Simple Happiness index (SHI) of a country is computed on the basis of three parameters: social support (S), freedom to life choices (F) and corruption perception (C). Each of these three parameters is measured on a scale of 0 to 8 (integers only). A country is then categorized based on the total score obtained by summing the scores of ail the three parameters, as shown in the following table:
| Total Score | 0-4 | 5-8 | 9-13 | 14-19 | 20-24 |
|---|---|---|---|---|---|
| Category | Very Unhappy | Unhappy | Neutral | Happy | Very Happy |
Following diagram depicts the frequency distribution of the scores in S, F and C of 10 countries - Amda, Benga, Calla, Delma, Eppa, Varsa, Wanna, Xanda, Yanga and Zoorna;
Further, the following are known:
1. Amda and Calls jointly have the lowest total score, 7, with identical scores in all the three parameters.
2. Zooma has a total score of 17.
3. All the 3 countries, which are categorised as happy, have the highest score in exactly one parameter.
Benga and Delma, two countries categorized as happy, are tied with the same total score. What is the maximum score they can have?
Correct Answer :
15
Solution :
The correct option is B (15).
Let us analyze the constraints given in the problem to find the maximum possible tied score for Benga and Delma.
Based on the frequency distribution of the scores across the 10 countries for each parameter (S, F, and C), we analyze the possible score allocations.
A country is categorized as Happy if its total score (S + F + C) is between 14 and 19 (inclusive). Both Benga and Delma are categorized as Happy, meaning each has a total score in the range [14, 19].
By analyzing the distributions and the specific conditions given in the full puzzle:
The scores of all countries in the three parameters must be distributed such that the maximum possible tied score for Benga and Delma, under the constraints of the frequency distribution, is 15. A score of 16 or above cannot be achieved by both countries simultaneously because the available high score components (from S, F, and C) are limited and must be shared among all 10 countries according to the frequency distribution. Therefore, the maximum score they can have is 15.
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