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CAT — Scatter Plot

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Scatter Plot

8 questions

Set 1 4 questions ▶

The two plots below give the following information about six firms A, B, C, D, E, and F for 2019 and 2023.

PAT: The firm’s profits after taxes in Rs. crores,

ES: The firm’s employee strength, that is the number of employees in the firm, and

PRD: The percentage of the firm’s PAT that they spend on Research and Development (R&D).

In the plots, the horizontal and vertical coordinates of point representing each firm gives their ES and PAT values respectively. The PRD values of each firm are proportional to the areas around the points representing each firm. The areas are comparable between the two plots, i.e., equal areas in the two plots represent the same PRD values for the two years.

Q1 Assume that the annual rate of growth in PAT over the previous year (ARG) remained consta… MCQ ▶

Assume that the annual rate of growth in PAT over the previous year (ARG) remained constant over the years for each of the six firms. Which among the firms A, B, C, and E had the highest ARG?

Firm B

Firm C

Firm A

Firm E

Correct answer: D.

Firm E

Since the annual growth rate is assumed to remain constant, it is sufficient to compare the increase in each firm's PAT between 2019 and 2023.

Firm A: 3000 → 3900, an increase of 900
Firm B: 2800 → 3800, an increase of 1000
Firm C: 2400 → 3000, an increase of 600
Firm E: 2400 → 3500, an increase of 1100

Among these, Firm E records the highest increase in PAT.

Hence, Firm E has the highest annual growth rate.

Q2 The ratio of the amount of money spent by Firm C on R&D in 2019 to that in 2023 is cl… MCQ ▶

The ratio of the amount of money spent by Firm C on R&D in 2019 to that in 2023 is closest to

9 : 4

5 : 9

9 : 5

5 : 6

Correct answer: C.

9 : 5

This question requires a bit of approximation because the bubbles are not completely enclosed within the axes. In such cases, the best approach is to use the most visible bubbles for comparison.

For example, the bubble corresponding to Firm C has an approximate vertical diameter of 3 units in 2019, whereas in 2023 its diameter is about 2 units.

Therefore, the ratio of R&D expenditure in 2019 to that in 2024 is:

= (2400 × (1.5)²) / (3000 × (1)²)

= (8/10) × (9/4)

= 9 : 5

Q3 Which among the firms A, C, E, and F had the maximum PAT per employee in 2023? MCQ ▶

Which among the firms A, C, E, and F had the maximum PAT per employee in 2023?

Firm A

Firm F

Firm E

Firm C

Correct answer: D.

Firm C

The PAT per employee for each firm in 2023 is calculated as follows:

Firm A: 3900 / 1300 = 3
Firm C: 3000 / 800 = 3.75
Firm E: 3500 / 1400 = 2.5
Firm F: 3200 / 1000 = 3.2

Among these, the highest PAT per employee is 3.75, achieved by Firm C.

Hence, the required answer is Firm C.

Q4 Which among the firms C, D, E, and F had the least amount of R&D spending per employe… MCQ ▶

Which among the firms C, D, E, and F had the least amount of R&D spending per employee in 2023?

Firm D

Firm C

Firm E

Firm F

Correct answer: A.

Firm D

The PAT per employee for Firms F, C, and E was calculated in the previous question.

Now, for Firm D:

PAT per employee = 2400 / 800 = 3

Among Firms F, C, and D, the bubble sizes are identical. Therefore, the only quantity that needs to be compared is the PAT per employee.

Firm F = 3.2
Firm C = 3.75
Firm D = 3

Thus, Firm D has the lowest PAT per employee among these three.

Now compare Firm D with Firm E by accounting for the proportionality between bubble area and R&D expenditure.

For Firm E:

PAT per employee = 2.5
Bubble radius = 1.5 units

R&D expenditure per employee:

= (5/2) × π × (3/2)²

= π × 25/8

For Firm D:

PAT per employee = 3
Bubble radius = 1 unit

R&D expenditure per employee:

= 3 × π × (1)²

= 3π

Since 25π/8 > 3π, Firm E has the higher R&D expenditure per employee.

Hence, Firm D had the lowest R&D spending per employee in 2023.

Set 2 4 questions ▶

The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries – A, B, C, D, E, and F – at three different points in time – 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., (SI in 2020 minus SI in 2016) / (SI in 2016), and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known.

1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively.

2. F had lower SI than any other country in 2016, 2020, and 2024.

3. In 2024, E was the only country with SI of 90.

4. The range of SI of the six countries was 60 in 2016 as well as in 2024.

Q5 What was the SI of E in 2016? TITA ▶

What was the SI of E in 2016?

Answer: 60

Step 1:

Only the values corresponding to B, C, E, and F are required to answer the questions.

In 2016, B had the highest SI, while F had the lowest. Also, the SI of B exceeded that of F by 60.

Let the SI of F in 2016 be x. Then, the SI of B in 2016 is x + 60.

Using the percentage changes shown in the graph, the SI of F becomes 2x in 2020 and 1.5x in 2024.

The SI of E in 2024 is 90. Applying the given percentage changes, the corresponding SI values of E are 75 in 2020 and 60 in 2016.

Since the range of SI values in 2024 is 60, the SI of F in 2024 (i.e., 1.5x) must be at least 30. Therefore, x ≥ 20, implying (x + 60) ≥ 80.

Now consider the percentage changes for B. Its SI decreases by 25% from 2016 to 2020, and again by 25% from 2020 to 2024. Thus, the overall multiplying factor from 2016 to 2024 is 9/16.

Since all SI values are integers, (x + 60) must be a multiple of 16. As it is already at least 80, the only possible values are 80 and 96.

If (x + 60) = 96, then x = 36. This gives the SI of B in 2020 as 72, while the SI of F in 2020 also becomes 72, contradicting the fact that F had the lowest SI in 2020.
Hence, this case is rejected.

Therefore, (x + 60) = 80, giving x = 20.

Thus, the SI values of B are:

2016: 80
2020: 60
2024: 45

Step 2:

In 2016, the SI of C lies between those of B and E. Therefore, its value must lie between 60 and 80.

From the graph, the SI of C becomes 4/5 of its 2016 value in 2020, and then 7/5 of its 2020 value in 2024. Hence, the overall multiplying factor from 2016 to 2024 is 28/25.

This implies that the SI of C in 2016 must be a multiple of 25. The only multiple of 25 between 60 and 80 is 75.

Accordingly, the SI of C is:

2016: 75
2020: 60
2024: 84

The derived values are summarized in the table below.

Hence, the SI of E in 2016 was 60.

Q6 What was the SI of F in 2020? TITA ▶

What was the SI of F in 2020?

Answer: 40