Board Examination
CAT 2020 Slot 1 · DILR · Medium · Data Interpretation
Passage / data set
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.
| Student | 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: I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations. II. The student who missed the Mathematics examination did not miss any other examination. III. 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.
Question 1 of 6
Who among the following did not appear for the Mathematics examination?
- A.
Carl
- B.
Alva
- C.
Esha
- D.
Foni
A
Explanation
For Carl, English=75, Hindi=80, Science=100, Social Science=90. Average of best three among these 4 scores = (80 + 100 + 90)/3 = 270/3 = 90, which matches his Mathematics score of 90. Thus, Carl missed the Mathematics examination.
Question 2 of 6
Which students did not appear for the English examination?
- A.
Cannot be determined
- B.
Alva and Bithi
- C.
Carl and Deep
- D.
Esha and Foni
D
Explanation
Esha: Hindi=85, Math=95, Science=60, Social Science=55. Average of best 3 = (85+95+60)/3 = 80, matching English score 80. Foni: English score 83 is the average of best 3 among (72, 78, 88, 83) => (78+88+83)/3 = 249/3 = 83, matching English score. Thus, Esha and Foni missed the English examination.
Question 3 of 6
What BEST can be concluded about the students who did not appear for the Hindi examination?
- A.
Two among Alva, Deep and Esha
- B.
Alva and Esha
- C.
Alva and Deep
- D.
Deep and Esha
C
Explanation
From the rules, exactly two students missed Hindi. Testing Alva and Deep shows that their Hindi scores match the required average condition.
Question 4 of 6
What BEST can be concluded about the students who missed the Science examination?
- A.
Deep and Bithi
- B.
Alva and Bithi
- C.
Alva and Deep
- D.
Bithi and one out of Alva and Deep
D
Explanation
Bithi missed Science, and the other student who missed Hindi also missed Science (which is either Alva or Deep).
Question 5 of 6
How many out of these six students missed exactly one examination?
3
Explanation
Carl, Foni, and one out of Alva/Deep missed exactly one exam. Thus, 3 students missed exactly one exam.
Question 6 of 6
For how many students can we be definite about which examinations they missed?
4
Explanation
We can definitely determine the missed exams for 4 students: Carl, Bithi, Esha, and Foni.
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