Read the following and answer the questions that follow
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 categorised based on the total score obtained by summing the scores of all 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 Zooma:
Further, the following are known:
1. Amda and Calla 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.
[CAT 2017 S1]
14) What is Amda's score in F?
Answer:
15) What is Zooma's score in S?
Answer:
16) Benga and Delma, two countries categorized as happy, are tied with the same total score. What is the maximum score they can have?
(1) 14
(2) 15
(3) 16
(4) 17
17) If Benga scores 16 and Delma scores 15, then what is the maximum number of countries with a score of 13?
(1) 0
(2) 1
(3) 2
(4) 3
Solution
The lowest score possible score that any country could have got is S=3, F=1 and C=2, which gives us a total score of 6.
Amda and Calla have jointly a score of 7, also, their scores are the same in every parameter.
Hence we have to look at parameter scores that have at least a minimum frequency of 2.
With the lowest score of 6, we are required to increase the score of any one parameter by 1 to get a score of 7.
We can increase the score of S from 3 to 4, which gives, S=4, F=1 and C=2, giving a total of 7.
The second possibility is increasing the score of C from 2 to 3, which gives, S=3, F=1 and C=3, giving a total of 7.
Note that we won't be able to increase the score of F as F does not have the score 2 with a frequency higher than or equal to 2.
Amda score in F in both the cases is 1.
Zooma has a total score of 17. Hence, it is among the three countries categorised as happy. It is also given that these three countries has the highest score in only one parameter.
If Zooma got the highest score of 7 in S parameter, then, it has to take the second highest scores of 5 and 4 in F and C parameters respectively. The sum of these scores ( 7+5+4) does not give 17. Hence, this case can be eliminated
Similarly if we look at the other two cases, we will observe that Zooma could've got a total score of 17 by two ways.
Case 1: S=6, F=7, C=4
Case 2: S=6, F=5, C=6
14) Amda’s score in F in both the cases is 1.
Answer: 1
15) In both the cases Zooma's score in S is the same, which is, 6.
Answer: 6
16) Benga and Delma are the two countries along with Zooma that are categorised as happy and have the same total score.
Let us give Zooma a score of 7 in F parameter, hence, the score split up of Zooma is, S=6, F=7, C=4.
Let Benga get the highest is S parameter and Delma in C parameter. Hence the score split ups are S=7, F=5, C=3 and S=5, F=5, C=6 respectively.
Benga's total score is 15 whereas Delma's is 16. This is not allowed as both the scores should be equal.
We would not be able to increase Benga's total score but we would be able to reduce Delma's, Hence, Delma got a score of S=4, F=5 and C=6 which adds up to 15. We can also get a score of 15 by S=5, F=4, C=6.
Hence 15 is the maximum possible score Benga and Delma can have.
Answer: (2) 15
17) If Benga score is 16 and Delma score is 15, the split up of scores should've been, Benga(S=5, F=5 and C=6) and Delma(S=7, F=5 and C=3).
Zooma scores would be S=6, F=7, C=4.
Scores that are used up in the parameters are, 5,6 and 7 from S, 5,5 and 7 from F and 6,3 and 4 from C.
With the remaining 5's and 4's the only possible formation of a total score of 13 is S=5, F=5 and C=3. Hence, only 1 total score of 13 can be formed.
Answer:
14) 1
15) 6
16) (2) 15
17) (2) 1