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.

Assuming that the ratio of men to women who received promotions at corporation V is 2 : 3, and that the count of men promoted at corporation W is 100% higher than the count of men promoted at corporation V, calculate the combined number of women who did not receive promotions at corporations V and W.

The correct answer is 222.

Let us break down the solution step-by-step using the data provided in the table for corporations V and W.

Step 1: Calculate the total number of personnel and promoted personnel at Corporation V.

For Corporation V:

• Number of Men = 400

• Number of Women = 350

• Total Personnel = 400 + 350 = 750

• Percentage of personnel promoted = 40%

Total promoted at V = 40% of 750

$\text{Total promoted at V}=\frac{40}{100}\times 750=300$

Step 2: Calculate the number of promoted men and women at Corporation V.

The ratio of men to women who received promotions at Corporation V is given as 2 : 3.

• Promoted Men at V =

$\frac{2}{2+3}\times 300=\frac{2}{5}\times 300=120$

• Promoted Women at V =

$\frac{3}{2+3}\times 300=\frac{3}{5}\times 300=180$

Step 3: Calculate the number of women who did not receive promotions at Corporation V.

• Total Women at V = 350

• Unpromoted Women at V = Total Women at V - Promoted Women at V

$\text{Unpromoted Women at V}=350-180=170$

Step 4: Calculate the total number of personnel and promoted personnel at Corporation W.

For Corporation W:

• Number of Men = 260

• Number of Women = 100

• Total Personnel = 260 + 100 = 360

• Percentage of personnel promoted = 80%

Total promoted at W = 80% of 360

$\text{Total promoted at W}=\frac{80}{100}\times 360=288$

Step 5: Calculate the number of promoted men and women at Corporation W.

The count of men promoted at Corporation W is 100% higher than the count of men promoted at Corporation V.

• Promoted Men at W = 120 + 100% of 120 = 120 + 120 = 240

Now, calculate the number of women promoted at Corporation W:

• Promoted Women at W = Total Promoted at W - Promoted Men at W

$\text{Promoted Women at W}=288-240=48$

Step 6: Calculate the number of women who did not receive promotions at Corporation W.

• Total Women at W = 100

• Unpromoted Women at W = Total Women at W - Promoted Women at W

$\text{Unpromoted Women at W}=100-48=52$

Step 7: Calculate the combined number of women who did not receive promotions at corporations V and W.

$\text{Combined Unpromoted Women}=170+52=222$

Thus, the combined number of women who did not receive promotions at corporations V and W is 222.