Question: Who among the following did not appear for the Mathematics examination?
Explanation:
For the subjects missed, the student gets average of top 2 or 3 scores.
∴ Among the six students given, no students would’ve missed that subject where they get highest of the lowest marks.
Also, in the missed subject(s) the student cannot get 2nd lowest marks.
∴ For the missed subject(s), the student will get 2nd highest or 3rd highest marks.
English is missed by 2 students. These two students can only be Esha and Foni.
(For Esha and Foni English is neither highest nor lowest)
Solving for Esha:
Esha has missed English.
∴ Marks in English should be average of top three of the remaining subjects.
Average of remaining top three marks = (95 + 85 + 60)/3 = 80 (which is equal to Esha’s marks in English).
One of the students missed only Mathematics. Carl is the only one who could’ve missed Mathematics.
Solving for Carl
∴ Carl will not miss any other exam.
One of the students missed Hindi and Science. This can be either Alva or Deep since they both have same marks in Hindi and Science.
One of the students missed only Hindi. This can be either Alva, Deep since their marks in Hindi is same as average of the remaining top 3 scores.
∴ One of Alva or Deep missed only Hind and the other missed Hindi and Science.
So far we have
Alva missed ⇒ only Hindi or Hindi and Science
Carl ⇒ only Mathematics
Deep missed ⇒ only Hindi or Hindi and Science
Esha missed ⇒ only English
Alva and Deep definitely missed Hindi
Esha and Foni definitely missed English
One of Alva or Deep missed Science
We need to find one more person who missed Science and two more people who missed Social Science.
One more person who could’ve missed Science is Bithi and two more people who could’ve missed Social Science are Bithi and Foni
∴ We finally have
Alva missed ⇒ only Hindi or Hindi and Science
Carl missed ⇒ only Mathematics
Bithi missed ⇒ Science and Social Science
Deep missed ⇒ Hindi and Science or only Hindi
Esha missed ⇒ only English
Foni missed ⇒ English and Social Science
∴ Carl missed the Mathematics exam.
Hence, option (a).