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.

If 20% of the employees in the Operations division transfer to the Finance division, causing the number of female staff members in the Finance division to increase to 373, what is the new total number of male staff members in the Finance division?

Correct Answer: The correct answer is 595 (Option 1).

Step-by-Step Explanation:

Step 1: Find the number of male staff in the Operations Division
We are given that the 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.

${\text{Male}}_{\text{Operations}}\times 1.25=800$

${\text{Male}}_{\text{Operations}}=\frac{800}{1.25}=640$

Step 2: Express all staff counts in terms of male staff in Finance
Let the number of male staff in the Finance division be ${\text{Male}}_{\text{Finance}}$.

From the given information:
1. Female staff in Operations is equal to male staff in Finance:
${\text{Female}}_{\text{Operations}}={\text{Male}}_{\text{Finance}}$
2. Total staff in Operations:
${\text{Total}}_{\text{Operations}}=640+{\text{Male}}_{\text{Finance}}$
3. Female staff in Finance is 150 fewer than male staff in Finance:
${\text{Female}}_{\text{Finance}}={\text{Male}}_{\text{Finance}}-150$
4. Total staff in Finance:
${\text{Total}}_{\text{Finance}}={\text{Male}}_{\text{Finance}}+({\text{Male}}_{\text{Finance}}-150)=2\times {\text{Male}}_{\text{Finance}}-150$
5. Female staff in Finance is also 150 more than female staff in Engineering:
${\text{Female}}_{\text{Engineering}}={\text{Female}}_{\text{Finance}}-150={\text{Male}}_{\text{Finance}}-300$
6. Total staff in Engineering:
${\text{Total}}_{\text{Engineering}}=800+({\text{Male}}_{\text{Finance}}-300)=500+{\text{Male}}_{\text{Finance}}$

Step 3: Solve for male staff in Finance using the given ratio
The ratio of total staff in Engineering to Finance is 19:15.

$\frac{500+{\text{Male}}_{\text{Finance}}}{2\times {\text{Male}}_{\text{Finance}}-150}=\frac{19}{15}$

Cross-multiplying and simplifying:

$15\times (500+{\text{Male}}_{\text{Finance}})=19\times (2\times {\text{Male}}_{\text{Finance}}-150)$

$7500+15\times {\text{Male}}_{\text{Finance}}=38\times {\text{Male}}_{\text{Finance}}-2850$

$7500+2850=38\times {\text{Male}}_{\text{Finance}}-15\times {\text{Male}}_{\text{Finance}}$

$10350=23\times {\text{Male}}_{\text{Finance}}$

${\text{Male}}_{\text{Finance}}=\frac{10350}{23}=450$

Step 4: Determine initial values before transfer
- Male staff in Finance = 450
- Female staff in Finance = 450 - 150 = 300
- Female staff in Operations = 450
- Total staff in Operations = 640 + 450 = 1090

Step 5: Calculate employee transfers to Finance
20% of employees in Operations transfer to Finance:

$\text{Total Transferred Staff}=20\%\times 1090=218$

The female staff in Finance increases from 300 to 373, which means:

$\text{Transferred Female Staff}=373-300=73$

The remaining transferred employees are males:

$\text{Transferred Male Staff}=218-73=145$

Step 6: Compute the new male staff in Finance
Adding the transferred male staff to the initial male staff in Finance:

$\text{New Male Staff in Finance}=450+145=595$

Thus, the new total number of male staff members in the Finance division is 595.