The table below provides details regarding the number of men and women working at five distinct corporations (V, W, X, Y, and Z), along with the proportion of total personnel (men + women) who received a promotion at each corporation. Review the dataset to answer the question that follows.

Corporation	Men	Women	% of personnel promoted
V	400	350	40%
W	260	100	80%
X	340	410	60%
Y	200	300	80%
Z	240	360	50%

Note: The total staff size at any corporation is the sum of the men and women working there.

How much greater or smaller is the combined count of promoted personnel from corporations V, W, and Y than the total number of women working in corporations W, X, and Y?

The correct option is 178.

To find how much greater or smaller the combined count of promoted personnel from corporations V, W, and Y is compared to the total number of women in corporations W, X, and Y, we break down the calculation into step-by-step parts.

Step 1: Calculate the total promoted personnel in corporations V, W, and Y

First, we calculate the total staff size (Men + Women) and then find the promoted count for each relevant corporation using the given percentages:

• Corporation V:

$\text{Total staff}=400+350=750$

$\text{Promoted personnel}=40\%\text{of}750=0.40\times 750=300$

• Corporation W:

$\text{Total staff}=260+100=360$

$\text{Promoted personnel}=80\%\text{of}360=0.80\times 360=288$

• Corporation Y:

$\text{Total staff}=200+300=500$

$\text{Promoted personnel}=80\%\text{of}500=0.80\times 500=400$

Sum of promoted personnel in V, W, and Y:

$\text{Total Promoted (V + W + Y)}=300+288+400=988$

Step 2: Calculate the total number of women working in corporations W, X, and Y

Directly extracting the values from the table:

• Women in W = 100

• Women in X = 410

• Women in Y = 300

Sum of women working in W, X, and Y:

$\text{Total Women (W + X + Y)}=100+410+300=810$

Step 3: Calculate the difference

$\text{Difference}=988-810=178$

Hence, the combined count of promoted personnel from V, W, and Y is 178 greater than the total number of women working in W, X, and Y.