The composite score for each city is computed as a weighted average of its ratings on these factors, where ratings range from 1 to 10. The fund allocation for each city will be directly proportional to its composite score, reflecting its overall attractiveness for establishing new offices based on market potential, infrastructure quality, and cost of living considerations.
If the composite scores of cities A, B, and C are 7.2, 7.8, and 6.5 respectively, calculate the total fund allocation for these three cities.
- 105 million USD
- 112.5 million USD
- 120 million USD
- 127.5 million USD
The Correct Option is B
Solution and Explanation
Total composite score for A, B, and C \(= 7.2 + 7.8 + 6.5 = 21.5\)
Total fund allocation for these cities = \(\left( \frac{21.5}{\text{Total composite score}} \right) \times 150 \text{ million USD}\)
Assuming equal weightage for all cities, total composite score
\(= 5 \times\) average composite score \(= 5 \times 7.2 = 36\)
Total fund allocation =\(\left( \frac{21.5}{36} \right) \times 150\) million USD = 112.5 million USD
If city D's fund allocation is 40 million USD and its composite score is 8, what is the composite score of city E, given that its fund allocation is 30 million USD?
- 6
- 6.5
- 7
- 7.5
The Correct Option is A
Solution and Explanation
Fund allocation is directly proportional to composite score.
Ratio of fund allocations for D and E = \(\frac{40}{30} = \frac{4}{3}\)
Ratio of composite scores for D and \(E = \frac{8}{x}\)
Equating the ratios: \(\frac{4}{3} = \frac{8}{x}\)
\(x = 2\times3 = 6\)
If the weightage for market potential is increased to 50%, and all other factors remain constant, would the total fund allocation for cities with above-average market potential:
- Increase
- Decrease
- Remain the same
- Cannot be determined
The Correct Option is A
Solution and Explanation
If a new factor, "Talent Availability," is introduced with a weightage of 15%, how would this affect the calculation of composite scores and fund allocation?
- Composite scores would increase, fund allocation would increase for all cities.
- Composite scores would decrease, fund allocation would decrease for all cities.
- Composite scores would change, fund allocation distribution might change.
- Composite scores would remain unchanged, fund allocation would remain unchanged.
The Correct Option is C
Solution and Explanation
If the average cost of living in city A is 20% higher than in city C, and the infrastructure score of city A is 2 points lower than city C, then which of the following statements is definitely true?
- City A has a higher market potential than city C
- City A has a lower composite score than city C.
- City A has a higher fund allocation than city C.
- None of the above
The Correct Option is D
Solution and Explanation
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