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: 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 categorized as happy, have the highest score in exactly one parameter.
The provided information can be depicted in the following table. A and C jointly obtained a total score of 7, with equal scores in all these parameters. Therefore, the possible combinations are either 1, 2, and 4 or 3, 3, and 1. Since Zooma has a score of 17, and all three countries in the happy category secured the highest score in exactly one parameter, Zooma can have a score of 7 in F, 6 in S, and 4 in C. This is because a score of 7 in S and 6 in C would be the scores of the other two countries, and Zooma cannot have a distribution of 7, 7, and 5, as there is no country that scored a 5 in C. Amda can have a distribution of 3, 3, 1, or 4, 2, 1. In either case, the only possible score for F is 1, as no other parameter has a score of 1 for two countries.
The provided information can be depicted in the following table. A and C jointly obtained a total score of 7, with equal scores in all these parameters. Therefore, the possible combinations are either 1, 2, and 4 or 3, 3, and 1. Since Zooma has a score of 17, and all three countries in the happy category secured the highest score in exactly one parameter, Zooma can have a score of 7 in F, 6 in S, and 4 in C. This is because a score of 7 in S and 6 in C would be the scores of the other two countries, and Zooma cannot have a distribution of 7, 7, and 5, as there is no country that scored a 5 in C. As mentioned earlier, Zooma's score in C is determined to be 6.
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Question: 3
Benga and Delma, two countries categorized as happy, are tied with the same total score. What is the maximum score they can have?
The provided information can be depicted in the following table. A and C jointly obtained a total score of 7, with equal scores in all these parameters. Therefore, the possible combinations are either 1, 2, and 4 or 3, 3, and 1. Since Zooma has a score of 17, and all three countries in the happy category secured the highest score in exactly one parameter, Zooma can have a score of 7 in F, 6 in S, and 4 in C. This is because a score of 7 in S and 6 in C would be the scores of the other two countries, and Zooma cannot have a distribution of 7, 7, and 5, as there is no country that scored a 5 in C. In the provided table, Zoom achieved the highest scores with 7 in F, 6 in S, and 4 in C. The optimal remaining scores for Benga and Dalma could be: As it is given that both had the same total score, it can only be 15 for both, i.e., Benga’s score in S or F was one less than the maximum possible.
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Question: 4
If Benga scores 16 and Delma scores 15, then what is the maximum number of countries with a score of 13?
The provided information can be depicted in the following table. A and C jointly obtained a total score of 7, with equal scores in all these parameters. Therefore, the possible combinations are either 1, 2, and 4 or 3, 3, and 1. Since Zooma has a score of 17, and all three countries in the happy category secured the highest score in exactly one parameter, Zooma can have a score of 7 in F, 6 in S, and 4 in C. This is because a score of 7 in S and 6 in C would be the scores of the other two countries, and Zooma cannot have a distribution of 7, 7, and 5, as there is no country that scored a 5 in C. Considering the scores of Zoom, Benga, and Delma as 17, 16, and 15, we get: If Benga scores 16 and Dalma scores 15 (as illustrated in the previous solution), the highest possible values that remain are:
