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.
| English | Hindi | Mathematics | Science | Social Science | |
| Alva | 80 | 75 | 70 | 75 | 60 |
| Bithi | 90 | 80 | 55 | 85 | 85 |
| Carl | 75 | 80 | 90 | 100 | 90 |
| Deep | 70 | 90 | 100 | 90 | 80 |
| Esha | 80 | 85 | 95 | 60 | 55 |
| Foni | 83 | 72 | 78 | 88 | 83 |
The following facts are also known.
- Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.
- The student who missed the Mathematics examination did not miss any other examination.
- 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.1 Who among the following did not appear for the Mathematics examination?
- Carl
- Esha
- Foni
- Alva
Explanation
Q.1 From the information given in point I, II and III , we can say 4 students appeared in each of English, Hindi, Science, and Social Science examinations. Or we can say there were exactly two students who missed each of four subjects English, Hindi, Science, and Social Science.
Now from the table given, it is clear that either Deep or Alva should have missed the Hindi and Science examination as they are the only students to have same marks in both subjects.
Also Alva , Bithi , Deep, Esha and Foni can’t miss mathematics, So only Carl missed Mathematics exam.
From Table we can say –
Foni’s marks we can say Foni was absent in English and Social Science.
Esha must have missed English Examination.
Baithi Should have missed Science and Social Science.
Now we can make the following table about the students who missed a particular subjects .
| Student | English | Hindi | Mathematics | Science | Social Science |
| Alva | 80 | 75 | 70 | 75 | 60 |
| Baithi | 90 | 80 | 55 | Missed | Missed |
| Carl | 75 | 80 | Missed | 100 | 90 |
| Deep | 70 | 90 | 100 | 90 | 80 |
| Esha | Missed | 85 | 95 | 60 | 55 |
| Foni | Missed | 72 | 78 | 88 | Missed |
Now As there were two students who missed Hindi and science . Baithi has already missed Science so one among Deep and Alva must missed Science and both of them missed Hindi.
Clearly Carl missed Mathematics . option 1)
Q.2 Which students did not appear for the English examination?
- Cannot be determined
- Carl and Deep
- Esha and Foni
- Alva and Bithi
Explanation
Q.2 From the information given in point I, II and III , we can say 4 students appeared in each of English, Hindi, Science, and Social Science examinations. Or we can say there were exactly two students who missed each of four subjects English, Hindi, Science, and Social Science.
Now from the table given, it is clear that either Deep or Alva should have missed the Hindi and Science examination as they are the only students to have same marks in both subjects.
Also Alva , Bithi , Deep, Esha and Foni can’t miss mathematics, So only Carl missed Mathematics exam.
From Table we can say –
Foni’s marks we can say Foni was absent in English and Social Science.
Esha must have missed English Examination.
Baithi Should have missed Science and Social Science.
Now we can make the following table about the students who missed a particular subjects .
| Student | English | Hindi | Mathematics | Science | Social Science |
| Alva | 80 | 75 | 70 | 75 | 60 |
| Baithi | 90 | 80 | 55 | Missed | Missed |
| Carl | 75 | 80 | Missed | 100 | 90 |
| Deep | 70 | 90 | 100 | 90 | 80 |
| Esha | Missed | 85 | 95 | 60 | 55 |
| Foni | Missed | 72 | 78 | 88 | Missed |
Now As there were two students who missed Hindi and science . Baithi has already missed Science so one among Deep and Alva must missed Science and both of them missed Hindi.
So Esha and Foni missed English .
Q.3 From the information given in point I, II and III , we can say 4 students appeared in each of English, Hindi, Science, and Social Science examinations. Or we can say there were exactly two students who missed each of four subjects English, Hindi, Science, and Social Science.
Now from the table given, it is clear that either Deep or Alva should have missed the Hindi and Science examination as they are the only students to have same marks in both subjects.
Also Alva , Bithi , Deep, Esha and Foni can’t miss mathematics, So only Carl missed Mathematics exam.
From Table we can say –
Foni’s marks we can say Foni was absent in English and Social Science.
Esha must have missed English Examination.
Baithi Should have missed Science and Social Science.
Now we can make the following table about the students who missed a particular subjects .
| Student | English | Hindi | Mathematics | Science | Social Science |
| Alva | 80 | 75 | 70 | 75 | 60 |
| Baithi | 90 | 80 | 55 | Missed | Missed |
| Carl | 75 | 80 | Missed | 100 | 90 |
| Deep | 70 | 90 | 100 | 90 | 80 |
| Esha | Missed | 85 | 95 | 60 | 55 |
| Foni | Missed | 72 | 78 | 88 | Missed |
Now As there were two students who missed Hindi and science . Baithi has already missed Science so one among Deep and Alva must missed Science and both of them missed Hindi.
Option 3) is correct .
Q.3 What BEST can be concluded about the students who did not appear for the Hindi examination?
- Two among Alva, Deep and Esha
- Deep and Esha
- Alva and Esha
- Alva and Deep
Explanation
Q.3 From the information given in point I, II and III , we can say 4 students appeared in each of English, Hindi, Science, and Social Science examinations. Or we can say there were exactly two students who missed each of four subjects English, Hindi, Science, and Social Science.
Now from the table given, it is clear that either Deep or Alva should have missed the Hindi and Science examination as they are the only students to have same marks in both subjects.
