CAT 2017 Slot 1 DILR Question & Solution
Data Set
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 ln exactly one parameter.
Question 1
What is Amda's score in F?
Solution:
The frequency distribution is:
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
or
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
Given Amda and Cadella score is 7 each with identical in all parameters. So it can score either 3,1,3 in S,F,C respectively or 4,1,2 in S,F,C respectively. In both the cases, its score in F is 1.
Question 2
What is Zooma's score in S?
Solution:
The frequency distribution is:
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
or
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
Zooma(Z) has a total score of 17 (comes under happy category), and other 2 countries, which are categorized as happy, have the highest score in exactly one parameter.
Suppose the other two countries are P and Q
Z have two possibilities for S, F, C : (6,7,4) & (6,5,6)
All the other cases are negated because "All the 3 countries, which are categorised as happy, have the highest score ln exactly one parameter."
For Example : 7,7,3 is not possible because 7 being the highest score is there in two parameters.
So, it scored 6 in S in both the cases.
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?
Solution:
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
Benga and Delma, two countries categorized as happy, are tied with the same total score.
The best numbers remaining are 7,5,6 which adds upto 18, If Benga scores 18, then Delma can't score 18.
Similarly both can't score 17 and 16. Both can score 15 and their distribution will be:
Benga: 7,5,3
Delma: 4,5,6 or 5,4,6
Question 4
If Benga scores 16 and Delma scores 15, then what is the maximum number of countries with a score of 13?
Solution:
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
Given that Benga scores 16, and Delma scores 15.
The possibility is Benga: 5,5,6 and Delma: 7,5,3
If Benga's distribution is 7,3,6 then Delma can't score 15.
Strike off those numbers.
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
We have to maximum number of countries with score 13. This score does not comes under the category of happy. So to score 13, the distribution can be 5,5,3. Hence, maximum 1 country is possible.