The Dean’s office recently scanned student results into the central computer system. When their character reading software cannot read something, it leaves the space blank. The scanner output reads as follows:
| Name | Finance | Marketing | Statistics | Strategy | Operations | GPA |
|---|
| Aparna | B | | F | | | 1.4 |
|---|
| Bikas | D | D | F | F | | |
|---|
| Chandra | D | A | F | F | | 2.4 |
|---|
| Deepak | A | B | D | D | | 3.2 |
|---|
| Fazal | D | F | B | D | | 2.4 |
|---|
| Gowri | C | C | A | B | | 3.8 |
|---|
| Hari | B | A | D | | | 2.8 |
|---|
| Ismet | B | A | | | | |
|---|
| Jagdeep | A | A | B | C | | 3.8 |
|---|
| Kunal | F | A | F | F | | 1.8 |
|---|
| Leena | B | A | B | F | | 3.2 |
|---|
| Manab | A | B | B | | | |
|---|
| Nisha | A | D | B | A | F | 3.6 |
|---|
| Osman | C | B | B | A | | 4.6 |
|---|
| Preeti | F | D | D | | | 3.2 |
|---|
| Rahul | A | C | A | F | | 4.2 |
|---|
| Sameer | C | F | B | | | |
|---|
| Tara | B | | | | | 2.4 |
|---|
| Utkarsh | F | C | A | | | 3.0 |
|---|
| Vipul | A | C | C | F | | 2.4 |
|---|
In the grading system, A, B, C, D, and F grades fetch \( 6, 4, 3, 2, \text{ and } 0 \) grade points respectively.
The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects. For example, Nisha’s GPA is:
\[ \text{GPA} = \frac{6 + 2 + 4 + 6 + 0}{5} = 3.6 \]
Some additional facts are also known about the students’ grades:
- Vipul obtained the same grade in Marketing as Aparna obtained in Finance and Strategy.
- Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.
- Tara received the same grade in exactly three courses.