Also Alva , Bithi , Deep, Esha and Foni can’t miss mathematics, So only Carl missed Mathematics exam.
From Table we can say –
Foni’s marks we can say Foni was absent in English and Social Science.
Esha must have missed English Examination.
Baithi Should have missed Science and Social Science.
Now we can make the following table about the students who missed a particular subjects .
| Student | English | Hindi | Mathematics | Science | Social Science |
| Alva | 80 | 75 | 70 | 75 | 60 |
| Baithi | 90 | 80 | 55 | Missed | Missed |
| Carl | 75 | 80 | Missed | 100 | 90 |
| Deep | 70 | 90 | 100 | 90 | 80 |
| Esha | Missed | 85 | 95 | 60 | 55 |
| Foni | Missed | 72 | 78 | 88 | Missed |
Now As there were two students who missed Hindi and science . Baithi has already missed Science so one among Deep and Alva must missed Science and both of them missed Hindi.
Option 3) is correct .
Q.4 What BEST can be concluded about the students who missed the Science examination?
- Bithi and one out of Alva and Deep
- Deep and Bithi
- Alva and Deep
- Alva and Bithi
Explanation
Q.4 From the information given in point I, II and III , we can say 4 students appeared in each of English, Hindi, Science, and Social Science examinations. Or we can say there were exactly two students who missed each of four subjects English, Hindi, Science, and Social Science.
Now from the table given, it is clear that either Deep or Alva should have missed the Hindi and Science examination as they are the only students to have same marks in both subjects.
Also Alva , Bithi , Deep, Esha and Foni can’t miss mathematics, So only Carl missed Mathematics exam.
From Table we can say –
Foni’s marks we can say Foni was absent in English and Social Science.
Esha must have missed English Examination.
Baithi Should have missed Science and Social Science.
Now we can make the following table about the students who missed a particular subjects .
| Student | English | Hindi | Mathematics | Science | Social Science |
| Alva | 80 | 75 | 70 | 75 | 60 |
| Baithi | 90 | 80 | 55 | Missed | Missed |
| Carl | 75 | 80 | Missed | 100 | 90 |
| Deep | 70 | 90 | 100 | 90 | 80 |
| Esha | Missed | 85 | 95 | 60 | 55 |
| Foni | Missed | 72 | 78 | 88 | Missed |
Now As there were two students who missed Hindi and science . Baithi has already missed Science so one among Deep and Alva must missed Science and both of them missed Hindi.
Correct option 4).
Q.5 How many out of these six students missed exactly one examination?
Explanation
Q.5 From the information given in point I, II and III , we can say 4 students appeared in each of English, Hindi, Science, and Social Science examinations. Or we can say there were exactly two students who missed each of four subjects English, Hindi, Science, and Social Science.
Now from the table given, it is clear that either Deep or Alva should have missed the Hindi and Science examination as they are the only students to have same marks in both subjects.
Also Alva , Bithi , Deep, Esha and Foni can’t miss mathematics, So only Carl missed Mathematics exam.
From Table we can say –
Foni’s marks we can say Foni was absent in English and Social Science.
Esha must have missed English Examination.
Baithi Should have missed Science and Social Science.
Now we can make the following table about the students who missed a particular subjects .
| Student | English | Hindi | Mathematics | Science | Social Science |
| Alva | 80 | 75 | 70 | 75 | 60 |
| Baithi | 90 | 80 | 55 | Missed | Missed |
| Carl | 75 | 80 | Missed | 100 | 90 |
| Deep | 70 | 90 | 100 | 90 | 80 |
| Esha | Missed | 85 | 95 | 60 | 55 |
| Foni | Missed | 72 | 78 | 88 | Missed |
Now As there were two students who missed Hindi and science . Baithi has already missed Science so one among Deep and Alva must missed Science and both of them missed Hindi.
So there are exactly 3 students Esha, Carl and one among Alva and Deep who missed exactly one subject.
Correct Answer: 3
Q.6 For how many students can we be definite about which examinations they missed?
Explanation
Q.6 From the information given in point I, II and III , we can say 4 students appeared in each of English, Hindi, Science, and Social Science examinations. Or we can say there were exactly two students who missed each of four subjects English, Hindi, Science, and Social Science.
Now from the table given, it is clear that either Deep or Alva should have missed the Hindi and Science examination as they are the only students to have same marks in both subjects.
Also Alva , Bithi , Deep, Esha and Foni can’t miss mathematics, So only Carl missed Mathematics exam.
From Table we can say –
Foni’s marks we can say Foni was absent in English and Social Science.
Esha must have missed English Examination.
Baithi Should have missed Science and Social Science.
Now we can make the following table about the students who missed a particular subjects .
| Student | English | Hindi | Mathematics | Science | Social Science |
| Alva | 80 | 75 | 70 | 75 | 60 |
| Baithi | 90 | 80 | 55 | Missed | Missed |
| Carl | 75 | 80 | Missed | 100 | 90 |
| Deep | 70 | 90 | 100 | 90 | 80 |
| Esha | Missed | 85 | 95 | 60 | 55 |
| Foni | Missed | 72 | 78 | 88 | Missed |
Now As there were two students who missed Hindi and science . Baithi has already missed Science so one among Deep and Alva must missed Science and both of them missed Hindi.
So except Alva and Deep we can easily tell which student missed which exam. So the correct answer will be 4.
