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.

What is the difference between the total number of male employees and the total number of female employees in the entire company?

The correct answer is 1040.

Step 1: Find the number of male staff members in the Operations 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.

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

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

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

Step 2: Express staff counts in terms of male staff in Finance

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

Female staff members in Operations equal male staff members in Finance:

$\text{Female (Operations)}=F_m$

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

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

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

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

Step 3: Solve for Male Staff in Finance ($F_m$)

Calculate total staff for Engineering and Finance divisions:

$\text{Total (Engineering)}=800+(F_m-300)=500+F_m$

$\text{Total (Finance)}=F_m+(F_m-150)=2F_m-150$

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

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

Cross-multiplying gives:

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

$7500+15F_m=38F_m-2850$

$23F_m=10350$

$F_m=450$

Step 4: Compute exact staff values for Operations, Engineering, and Finance

Using $F_m=450$:

Operations Division:
- Male = 640
- Female = 450
- Total = 640 + 450 = 1090

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

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

Step 5: Determine staff counts for Marketing

The total startup staff is 3540. Therefore, staff in Marketing is:

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

Female staff in Marketing is 87.5% (or 7/8) of male staff in Marketing ($M_m$):

$\text{Total (Marketing)}=M_m+\frac{7}{8}{M}_m=\frac{15}{8}{M}_m=750$

$M_m=\frac{750\times 8}{15}=400$

$\text{Female (Marketing)}=750-400=350$

Step 6: Compute total male employees, total female employees, and the difference

Total male employees in the company:

$\text{Total Male}=640+400+800+450=2290$

Total female employees in the company:

$\text{Total Female}=450+350+150+300=1250$

Difference between total male and total female employees:

$\text{Difference}=2290-1250=1040$

Therefore, the difference between the total number of male employees and the total number of female employees in the entire company is 1040.