CAT — Bubble Charts
4 questions, free to view. Click any question to see the answer and explanation.
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.
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
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.
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
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
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
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.
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
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.
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