Thanks, I was making the box set, my bad

I have a doubt if we use maximum overlap here then the answer is coming out to be 30!

A survey of 208 companies revealed:
- $\(\mathbf{1 2 0}\)$ companies use the switch mode to receive calls.
- 90 companies use the voice call facility to receive calls.
- All companies use at least one of these two facilities.

We need to compare:
- Quantity A: The number of companies that use the switch mode but not the voice call facility.
- Quantity B: 88.

Step 1: Define the Variables
Let:
- $S=$ Number of companies using the switch mode.
- $V=$ Number of companies using the voice call facility.
- $\(S \cap V=\)$ Number of companies using both facilities.
- $S$ only $=$ Number of companies using only the switch mode (Quantity A).

Given:
- $S=120$
- $V=90$
- Total companies = 208 (all use at least one facility)..

Step 2: Apply the Principle of Inclusion-Exclusion
The total number of companies using at least one facility is:

$$
\(S+V-(S \cap V)=208\)
$$


Substitute the known values:

$$
\(\begin{gathered}
120+90-(S \cap V)=208 \\
210-(S \cap V)=208 \\
S \cap V=210-208=2
\end{gathered}\)
$$


Step 3: Calculate Quantity A (Switch Mode Only)
The number of companies using only the switch mode is:

$$
\(S \text { only }=S-(S \cap V)=120-2=118\)
$$


Step 4: Compare Quantity A and Quantity B
- Quantity A: 118
- Quantity B: 88

Since $118>88$, Quantity A is greater than Quantity B .
Final Answer
$\(\{\mathrm{A}\}\)$