CAT 2017 Slot 1 — DILR Question 16
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:
âââââââ
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.
If Benga scores 16 and Delma scores 15, then what is the maximum number of countries with a score of 13?
Answer & solution
- A
0
1
- C
2
- D
3
Let us tabulate the information given in the bar graph depicting the number of countries against the happiness index score for each attribute.
âââââââ
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 we take scores of Zooma as 7 in F, 6 in S and 4 in C, then Benga can get a score of 16 only by scoring 6 in C and 5 each in S and F.
Benga getting a score of by 16 by scoring 7 in S, 5 in F and 4 in C is not possible as Zooma scores 4 in C. Then Delma can score 15 by scoring 7 in S, 5 in F and 3 in C.
If we assume Zooma scored 6 in C, 6 in S and 5 in F, then Benga can get a score of 16 by scoring 7 and 5 in S and F (not essentially in that order) and 4 in C.
Delma then can also get a score of 15 by scoring 7 and 5 in S and F (again not essentially in that order) and 3 in C. The 2 cases can be as listed below:
âââââââ
âââââââ
So we will have one score each of 5 in F and S each. From other scores of 4 and 3 we will have either three 4’s in S, one 4 in F, one 3 in S and two 3’s in F and C or one 4 in S, F and C each, two 3’s in F and four 3’s in C.
These 2 cases are also dependent on the individual score S of Amda and Calla. In either case, as there is only one 5 in S and F and only one 4 in C, there is a possibility of only are score of 13 by having S-5, F-5, C-3 in the 1st case or a score of S-5, F-4, C-4 or F-5, S-4, C-4 in the 2nd case.
Hence, option (b).