CAT 2025 Lesson : Bar Graph - Case 5

Directions for questions 16 to 19: Answer the questions on the basis of the information given below:

An International Organisation produces a Competitive Index of countries every two years based on eight factors (Institutions, Infrastructure, Macroeconomic Environment, Higher Education, Market Efficiency, Technological Readiness, Business Sophistication and Innovation). The last three indices were developed in 2010, 2012 and 2014. The scores for all eight factors of XYZ country are shown in the graph below:

[IIFT 2015]

16) If Factor performance is measured as 0.30 x Factor Score in 2014 + 0.35 x Factor Score in 2012 + 0.35 x Factor Score in 2010, then which of the following has the best Factor Performance?

(1) Innovation
(2) Business Sophistication
(3) Infrastructure
(4) Macroeconomic Environment

17) If Factor Performance is measured as $\dfrac{\mathrm{Factor \ Score \ 2014 - Factor \ Score \ 2012}}{\mathrm{Factor \ Score \ 2010}}$ then, which of the following has the best Factor Performance?

(1) Innovation
(2) Business Sophistication
(3) Infrastructure
(4) Macroeconomic Environment

18) Which of the following factors has the highest average score across indices of 2010, 2012 and 2014?

(1) Infrastructure
(2) Institutions
(3) Technological Readiness
(4) Market Efficiency

19) Which among the following factors had the least growth rate in 2014 versus scores of 2010?

(1) Business Sophistication
(2) Institutions
(3) Technological Readiness
(4) Infrastructure

Solution

16) The following table shows the scores of all the eight factors of XYZ country.



Factor performance = $0.30 \times \text{Factor score in 2014} + 0.35 \times \text{Factor score in 2012} + 0.35 \times \text{Factor score in 2010}$

Factor performance for Innovation = $0.30 \times 4.5 + 0.35 \times 4 + 0.35 \times 4.25$ = 4.24

Factor performance for Business Sophistication = $0.30 \times 5.25 + 0.35 \times 4.75 + 0.35 \times 4.5$ = 4.81
Factor performance for Infrastructure = $0.30 \times 5.25 + 0.35 \times 4 + 0.35 \times 4$ = 4.38

Factor performance for Macroeconomic Environment = $0.30 \times 5.5 + 0.35 \times 4.5 + 0.35 \times 4.75$ = 4.89

Macroeconomic Environment has the best Factor Performance.

Alternate Method

Factor score of Innovation and Infrastructure in the year 2010 and 2012 is lower than the Factor score of Macroeconomic Environment and Business Sophistication. Therefore, comparing the Factor score of Macroeconomic Environment and Business Sophistication alone is enough to find the best performance factor.

Factor performance for Business Sophistication = $\dfrac{3}{10} \times \dfrac{21}{4} + \dfrac{7}{20} \times \dfrac{19}{4} + \dfrac{7}{20} \times \dfrac{9}{2}$

= $\dfrac{6 \times 21}{80} + \dfrac{7 \times 19}{80} + \dfrac{7 \times 18}{80}$

= $\dfrac{6 \times 21}{80} + \dfrac{7 \times 37}{80}$

= $\dfrac{385}{80}$

Factor performance for Macroeconomic Environment = $\dfrac{3}{10} \times \dfrac{11}{2} + \dfrac{7}{20} \times \dfrac{9}{2} + \dfrac{7}{20} \times \dfrac{19}{4}$

= $\dfrac{3 \times 44}{80} + \dfrac{7 \times 18}{80} + \dfrac{7 \times 19}{80}$

= $\dfrac{3 \times 44}{80} + \dfrac{7 \times 37}{80}$

= $\dfrac{391}{80}$

$\dfrac{391}{80}$ > $\dfrac{385}{80}$, therefore Macroeconomic Environment has the best Factor performance.

Answer: (4) Macroeconomic Environment

17) The following table shows the scores of all the eight factors of XYZ country.



Factor performance = $\dfrac{\text{Factor score 2014 - Factor score 2012}}{\text{Factor score 2010}}$

Factor performance for Innovation = $\dfrac{4.5 - 4}{4.25}$ = $\dfrac{0.5}{4.25}$

Factor performance for Business Sophistication = $\dfrac{5.25 - 4.75}{4.5}$ = $\dfrac{0.5}{4.5}$

Factor performance for Infrastructure = $\dfrac{5.25 - 4}{4}$ = $\dfrac{1.25}{4}$

Factor performance for Macroeconomic Environment = $\dfrac{5.5 - 4.5}{4.75}$ = $\dfrac{1}{4.75}$

$\dfrac{1.25}{4}$ > $\dfrac{1}{4.75}$ > $\dfrac{0.5}{4.25}$ > $\dfrac{0.5}{4.5}$, therefore Infrastructure has the best Factor performance.

Answer: (3) Infrastructure

18) The following table shows the scores of all the eight factors of XYZ country.



To find the highest average score across indices 2010, 2012 and 2014, it is enough to calculate the highest sum of scores across indices 2010, 2012 and 2014

Sum of scores of Infrastructure = 4 + 4 + 5.25 = 13.25

Sum of scores of Institutions = 4.25 + 4.75 + 4.5 = 13.5

Sum of scores of Technological Readiness = 3.5 + 3.75 + 5.5 = 12.75

Sum of scores of Market Efficiency = 4.25 + 4.5 + 4.25 = 13

Institutions have the highest average score.

Answer: (2) Institutions

19) The following table shows the scores of all the eight factors of XYZ country.



Growth rate of Business Sophistication = $\dfrac{5.25 - 4.5}{4.5} \times 100$% = $\dfrac{0.75}{4.5} \times 100$%

Growth rate of Institutions = $\dfrac{4.5 - 4.25}{4.25} \times 100$% = $\dfrac{0.25}{4.25} \times 100$%

Growth rate of Technological Readiness = $\dfrac{5.5 - 3.5}{3.5} \times 100$% = $\dfrac{2}{3.5} \times 100$%

Growth rate of Infrastructure = $\dfrac{5.25 - 4}{4} \times 100$% = $\dfrac{1.25}{4} \times 100$%

$\dfrac{2}{3.5} \times 100$% > $\dfrac{1.25}{4} \times 100$% > $\dfrac{0.75}{4.5} \times 100$% > $\dfrac{0.25}{4.25} \times 100$%

Institutions have the least growth rate.

Answer: (2) Institutions

Answer:
16) (4) Macroeconomic Environment
17) (3) Infrastructure
18) (2) Institutions
19) (2) Institutions