Solution
Understanding the set :-
- This set gives information about an examination, with 5 subjects (English, Hindi, Mathematics, Science and Social Science) out of which a few of the examinations could not be conducted.
- Students missed whether - 0/1/or 2 papers
- If a student missed only one examination - 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 - 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.
- If a student appeared in all five examinations - the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations.
| Name | 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 most important thing to understand in this set is,
i) If the student miss 2 papers - marks in the paper missed will be the average of the marks in the paper given.
=> for eg - if the marks in 3 subjects is 80, 90, 100
then, marks in other two subjects will be 90 each.
ii) If the student miss 1 papers - marks in the paper missed will be the average of the best 3 paper given.
=> for eg - if the marks in 4 subjects is 70, 80, 90, 100
then, marks in other two subjects will be 90 (average of best three papers).
| Name | 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 |
Clue 2 says,
The student who missed the Mathematics examination did not miss any other examination.
This indicates that the Maths score is bound to be the average of the best 3 out of the 4 exam scores obtained by this candidate.
Based on this inference, we can proceed with identifying the math score that can be represented as an average of the rest of the scores.
A) For Deep and Esha :
Their scores in mathematics is 100 and 95 respectively.
Which is highest compared to other subjects
=> Their Maths score can't be the average
=> Deep and Esha haven't missed their maths exam.
| Name | English | Hindi | Mathematics | Science | Social Science |
|---|---|---|---|---|---|
| Alva | 80 | 75 | 70 (x) | 75 | 60 |
| Bithi | 90 | 80 | 55 (x) | 85 | 85 |
| Carl | 75 (x) | 80 (x) | 90 (missed) | 100 (x) | 90 (x) |
| Deep | 70 | 90 | 100 (x) | 90 | 80 |
| Esha | 80 | 85 | 95 (x) | 60 | 55 |
| Foni | 83 | 72 | 78 (x) | 88 | 83 |
For Alva:
Average of best three = 80 + 75 + 75 / 3 which is not equal to their mathematics score.
For Bithi :
Average of best three is not equal to their mathematics score.
For Foni :
Average of best three is not equal to their mathematics score.
For Carl :
Average of best three 100 + 90 + 80 / 3 = 90 which is equal to his maths score.
Therefore, Carl has missed his mathematics paper
Also, it is the only paper he has missed.
| Name | English | Hindi | Mathematics | Science | Social Science |
|---|---|---|---|---|---|
| Alva | 80 (x) | 75 (missed) | 70 (x) | 75 | 60 (x) |
| Bithi | 90 | 80 (x) | 55 (x) | 85 | 85 |
| Carl | 75 (x) | 80 (x) | 90 (missed) | 100 (x) | 90 (x) |
| Deep | 70 (x) | 90 (missed) | 100 (x) | 90 | 80 (x) |
| Esha | 80 | 85 (x) | 95 (x) | 60 | 55 |
| Foni | 83 | 72 (x) | 78 (x) | 88 | 83 |
Clue 3 says,
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.
Now doing the same we did for maths :
- For Alva -
Average of best three = 80 + 75 + 70 / 3 = 75 = his Hindi score
- For Bithi -
Average of best three = 90 + 85 + 85 / 3 which is not equal to bithi's hindi score.
therefore, bithi haven't missed her hindi paper
- For Carl :
We already know carl has only missed his mathematics paper.
- For Deep :
Average of best three = 100 + 90 + 80 / 3 = his score in hindi paper.
- For Esha :
Average of best three is not equal to her hindi score.
- For Foni :
Average of best three is not equal to her hindi score.
=> Two students who missed their Hindi paper are Alva and Deep.
And, One of them did not missed any other paper.
| Name | English | Hindi | Mathematics | Science | Social Science |
|---|---|---|---|---|---|
| Alva | 80 (x) | 75 (missed) | 70 (x) | 75 | 60 (x) |
| Bithi | 90 (x) | 80 (x) | 55 (x) | 85 | 85 |
| Carl | 75 (x) | 80 (x) | 90 (missed) | 100 (x) | 90 (x) |
| Deep | 70 (x) | 90 (missed) | 100 (x) | 90 | 80 (x) |
| Esha | 80 (missed) | 85 (x) | 95 (x) | 60 (x) | 55 (x) |
| Foni | 83 (missed) | 72 (x) | 78 (x) | 88 (x) | 83 |
For English,
We know 4 students have given english paper.
Three of them are Alva, Carl, and Deep
Now checking for other three :
- Bithi :
She has highest score in english
=> English can't be the average of Bithi.
Therefore, Esha and Foni have missed their English paper.
| Name | English | Hindi | Mathematics | Science | Social Science |
|---|---|---|---|---|---|
| Alva | 80 (x) | 75 (missed) | 70 (x) | 75 | 60 (x) |
| Bithi | 90 (x) | 80 (x) | 55 (x) | 85 | 85 (missed) |
| Carl | 75 (x) | 80 (x) | 90 (missed) | 100 (x) | 90 (x) |
| Deep | 70 (x) | 90 (missed) | 100 (x) | 90 | 80 (x) |
| Esha | 80 (missed) | 85 (x) | 95 (x) | 60 (x) | 55 (x) |
| Foni | 83 (missed) | 72 (x) | 78 (x) | 88 (x) | 83 (missed) |
For Social science ,
We know 4 people have given English paper
which are, Alva, Carl, Deep, Esha.
Therefore, Two students who have not given Social science paper are - Bithi and Foni.
| Name | English | Hindi | Mathematics | Science | Social Science |
|---|---|---|---|---|---|
| Alva | 80 (x) | 75 (missed) | 70 (x) | 75 | 60 (x) |
| Bithi | 90 (x) | 80 (x) | 55 (x) | 85 (missed) | 85 (missed) |
| Carl | 75 (x) | 80 (x) | 90 (missed) | 100 (x) | 90 (x) |
| Deep | 70 (x) | 90 (missed) | 100 (x) | 90 | 80 (x) |
| Esha | 80 (missed) | 85 (x) | 95 (x) | 60 (x) | 55 (x) |
| Foni | 83 (missed) | 72 (x) | 78 (x) | 88 (x) | 83 (missed) |
For science,
Now , we know 4 students have given Science paper.
Three we have found to be - Carl, Esha, Foni
So two students who have missed science paper will be among - Alva, Bithi, and Deep
Now, we know, Alva ad Deep have missed their Hindi paper.
And, clue 3 says,
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.
=> One of Alva and Deep have not missed any other exam.
=> Only one of Alva and Bithi have missed their Science exam
=> Bithi will definately miss her Science exam and along with her one of Alva and Deep will miss the exam.
| Name | English | Hindi | Mathematics | Science | Social Science |
|---|---|---|---|---|---|
| Alva | 80 (x) | 75 (missed) | 70 (x) | 75 | 60 (x) |
| Bithi | 90 (x) | 80 (x) | 55 (x) | 85 (missed) | 85 (missed) |
| Carl | 75 (x) | 80 (x) | 90 (missed) | 100 (x) | 90 (x) |
| Deep | 70 (x) | 90 (missed) | 100 (x) | 90 | 80 (x) |
| Esha | 80 (missed) | 85 (x) | 95 (x) | 60 (x) | 55 (x) |
| Foni | 83 (missed) | 72 (x) | 78 (x) | 88 (x) | 83 (missed) |
We are definite about Bithi, Carl, Esha and Foni
More from this set:
Question 13