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Read the following passage:
In 2021, IIFT has announced the “Student of the year” competition which has twosteps: - the preliminary stage and the final stage. The preliminary stage comprised of overall academic excellence in the five trimesters of the coursework. When the results of the preliminary stage were announced, it was found that only five students -Aavanya, Aarav, Saanvi, Vagisha, and Raghav qualified to compete in the final stage of “Student of the year 2021” competition. In the final stage there were five rounds of extra-curricular activities wherein the students could score from 1 to 10 points in each round. These five extra-curricular activity rounds were Debate, Extempore, Business quiz, B-plan competition, and Case Study analysis. The student with maximum points across these five rounds would be considered as winner and would take the prestigious trophy of “Student of the year 2021”.
So at the end of these five rounds of competitions, when the Jury asked for the scorecard to find out the final winner, the scorer informed them that due to some technical glitches several entries have been deleted and jury was presented with following table:
However, the scorer has made the following observations too:
(i) No two students have scored equal points in the same round.
(ii) Vagisha has scored an odd number point in case study analysis round.
(iii) Aarav’s total score point was in the multiple of 8, and it was the least among all.
(iv) There was no tie between any two students in the overall/total points.
(v) Vagisha has scored same points in the following rounds: Debate round, and Extempore round.
(vi) None of the missing scores were less than 4 in any round.
(vii) Aavanya won the competition and won the prestigious trophy of “Student of the year 2021”.
Choose the correct pair of possibilities:
Possibility I: Raghav scored 8 points in debate round.
Possibility II: Vagisha's score in extempore round is twice of Aarav in the same round.
Possibility III: Vagisha scored 6 points in the debate round.
Possibility IV: Vagisha scores more points than Aavanya in the business quiz round.
From statement 6, all the missing points are at least 4.
From statement 3, Aarav's total is a multiple of 8 and is the least among the 5. The only possible score for Aarav is 24. Thus, the missing values are (4, 4, 4, 5).
Aavanya's total score is 35 and the total of points mentioned in the table is 26. Thus, the only possible values for the blanks are 4 and 5.
From statement 1, no two students have scored equal points in the same round.
Let Vagisha's score in the Debate and Extempore rounds be $$x$$. Thus, the table becomes as shown below.
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Possibility (I): Raghav scored 8 points in the debate round.
The total value of the blanks will be = $$29-8-3-10=7$$. Since each of the blanks has at least 4 points, this case is not possible.
Possibility (II): Vagisha's score in the extempore round is twice of Aarav's in the same round.
Thus, $$x=8 or 10$$
If $$x=8$$, the total of remaining blanks = $$33-8-8-8=9$$. The only possible values for the blanks are 4 and 5. Since, Both BP and CP already have 4 points, Vagisha cannot get 4 points. Thus, this case is not possible.
If $$x=10$$, the total of remaining blanks = $$33-8-10-10=5$$. Thus, this case is also not possible.
Possibility (III): Vagisha scored 6 points in the debate round.
If $$x=6$$, the total of remaining blanks = $$33-8-6-6=13$$. In this case, the remaining scores can be 6 and 7, respectively, such that it satisfies the condition in statement 2. Thus, this case is possible.
Possibility (IV): Vagisha scores more points than Aavanya in the business quiz round.
Let Vagisha scores 8 points in BQ and $$x=4$$. Thus, Vagisha's points in the CP round = $$33-4-4-8-8=9$$. Since Aavanya already scored 9 points in CP, this is not possible.
Let Vagisha scores 8 points in BQ and $$x=6$$. Thus, Vagisha's points in the CP round = $$33-8-6-6-8=5$$. This looks plausible but in this case, Raghav's possible points do not fit the conditions.
Similarly, for other cases, this possibility is found to be invalid.
Hence, the answer is option C.
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