critical Reasoning

problem in official guide 12th edition page:38 problem no:31

Cheever College offers several online courses via remote computer connection, in addition to traditional classroom-based courses. A study of student performance at Cheever found that, overall, the average student grade for online courses matched that for classroom-based courses. In this calculation of the average grade, course withdrawals were weighted as equivalent to a course failure, and the rate of withdrawal was much lower for students enrolled in classroom-based courses than for students enrolled in online courses.

If the statements above are true, which of the following must also be true of Cheever College?

(A) Among students who did not withdraw, students enrolled in online courses got higher grades, on average, than students enrolled in classroom-based courses.
(B) The number of students enrolled per course at the start of the school term is much higher, on average, for the online courses than for the classroom-based courses.
(C) There are no students who take both an online and a classroom-based course in the same school term.
(D) Among Cheever College students with the best grades, a significant majority take online, rather than classroom-based, courses.
(E) Courses offered online tend to deal with subject matter that is less challenging than that of classroom-based courses.

Answer by OG is 'A'

My opinion is that 'A' is wrong answer.. below is my explanation....

Case 1: Number of students in both 'online' and 'classrooms' are equal

Assume 5 students in each class

3 students withdrew or fail in the online class ( 3 students have score of zero)
2 students withdrew or fail in the classroom ( 2 students have score of zero)
This satisfies the given: the rate of withdrawal was much lower for students enrolled in classroom-based courses than for students enrolled in online courses.

assume average score for online = average score for classroom = 15

average score for online=total student grades/number of students in online class= (5+70+0+0+0)/5 =15
average score for classroom= student grades/number of students in classroom = (20+5+50+0+0)/5 =15

average score for online for students who did not withdraw = (5+70)/2= 37.5
average score for classroom for students who did not withdraw = (20+5+50)/3= 25

since 37.5 is greater than 25 then Answer 'A' is correct.

Case 2: Number of students in both 'online' and 'classrooms' are different

assume 10 students in online , 5 students in classroom

3 students withdrew or fail in the online class ( 3 students have score of zero)
2 students withdrew or fail in the classroom ( 2 students have score of zero)

assume average score for online = average score for classroom = 15

average score for online== (24+24+24+24+24+0+0+0)/8 =15
average score for classroom= (20+5+50+0+0)/5 =15

average score for online for students who did not withdraw = (24+24+24+24+24)/5= 24
average score for classroom for students who did not withdraw = (20+5+50)/3= 25

since 24 is less than 25 , then Answer 'A' is wrong !!!!!

Can please someone explain what I might be doing wrong ?

I was typing this as Rich was typing something similar...

The flaw in your explanation is that it says "the rate of withdrawal" is much lower for traditional classes - not the number of withdrawals.

3 out of 10 is a lower rate than 2 out of 5.



Can I say one more thing? It is a good idea to wrestle with these Official Guide questions, but the way to wrestle with them is to try to figure out how you can get them right in the future. These questions are tested over and over, you can believe that the official answers that you actually find in the printed version of the official guide are correct. Answers that you find online need to be confirmed, however.

Thanks a lot.. Rich and David for your help .. this was very helpful