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.

Determine the ratio of the promoted personnel in X and Z combined to the average number of staff members in V and Y.

The correct option is 6 : 5.

Step-by-Step Explanation:

Step 1: Calculate the total staff size for each relevant corporation

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

• Corporation V: Men = 400, Women = 350
Total staff in V = 400 + 350 = 750

• Corporation X: Men = 340, Women = 410
Total staff in X = 340 + 410 = 750

• Corporation Y: Men = 200, Women = 300
Total staff in Y = 200 + 300 = 500

• Corporation Z: Men = 240, Women = 360
Total staff in Z = 240 + 360 = 600

Step 2: Calculate the number of promoted personnel in Corporations X and Z combined

From the table, 60% of total personnel received a promotion in Corporation X, and 50% in Corporation Z.

Promoted personnel in Corporation X:

$60\%\times 750=\frac{60}{100}\times 750=450$

Promoted personnel in Corporation Z:

$50\%\times 600=\frac{50}{100}\times 600=300$

Combined promoted personnel in X and Z:

$450+300=750$

Step 3: Calculate the average number of staff members in Corporations V and Y

Average staff in V and Y = (Total staff in V + Total staff in Y) ÷ 2

$\text{Average staff}=\frac{750+500}{2}=\frac{1250}{2}=625$

Step 4: Determine the required ratio

Ratio = (Promoted personnel in X and Z combined) : (Average staff in V and Y)

$\text{Ratio}=750:625$

Dividing both sides of the ratio by their greatest common divisor, 125:

$\frac{750}{125}:\frac{625}{125}=6:5$

Thus, the required ratio is 6 : 5.