Mabel is studying for an entrance exam which has a verbal section and quantitati
ID: 1206639 • Letter: M
Question
Mabel is studying for an entrance exam which has a verbal section and quantitative section. She has 10 hours to study and wants to maximize her combined score. Her schedule relating expected scores and studying are given below.
a. What is the marginal gain by spending an extra hour on verbal and quantitative part of the exam? (write up the table in your answer book)
b. In order to maximize her combined score what is the criteria? Using the criteria you set, how many hours should she put into the verbal section and how many into the quantitative section?
Explanation / Answer
Answer:
a. What is the marginal gain by spending an extra hour on verbal and quantitative part of the exam?
The marginal gain from extra hours for Verbal = Change Verbal in score/ Change in hours
Example: 65 – 55 / 2 – 1 = 10
The marginal gain from extra hours for Quantitative = Change Quantitative in score/ Change in hours
Example: 78 – 70 / 2 – 1 = 8
The marginal gain from extra hours for both parts of the exam explained in the following table:
Hours
Verbal
Marginal gain from Verbal
Quantitative
Marginal gain from Quantitative
1
55
-
70
-
2
65
10
78
8
3
75
10
87
9
4
84
9
90
3
5
91
7
92.5
2.5
6
94
3
94.5
2
7
96.5
2.5
96
1.5
8
98.5
2
97
1
9
99
0.5
97.5
0.5
10
99
0
97.9
0.4
b. In order to maximize her combined score what is the criteria? Using the criteria you set, how many hours should she put into the verbal section and how many into the quantitative section?
To maximize her score with spending additional 5 hours, that is 2hours should she put into the verbal section and 3hours into the quantitative section.
Hours
Verbal
Marginal gain from Verbal
Quantitative
Marginal gain from Quantitative
1
55
-
70
-
2
65
10
78
8
3
75
10
87
9
4
84
9
90
3
5
91
7
92.5
2.5
6
94
3
94.5
2
7
96.5
2.5
96
1.5
8
98.5
2
97
1
9
99
0.5
97.5
0.5
10
99
0
97.9
0.4
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