CAT 2020 Slot 1 — DILR Question 9
Answer the next 6 questions based on the information given below.
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.
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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.
Who among the following did not appear for the Mathematics examination?
Answer & solution
Carl
- B
Esha
- C
Foni
- D
Alva
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).