The distribution of employees at the rank of executives, across different companies C1, C2, …, C6 is presented in the chart given above. The ratio of executives with a management degree to those without a management degree in each of these companies is provided in the table above. The total number of executives across all companies is 10,000. The total number of management degree holders among the executives in companies C2 and C5 together is_____.

The correct option is 1900.

Step-by-step Explanation:

From the pie chart in the provided image, we can observe the percentage distribution of executives in each company. We are given that the total number of executives across all companies is 10,000.

First, let's calculate the total number of executives in companies C2 and C5 based on the percentages given in the pie chart:

• Company C2 has 5% of the total executives:

$$\text{Total executives in C2}=5\%\text{ of }\mathrm{10,000}=\frac{5}{100}\times \mathrm{10,000}=500$$

• Company C5 has 20% of the total executives:

$$\text{Total executives in C5}=20\%\text{ of }\mathrm{10,000}=\frac{20}{100}\times \mathrm{10,000}=\mathrm{2,000}$$

Next, we use the table in the image to determine the number of management degree holders using the ratio of executives with a management degree to those without in each company:

• For Company C2, the ratio is 1:4. This indicates that out of every 5 executives (1 + 4), 1 executive holds a management degree. The number of management degree holders in C2 is calculated as:

$$\text{Management degree holders in C2}=\frac{1}{1+4}\times 500=\frac{1}{5}\times 500=100$$

• For Company C5, the ratio is 9:1. This indicates that out of every 10 executives (9 + 1), 9 executives hold a management degree. The number of management degree holders in C5 is calculated as:

$$\text{Management degree holders in C5}=\frac{9}{9+1}\times \mathrm{2,000}=\frac{9}{10}\times \mathrm{2,000}=\mathrm{1,800}$$

Finally, we add the management degree holders from both companies together to find the total:

$$\text{Total management degree holders}=100+\mathrm{1,800}=\mathrm{1,900}$$