Tie at the Interview Cutoff: Arithmetic and Rule Changes
A coaching institute conducts a 200-mark mock PGT exam: Section A (General Awareness, Reasoning, Arithmetic, Language) 100 marks and Section B (subject) 100 marks. There are 2,400 candidates and 300 vacancies; the institute's policy is to call three times the vacancies, so 900 candidates, for interview. Qualifying marks are 40 in each section. The draft merit list uses simple total marks, with a tie-break of higher Section A. At total 120, 55 candidates are tied. Of these, 40 can be called; 15 must be excluded. Candidate X has A=62, B=58. Candidate Y has A=56, B=64. X is ranked 40th in the tie group under the stated rule; Y is 41st. A subject panel argues that Section B should carry 60 per cent weight because it is post-specific, and that Y should therefore be called. The institute must decide whether to change the rule after the exam, and how to document the decision. A further proposal is to lower the total cutoff to 118, which would add 70 candidates.
1. Verify the arithmetic of the 900-call list and the tie. How many of the 55 tied candidates can be called, and what is the call ratio if the cutoff is lowered to 118?
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Above 120 there are 860 candidates. The 900th call therefore falls inside the 55 candidates at 120: 900 − 860 = 40 can be called and 55 − 40 = 15 must be excluded. The tie is real because the selection boundary cuts through an equal-total group.
If the total cutoff is lowered to 118, the additional eligible pool is 70. Total eligible becomes 860 + 55 + 70 = 985. With 300 vacancies, the call ratio is 985/300 = 3.28, which exceeds the 1:3 policy. Lowering the cutoff without increasing vacancies would break the stated ratio; the institute would need either to cap the call list at 900 or to revise the policy prospectively.
2. Apply the stated tie-break and the panel's proposed weighting to X and Y. Who is selected under each, and which rule should govern?
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Under the stated rule, X and Y both have 120. The tie-break is higher Section A: X has 62 against Y's 56, so X is selected. Under the panel's 40:60 weighting, X = 0.4(62) + 0.6(58) = 24.8 + 34.8 = 59.6; Y = 0.4(56) + 0.6(64) = 22.4 + 38.4 = 60.8, so Y would be selected.
The governing rule should be the one published in the notification before the exam. A weighting change after candidates have written the paper is retroactive and unfair unless the original notification was ambiguous or contained a demonstrable error. The panel's subject-specific argument is a reason to change the rule for the next cycle, not to re-rank this cycle. The institute should retain X and record the clause relied on.
3. Draft a short grievance response explaining the decision and one process safeguard for future exams.
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A grievance response should: (a) quote the notification clause on total marks and the Section A tie-break; (b) show the arithmetic - 860 above 120, 40 of 55 tied candidates called, X at 62 in Section A and Y at 56; (c) state that the weighting proposal was considered and rejected because it was not published before the exam; (d) confirm that all tied candidates were treated by the same rule. A future safeguard is to publish the weighting, tie-break order, and call ratio in the advertisement, and to add a final deterministic tie-break such as date of birth or roll number. A pre-result audit of the boundary group would catch the problem before grievances arise.