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.
What BEST can be concluded about the students who did not appear for the Hindi examination?
What BEST can be concluded about the students who missed the Science examination?
From the fourth paragraph, it is very clear that if the student miss exactly two exams, them his / her marks in those two subjects would be the average of best two scores and would also be “EQUAL”
By properly analysing the table, we can conclude that Esha is the only student who do not score equal marks in any two subjects. Hence, Esha is one of the student who missed exactly one subject.
Marks obtained by the student in the missed examination is the average of Best three scores, and the average/mean cannot be lowest or highest value.
Considering this concept of averages, Isha can miss examination of English, Hindi or Science.
If Esha missed English Exam, then her marks in that exam would be \(\frac{{95 + 85 + 60}}{3}\) or 80. Eventually she scored 80 only in English. Hence Esha could miss examination of English
If Esha missed Hindi Exam, then her marks would be \(\frac{{95 + 85 + 60}}{3}\) or 60. This contradicts with value given the table if Esha missed science Exam, then her marks in science exam would be \(\frac{{80 + 85 + 95}}{3}\) or 86.6. Again contradiction
In conclusion, Esha missed the exam of exactly subject that is English
From the second fact, we can infer that one of student missed exam of only Mathematics.
If Alva missed Maths exam, then her scored would be \(\frac{{80 + 75 + 75}}{3} = 76.66\). This value contradicts with value given the table Hence Alva did not miss the Math Exam
If Bithi missed the Maths Exam, then her score would not be the lowest score (55)
If Carl missed the Maths exam, then his score would be\(\frac{{80 + 100 + 90}}{3}\) o r 270 Carl could be the student who missed the maths exam.
If Deep missed the Maths exam then he can’t score the highest marks of 100
If Foni missed the Maths exam then her score in that exam would be \(\frac{{83 + 88 + 83}}{3}\) Or 84.6.
This contradicts with value given in the table. In conclusion, Carl is the student who missed the exam of only mathematics.
From the third fact, we can conclude that one student missed only Hindi exam. Another student missed two exams one Hindi and one more. Two students among Alva, Bithi, Deep and Foni would be in this category.
If Alva missed only Hindi exam, then her score would be \(\frac{{80 + 70 + 75}}{3}\) or 75 marks score. If Alva missed two exams, then her score in both the exam would be equal.
Alva can miss Hindi and science, and her score in both these exam in the average of \(\frac{{80 + 70}}{2} = 75\) marks scored
In conclusion, Alva can miss only Hindi exam or Hindi and science both
If Bithi missed Hindi exam, then the score would be \(90 + 85 + 85\) or 86.6.The contradicts with value in the table
If Deep missed Hindi exam, then his score would be \(\frac{{100 + 90 + 80}}{3}\) or 90. Makes score
If Deep missed Hindi and science, then his score would be \(\frac{{100 + 80}}{2}\) or 90. Again marks score
In conclusion Deep missed the exam of only Hindi or Hindi and science If Foni missed Hindi, then her score would be \(\frac{{83 + 88 + 83}}{3} = 87.66.\) This contradicts with value of given that table
After analysing the third fact, we can conclude that one among Alwa and deep missed only Hindi and the other missed Hindi and science.
So far we have analysed missed exams as Alwa, Carl. Deep and Foni.
Only Bithi and Foni left
From the first fact, we can conclude that
Exactly two students missed English exam.
Exactly two students missed Hindi exam.
Exactly two students missed Science and Exactly two students missed Social, Science
Social Science was missed by two students and those 2 students must be Bithi and Foni
We need to make sure apart from Esha, one more student missed English exam. Between Bithi and Foni, the scores are equal in Social score and English. In conclusion, Foni missed the exams of English and Social.
We also need to make sure apart from Alva or Deep, one more student missed Science exam and the only possibility is Bithi.
Alwa \( \to \) Only Hindi or Hindi + Science
Bithi \( \to \) Science and Social Science
Carl \( \to \) Only mathematics
Deep \( \to \) Only Hindi or Hindi and Science
Foni \( \to \) English and social science
Question 1: Option: 4
Question 2: Option: 3
Question 3: Option: 1
Question 4: Option: 4
Question 5: Answer: 3
Question 6: Answer: 4
