There are two examinations, A and B in a subject which are evaluated out of 30 and 70 marks, respectively. In order to pass the course the student has to get at least 40% in total and at least 40 % in B. The following are the marks of the students S1 to S4. The only student/s to have passed is/are Students A B S1 12 28 S2 10 29 S3 16 27 S4 05 29
S1
Pass Course Criteria Analysis
To pass the course, a student must meet two conditions:
- Get at least 40% of the total marks.
- Get at least 40% in Examination B.
Let's first calculate the minimum marks required for each condition.
The maximum marks for Examination A are 30, and for Examination B are 70. The total maximum marks for the course is \(30 + 70 = 100\).
Minimum total marks required to pass:
\( 40\% \text{ of } 100 = \frac{40}{100} \times 100 = 40 \text{ marks} \)
Minimum marks required in Examination B to pass:
\( 40\% \text{ of } 70 = \frac{40}{100} \times 70 = \frac{2800}{100} = 28 \text{ marks} \)
So, a student passes if they score at least 40 total marks AND at least 28 marks in Exam B.
Student Performance Evaluation
Now, let's evaluate each student based on these criteria. We will calculate their total marks and check if they meet both passing conditions.
| Student | Marks in A (out of 30) | Marks in B (out of 70) | Total Marks (out of 100) | Total Marks ≥ 40? | Marks in B ≥ 28? | Passed? |
|---|---|---|---|---|---|---|
| S1 | 12 | 28 | \(12 + 28 = 40\) | Yes (\(40 \ge 40\)) | Yes (\(28 \ge 28\)) | Yes |
| S2 | 10 | 29 | \(10 + 29 = 39\) | No (\(39 < 40\)) | Yes (\(29 \ge 28\)) | No (Failed Total) |
| S3 | 16 | 27 | \(16 + 27 = 43\) | Yes (\(43 \ge 40\)) | No (\(27 < 28\)) | No (Failed in B) |
| S4 | 05 | 29 | \(05 + 29 = 34\) | No (\(34 < 40\)) | Yes (\(29 \ge 28\)) | No (Failed Total) |
From the evaluation, only Student S1 meets both passing conditions (Total marks ≥ 40 and Marks in B ≥ 28).
Identifying Passing Students
Based on the analysis:
- S1 passed because the total marks (40) are ≥ 40 and marks in B (28) are ≥ 28.
- S2 failed because the total marks (39) are < 40, even though marks in B were sufficient.
- S3 failed because marks in B (27) are < 28, even though total marks were sufficient.
- S4 failed because the total marks (34) are < 40, even though marks in B were sufficient.
Therefore, the only student who passed the course is S1.
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