Question

as the day wears on.

time	total flashcards reviewed
8:00 am	100
9:00 am	175
10:00 am	225
11:00 am	250

use the table to answer the following questions.

the marginal, or additional, gain from ananya’s second hour spent working, from 8:00 am to 9:00 am, is \boxed{75} flashcards.

the marginal gain from ananya’s fourth hour spent working, from 10:00 am to 11:00 am, is \boxed{25} flashcards.

the following week, ananya meets with her biomedical engineering instructor, who offers her some helpful study advice. based on years of experience, the instructor notes that reviewing 37.5 flashcards tends to improve a student’s test score by about the same amount as spending an hour reviewing lecture notes. for simplicity, assume students are able to review lecture notes at a constant pace, with equal effectiveness across each hour of study.

given this information, in order to use her 4 hours of time spent studying to get the highest possible test score, how many hours should she have spent reviewing flashcards, and how many hours should she have spent reviewing lecture notes?

\\(\circ\\) 0 hours reviewing flashcards, 4 hours reading
\\(\circ\\) 1 hour reviewing flashcards, 3 hours reading
\\(\circ\\) 2 hours reviewing flashcards, 2 hours reading
\\(\circ\\) 3 hours reviewing flashcards, 1 hour reading

Explanation:

Step1: Calculate marginal gains for each hour of flashcards

• 1st hour (7 - 8 AM): Gain = 100 - 0 = 100 flashcards. Equivalent lecture notes gain: 100 / 37.5 ≈ 2.67 (but we compare per hour, so 1 hour of flashcards here gives more than 1 hour of lecture notes (which is 37.5 flashcards equivalent)).
• 2nd hour (8 - 9 AM): Gain = 175 - 100 = 75. 75 > 37.5, so better to do flashcards.
• 3rd hour (9 - 10 AM): Gain = 225 - 175 = 50. 50 > 37.5, better to do flashcards.
• 4th hour (10 - 11 AM): Gain = 250 - 225 = 25. 25 < 37.5, so better to do lecture notes here.

Step2: Allocate hours

We want to use hours where flashcards give more than 37.5 flashcards equivalent (i.e., marginal gain > 37.5).

• 1st hour: 100 > 37.5 → flashcards.
• 2nd hour: 75 > 37.5 → flashcards.
• 3rd hour: 50 > 37.5 → flashcards.
• 4th hour: 25 < 37.5 → lecture notes.

So total flashcards hours: 3, lecture notes hours: 1.

Answer:

D. 3 hours reviewing flashcards, 1 hour reading