In a recruitment process, the selection of candidates is based on their performance in three components. The weightages of the components 1, 2 and 3 are 0.2, 0.3 and 0.5, respectively. Use the data given below and find the cutoff score if exactly three candidates are to be selected:

The correct option is (a) - 5.1.

[as per provisional answerkey]

Solution

The question asks for the cutoff score such that exactly three candidates are selected. The final score for each candidate is calculated using the weighted average formula:
Final Score = (Score 1 * 0.2) + (Score 2 * 0.3) + (Score 3 * 0.5)

Let's calculate the final score for each candidate:
Candidate 1: $(5\times 0.2)+(4\times 0.3)+(6\times 0.5)=1.0+1.2+3.0$ = 5.2
Candidate 2: $(4\times 0.2)+(6\times 0.3)+(5\times 0.5)=0.8+1.8+2.5$ = 5.1
Candidate 3: $(3\times 0.2)+(2\times 0.3)+(8\times 0.5)=0.6+0.6+4.0$ = 5.2
Candidate 4: $(9\times 0.2)+(4\times 0.3)+(3\times 0.5)=1.8+1.2+1.5$ = 4.5
Candidate 5: $(8\times 0.2)+(8\times 0.3)+(2\times 0.5)=1.6+2.4+1.0$ = 5.0

Now, let's arrange the scores in descending order:
1. Candidate 1: 5.2
2. Candidate 3: 5.2
3. Candidate 2: 5.1
4. Candidate 5: 5.0
5. Candidate 4: 4.5

To select exactly three candidates (Candidates 1, 3, and 2), the cutoff must be the score of the third-ranked candidate. If the cutoff is set at 5.1, candidates with scores ≥ 5.1 are selected. This includes Candidate 1 (5.2), Candidate 3 (5.2), and Candidate 2 (5.1), totaling exactly three candidates.

Why the other options are incorrect

• Option (b) - 5.2: If the cutoff were 5.2, only Candidate 1 and Candidate 3 would be selected (2 candidates), failing the requirement of selecting exactly three.
• Option (c) - 5.3: If the cutoff were 5.3, no candidates would be selected as the highest score achieved is 5.2.
• Option (d) - 5.4: Similar to 5.3, a cutoff of 5.4 is higher than all individual scores, resulting in zero selections.

Key Concept

Weighted Average and Ranking: The cutoff for selecting 'n' candidates is determined by the score of the n-th candidate when all scores are sorted in descending order.