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?

Answer 1

The student should reallocate more time to question 2 on the physics exam, as it yielded more points per amount of time spent compared to question 1.

Step-by-step explanation:

The student is asking how they should reallocate their time between two questions on a physics exam to potentially score higher overall. Given that the student earned 4 extra points in the last few seconds on question 1 and 10 extra points on question 2, with total scores of 48 and 12 respectively, and spent the same amount of time on each, the data suggests that question 2 yields a higher return on investment of time. Therefore, it would be more efficient to spend more time on question 2 if the exam were to be taken again.

However, it is also essential to consider whether the questions carry the same weight and if the student feels they can maintain the same efficiency over a prolonged period. Without more information, it is assumed that the points per time ratio would remain constant, and reallocating time to question 2 would likely increase the total score.

Answer 2

If you could take the exam again, you should spend more time solving the question 2.

Step-by-step explanation:

In the last few seconds of each question, you gained:

4 extra points in question 1. These points are a small fraction of your question 1 score.

10 extra points in question 2. These points are a large fraction of your question 2 score.

You gained 6 extra points in question 2 from the extra time. These 10 extra points are also a large fraction of the question 2 score, while your question 1 score was already good enough. This means that if you could take the exam again, you should spend more time solving the question 2.