Danny Featherweight is taking a tough course in law school. His professor agreed to give him a course grade of max{ 2x, 3y} where x and y are the number of answers he gets right on the first and second midterms, respectively. Danny needs a course grade of 150 to pass. He finds that for the first midterm, for every A minutes of study, he will get one more answer right. For the second midterm, for every B minutes that he studies, he will get one more answer right. If he doesn't study at all, Danny will get nothing right on either exam. All Danny cares about is passing. He doesn't want to waste any time getting a higher grade than he needs.
A) If, then Danny will not study for the second exam.
B) The ratio of the time Danny spends on exam 1 to the time he spends on exam 2 will be.
C) The ratio of the time Danny spends on exam 2 to the time he spends on exam 1 will be.
D) If A

Question

Danny Featherweight is taking a tough course in law school. His professor agreed to give him a course grade of max{ 2x, 3y} where x and y are the number of answers he gets right on the first and second midterms, respectively. Danny needs a course grade of 150 to pass. He finds that for the first midterm, for every A minutes of study, he will get one more answer right. For the second midterm, for every B minutes that he studies, he will get one more answer right. If he doesn't study at all, Danny will get nothing right on either exam. All Danny cares about is passing. He doesn't want to waste any time getting a higher grade than he needs.
A) If, then Danny will not study for the second exam.
B) The ratio of the time Danny spends on exam 1 to the time he spends on exam 2 will be.
C) The ratio of the time Danny spends on exam 2 to the time he spends on exam 1 will be.
D) If A < B, then Danny will not study for the first exam.
E) Danny will spendminutes studying for each exam.

Quizplus · Accepted Answer

Since Danny only cares about passing and getting the minimum grade he needs, he should try to maximize his course grade with the least amount of studying possible. In order to do this, he should focus on the midterm that will give him the highest possible grade.

The maximum grade he can get on the first midterm is 2x, while the maximum grade he can get on the second midterm is 3y. Therefore, he should focus on the second midterm since it has the potential to give him a higher grade.

If Danny doesn't study for the second exam, his maximum grade will be 2x. If he studies for the second exam, the maximum grade he can get is 3y, which may or may not be higher than 2x (depending on the value of x and y). Therefore, it's not worth the risk of studying for the second exam if he only cares about passing.

Therefore, the best choice is A.

Danny Featherweight Is Taking a Tough Course in Law School