Directions: Read the following information carefully and answer the question that follows.

In a technology startup with a total of 3540 staff members, employees work in one of four distinct divisions: Operations, Marketing, Engineering, and Finance. The number of female staff members in the Marketing division is 87.5% of the male staff members in that same division. The total number of male staff members in the Engineering division is 800, which is 25% higher than the number of male staff members in the Operations division. The count of female staff members in the Operations division is equal to the number of male staff members in the Finance division. Female staff members in the Finance division are 150 fewer than the male staff members in the same division, and also 150 more than the female staff members in the Engineering division. Finally, the ratio of the total staff members in the Engineering division to the total staff members in the Finance division is 19:15.

The total number of staff members in the Marketing division is what percentage more or less than the total number of staff members in the Finance division?

Correct Answer: 0%

Let us analyze the given information step-by-step to calculate the number of male and female staff members in each division (Operations, Marketing, Engineering, and Finance).

Step 1: Calculate male staff members in Engineering and Operations

The total number of male staff members in the Engineering division is given as 800.
This number is 25% higher than the number of male staff members in the Operations division.

$\text{Male (Engineering)}=\; 800$

$\text{Male (Engineering)}=\; 1.25\; \times \text{Male (Operations)}$

$800\; =\; 1.25\; \times \text{Male (Operations)}$

$\text{Male (Operations)}=\frac{800}{1.25}=\; 640$

Step 2: Express female staff members in Operations, Finance, and Engineering

Let the number of male staff members in the Finance division be $x$.

From the problem statement:

1. The count of female staff members in Operations is equal to male staff members in Finance:

$\text{Female (Operations)}=\; x$

2. Female staff members in Finance are 150 fewer than male staff members in Finance:

$\text{Female (Finance)}=\; x\; -\; 150$

3. Female staff members in Finance are also 150 more than female staff members in Engineering:

$\text{Female (Engineering)}=\text{Female (Finance)}-\; 150\; =\; (x\; -\; 150)\; -\; 150\; =\; x\; -\; 300$

Step 3: Determine total staff members in Engineering and Finance in terms of $x$

Total staff in Engineering:

$\text{Total (Engineering)}=\text{Male (Engineering)}+\text{Female (Engineering)}=\; 800\; +\; (x\; -\; 300)\; =\; x\; +\; 500$

Total staff in Finance:

$\text{Total (Finance)}=\text{Male (Finance)}+\text{Female (Finance)}=\; x\; +\; (x\; -\; 150)\; =\; 2x\; -\; 150$

Step 4: Solve for $x$ using the given division ratio

The ratio of total staff members in Engineering to Finance is 19:15.

$\frac{x+500}{2x-150}=\frac{19}{15}$

Cross-multiplying to find $x$:

$15\; \times \; (x\; +\; 500)\; =\; 19\; \times \; (2x\; -\; 150)$

$15x\; +\; 7500\; =\; 38x\; -\; 2850$

$38x\; -\; 15x\; =\; 7500\; +\; 2850$

$23x\; =\; 10350$

$x=\frac{10350}{23}=450$

Step 5: Calculate total staff members in each known division

Substituting $x=450$:

• Operations Division:
Male = 640
Female = 450
Total (Operations) = 640 + 450 = 1090

• Engineering Division:
Male = 800
Female = 450 - 300 = 150
Total (Engineering) = 800 + 150 = 950

• Finance Division:
Male = 450
Female = 450 - 150 = 300
Total (Finance) = 450 + 300 = 750

Step 6: Calculate total staff members in the Marketing division

The company has a total of 3540 staff members across all four divisions.

$\text{Total (Marketing)}=\; 3540\; -\; (\text{Total Operations}+\text{Total Engineering}+\text{Total Finance})$

$\text{Total (Marketing)}=\; 3540\; -\; (1090\; +\; 950\; +\; 750)\; =\; 3540\; -\; 2790\; =\; 750$

Step 7: Calculate the required percentage difference

We need to compare total staff members in Marketing (750) to total staff members in Finance (750):

$\text{Percentage Difference}=\frac{750-750}{750}\times \; 100\%\; =\; 0\%$

Thus, the total number of staff members in Marketing is 0% more or less than in Finance.