Question

suppose that in the last few seconds you devoted to question 1 on your physics exam you earned 4 extra points, while in the last few seconds you devoted to question 2 you earned 10 extra points. you earned a total of 48 and 12 points, respectively, on the two questions, and the total time you spent on each was the same. if you could take the exam again, how—if at all—should you reallocate your time between these questions?
○ spend more time on question 1. you get more points from question 1 than you do on question 2.
○ spend more time on question 2. you’ll get more extra points on question 2 than you’ll lose on question 1.
○ do it the same way. you get 60 points that way.

Explanation:

To determine the optimal time allocation, we analyze the marginal (extra) points per unit time. Let the time spent on each question's last few seconds be \( t \). For question 1, marginal points per \( t \) is \( \frac{4}{t} \) (4 extra points in time \( t \)). For question 2, marginal points per \( t \) is \( \frac{10}{t} \) (10 extra points in time \( t \)). Since \( \frac{10}{t}>\frac{4}{t} \), spending more time on question 2 gives more extra points per unit time. The first option is wrong (total points ≠ marginal points), the third is wrong (60 is total, but marginal analysis matters). So the correct reasoning is the second option: spending more time on question 2 gives more extra points per time.

Answer:

Spend more time on question 2. You'll get more extra points on question 2 than you'll lose on question 1.