Analyze the details below and answer the question.

There are 450 employees in a company who use three (A, B and C) different communication systems. The ratio of the total number of employees who use only system A, only system B, and only system C is 5 : 7 : 3 respectively. Employees who use all three systems are 50% of the employees who use only system B. The sum of the employees who use only system B and system C and those who use only system A and system B is 50. The number of employees who use only system A and system C is 30.

What is the difference between the number of employees who use only system B and the number of employees who use only system A & system B?

Correct Answer: Can’t be determined.

Let us analyze the given information step-by-step using a Venn diagram approach for three communication systems: A, B, and C.

Let the number of employees who use:

• Only system A = 5x

• Only system B = 7x

• Only system C = 3x

We are given:

• Total number of employees = 450

• Employees who use all three systems (A ∩ B ∩ C) = 50% of (Only system B) = $\frac{7x}{2}$ = 3.5x

• Employees who use only system A & system C = 30

• Sum of employees who use (only B & C) and (only A & B) = 50

Let the number of employees using only system A & B be y.

Then, the number of employees using only system B & C = 50 - y.

Now, let us calculate the sum of all region counts in the Venn diagram:

Total = (Only A) + (Only B) + (Only C) + (Only A & C) + (Only A & B) + (Only B & C) + (All three systems)

Substituting the values into the equation:

$450=5x+7x+3x+30+y+(50-y)+3.5x$

Simplifying the right side of the equation:

$450=18.5x+80$

$18.5x=370$

$x=\frac{370}{18.5}=20$

Using the value of x, we can find the individual counts:

• Only system A = 5 × 20 = 100

• Only system B = 7 × 20 = 140

• Only system C = 3 × 20 = 60

The question asks for the difference between the number of employees who use only system B and the number of employees who use only system A & system B (y).

Difference = 140 - y

Since the specific value of y (employees using only system A & system B) is not individually given and cannot be uniquely determined from the given sum (y + (50 - y) = 50), the exact difference cannot be found.

Therefore, the answer Can’t be determined.