CAT 2017 Slot 1 — DILR Question 15
Answer the following question based on the information given below.
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 all the three parameters, as shown in the following table:
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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 Zooma:
Further, the following are known:
- Amda and Calla jointly have the lowest total score, 7, with identical scores in all the three parameters.
- Zooma has a total score of 17.
- All the 3 countries, which are categorized 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?
Answer & solution
- A
14
15
- C
16
- D
17
Let us tabulate the information given in the bar graph depicting the number of countries against the happiness index score for each attribute.
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There are 2 possibilities for Amda and Calla’s scores. Since each of them has identical scores for each of the 3 attributes, we need a pair of identical scores for each of the 3 attributes.
If Zooma had scores of 6, 6 and 5 in C, S and F respectively, then Benga and Delma would have their highest scores in S and F (not nesessarily in that order).
Further, the country which scored the highest is S could score 5 in F and the country which scored the highest in F could score 5 in S.
Now since both Benga and Delma have equal scores and the equal score has to be in the category of C for both of them, the only possibility for this is when each of them scores 3 in C (as for no score higher than 3 do we have a pair of identical scores for C). So the maximum possible score when Benga and Delma have equal scores is 7 + 5 + 3 = 15
If Zooma gets a score of 7 in F, 6 in S and 4 in C, then one amongst Benga and Delma will get a score of 7 in S and the other a score of 6 in C.
The country with a score of 7 in S could score 5 in F. However since Zooma has scored 4 in C, the country with a score of 7 in S and 5 in F can only have a score of 3 in C.
This gives a total of 15. So the country with a score of 6 in C can have a score of 5 and 4 in F and S (though not essentially in that order). So in this case too the maximum possible score is 15.
Hence, option (b).