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.

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The correct option is 222.

Step-by-Step Breakdown:

1. Calculations for Corporation V:

From the table, Corporation V has:

• Number of men = 400
• Number of women = 350

Total personnel at Corporation V = 400 + 350 = 750

Percentage of personnel promoted at V = 40%

Total number of promoted personnel at V:

$40\%of750=\frac{40}{100}\times 750=300$

The ratio of promoted men to promoted women at V is 2 : 3.

• Men promoted at V =

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

• Women promoted at V =

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

Now, calculate the number of women who did not receive promotions at Corporation V:

Women NOT promoted at V = Total women at V - Women promoted at V

$350-180=170$

2. Calculations for Corporation W:

From the table, Corporation W has:

• Number of men = 260
• Number of women = 100

Total personnel at Corporation W = 260 + 100 = 360

Percentage of personnel promoted at W = 80%

Total number of promoted personnel at W:

$80\%of360=\frac{80}{100}\times 360=288$

Given that the count of men promoted at Corporation W is 100% higher than at Corporation V:

Men promoted at W = 120 + 100% of 120 = 120 + 120 = 240

Therefore, the number of women promoted at Corporation W is:

Women promoted at W = Total promoted at W - Men promoted at W

$288-240=48$

Now, calculate the number of women who did not receive promotions at Corporation W:

Women NOT promoted at W = Total women at W - Women promoted at W

$100-48=52$

3. Combined Number of Women Not Promoted at V and W:

Combined non-promoted women = (Women NOT promoted at V) + (Women NOT promoted at W)

$170+52=222$

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