Two of the mathematics professors at Enormous State are Professor A (known for easy grading) and Professor F (known for tough grading). Last semester, roughly half of Professor F's class consisted of former students of Professor A; these students apparently felt encouraged by their (utterly undeserved) high grades. (Professor F's own former students had fled in droves to Professor A's class to try to shore up their grade point averages.) At the end of the semester, as might have been predicted, all of Professor A's former students wound up with a C- or lower. The rest of the students in the class--former students of Professor F who had decided to "stick it out"-fared better, and three quarters of them earned higher than a C-. After discovering what had befallen them, all the students who earned C- or lower got together and decided to send a delegation to the Department Chair to complain that their grade point averages had been ruined by this callous and heartless beast! The contingent was to consist of 20 representatives selected at random from among them. How many of the 20 would you estimate to have been former students of Professor A ?
A)4
B) 17
C) 15
D) 10
E) 16

Question

Two of the mathematics professors at Enormous State are Professor A (known for easy grading) and Professor F (known for tough grading). Last semester, roughly half of Professor F's class consisted of former students of Professor A; these students apparently felt encouraged by their (utterly undeserved) high grades. (Professor F's own former students had fled in droves to Professor A's class to try to shore up their grade point averages.) At the end of the semester, as might have been predicted, all of Professor A's former students wound up with a C- or lower. The rest of the students in the class--former students of Professor F who had decided to "stick it out"-fared better, and three quarters of them earned higher than a C-. After discovering what had befallen them, all the students who earned C- or lower got together and decided to send a delegation to the Department Chair to complain that their grade point averages had been ruined by this callous and heartless beast! The contingent was to consist of 20 representatives selected at random from among them. How many of the 20 would you estimate to have been former students of Professor A  ?
A)4
B) 17
C) 15
D) 10
E) 16

Quizplus · Accepted Answer

Given that all of Professor A's former students ended up with a C- or lower and that they made up roughly half of Professor F's class, it's reasonable to assume that a significant majority of the students who received a C- or lower were from Professor A's class. Since the question asks for an estimate and considering that the other half of the class (Professor F's former students) did better overall, with three quarters of them earning higher than a C-, it's logical to conclude that most of the students who received a C- or lower were Professor A's students. Therefore, estimating that 16 out of the 20 representatives would have been former students of Professor A seems reasonable, given the distribution of grades and the initial class composition.

Two of the Mathematics Professors at Enormous State Are Professor