The Scholarship Shortlist
A selection board must rank four candidates for two scholarships using three weighted criteria: academic score (weight 50%), leadership (weight 30%), and interview (weight 20%). Scores are out of 100.
- Candidate A: academic 88, leadership 60, interview 70
- Candidate B: academic 80, leadership 85, interview 65
- Candidate C: academic 84, leadership 70, interview 90
- Candidate D: academic 92, leadership 55, interview 60
A rule states that no candidate with an interview score below 65 may receive a scholarship, regardless of weighted total. The board must also break any tie in favour of the higher leadership score.
1. Compute each candidate's weighted total and produce a ranking.
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Weighted total = 0.5·academic + 0.3·leadership + 0.2·interview.
- A: 0.5×88 + 0.3×60 + 0.2×70 = 44 + 18 + 14 = 76.0
- B: 40 + 25.5 + 13 = 78.5
- C: 42 + 21 + 18 = 81.0
- D: 46 + 16.5 + 12 = 74.5
Ranking by total: C (81.0) > B (78.5) > A (76.0) > D (74.5).
2. Apply the eligibility rule and decide who receives the two scholarships. Show the effect of the rule explicitly.
Read the worked answer
Interview threshold is 65. A has 70 (eligible), B has 65 (eligible - the rule says below 65, so 65 passes), C has 90 (eligible), D has 60 (ineligible). D is removed despite ranking fourth anyway, so the top two eligible are C and B. Note the trap: D's high academic score (92) is the strongest single number but cannot rescue an ineligible interview score. The correct answer is C and B; a student who awards D on academic merit alone has ignored the hard rule.
3. Suppose the weights were changed to academic 40%, leadership 40%, interview 20%. Does the outcome change? Justify.
Read the worked answer
Recompute:
- A: 0.4×88 + 0.4×60 + 0.2×70 = 35.2 + 24 + 14 = 73.2
- B: 32 + 34 + 13 = 79.0
- C: 33.6 + 28 + 18 = 79.6
- D: 36.8 + 22 + 12 = 70.8 (still ineligible)
Eligible ranking: C (79.6) > B (79.0) > A (73.2). The same two candidates (C and B) win, and the order is unchanged, though the margin between C and B narrows from 2.5 to 0.6. Conclusion: the outcome is robust to this weight change - a useful check that the decision is not an artefact of arbitrary weights.