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 ratio of the number of male staff members in the Marketing and Engineering divisions combined to the number of female staff members in the Engineering and Operations divisions combined?

Correct Answer: The correct option is 2:1.

Step-by-step Explanation:

Let us analyze the given information step-by-step to calculate the number of male and female staff members across all four divisions: Operations, Marketing, Engineering, and Finance.

1. Operations and Engineering Divisions (Male Staff):

We are given that 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.

$\text{Male staff in Engineering (}{M}_E\text{) = 800}$

Let the male staff in the Operations division be $M_O$. Since $M_E$ is 25% higher than $M_O$:

$1.25\times M_O=800$

$M_O=\frac{800}{1.25}=640$

2. Expressing Division Staff in terms of Male Staff in Finance:

Let the male staff members in the Finance division be represented by $M_F$.

From the problem statement, we have the following relations:

• The count of female staff members in the Operations division ($F_O$) is equal to the male staff members in the Finance division:

$F_O=M_F$

• Female staff members in the Finance division ($F_F$) are 150 fewer than the male staff members in Finance:

$F_F=M_F-150$

• Female staff members in Finance ($F_F$) are also 150 more than female staff members in Engineering ($F_E$):

$F_E=F_F-150=(M_F-150)-150=M_F-300$

3. Solving for Staff Count in Engineering and Finance:

The ratio of total staff members in the Engineering division to the Finance division is given as 19:15.

Total staff in Engineering = $M_E+F_E=800+(M_F-300)=500+M_F$

Total staff in Finance = $M_F+F_F=M_F+(M_F-150)=2M_F-150$

Forming the ratio equation:

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

Cross-multiplying to solve for $M_F$:

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

$7500+15M_F=38M_F-2850$

$7500+2850=38M_F-15M_F$

$10350=23M_F$

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

Substituting $M_F=450$ back into our equations:

• Female staff in Operations ($F_O$) = 450
• Female staff in Finance ($F_F$) = 450 - 150 = 300
• Female staff in Engineering ($F_E$) = 450 - 300 = 150

Totals for each of these divisions:

• Operations division total = 640 + 450 = 1090
• Engineering division total = 800 + 150 = 950
• Finance division total = 450 + 300 = 750

4. Marketing Division Staff:

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

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

The female staff members in the Marketing division ($F_{}$) are 87.5% of the male staff members in that same division ($M_{}$). Note that 87.5% = 0.875 = 7/8.

$M_M+F_M=M_M+0.875M_M=1.875M_M=750$

Writing 1.875 as a fraction (15/8):

$\frac{15}{8}{M}_M=750$

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

5. Calculating the Required Ratio:

We are asked to find the ratio of:

(Male staff in Marketing and Engineering combined) : (Female staff in Engineering and Operations combined)

• Male staff in Marketing and Engineering combined = $400+800=1200$

• Female staff in Engineering and Operations combined = $150+450=600$

Now, calculate the ratio:

$\text{Ratio}=\frac{1200}{600}=\frac{2}{1}=2:1$

Thus, the required ratio is 2:1.