In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations.
The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations.
If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for.
If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for.
The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.
The following facts are also known.
I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.
II. The student who missed the Mathematics examination did not miss any other examination.
Ill. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.
Q. 5 Who among the following did not appear for the Mathematics examination?
1) Alva
2) Foni
3) Esha
4) Carl
Q. 6 Which students did not appear for the English examination?
1) Cannot be determined
2) Carl and Deep
3) Esha and Foni
4) Alva and Bithi
Q. 7 What BEST can be concluded about the students who did not appear for the Hindi examination?
1) Alva and Deep
2) Deep and Esha
3) Alva and Esha4) Two among Alva, Deep and Esha
Q. 8 What BEST can be concluded about the students who missed the Science examination?
1) Deep and Bithi
2) Alva and Deep
3) Alva and Bithi
4) Bithi and one out of Alva and Deep
Q. 9 How many out of these six students missed exactly one examination? _______ TITA
Q. 10 For how many students can we be definite about which examinations they missed? _______ TITA
Answer
- Esha & Foni
- Alva and Deep
- Bithi & Alva/Deep
- 3 Students
- 4 Students
Based on the information provided in points I, II, and III, we can conclude that there were either 4 students who took each of the English, Hindi, Science, and Social Science exams, or exactly two students who missed each of these four subjects.
Looking at the table provided, it becomes evident that either Deep or Alva must have missed the Hindi and Science exams, as they are the only students with identical marks in both of these subjects. Additionally, Alva, Bithi, Deep, Esha, and Foni cannot have missed the Mathematics exam. Therefore, Carl is the only one who missed the Mathematics exam.
Based on the table, we can deduce the following:
- Foni’s marks suggest that she was absent for the English and Social Science exams.
- Esha must have missed the English Examination.
- Bithi should have missed the Science and Social Science exams.
Now, we can create a table indicating which subjects each student missed:
| Student | Missed Subjects |
|---|---|
| Alva | Hindi, Science |
| Bithi | Science, Social Science |
| Carl | Mathematics |
| Deep | Hindi, Science |
| Esha | English |
| Foni | English, Social Science |
