3. A panel of 10 interviewers was to interview two candidates \( A \) and \( B \) to decide who was suitable for a job. 7 said \( A \) was suitable, 5 said \( B \) was suitable while 2 said neither \( A \) nor \( B \) was suitable. (i) How many said both \( A \) and \( B \) were suitable. (ii) How many said \( A \) alone was suitable.

To solve the problem, we can use a Venn diagram or simple set theory concepts to find the numbers. Given: - 7 said \( A \) was suitable. - 5 said \( B \) was suitable. - 2 said neither were suitable. - Total interviewers: 10. (i) Let’s find out how many said both \( A \) and \( B \) were suitable. Since 2 said neither were suitable, the number of interviewers who said either \( A \) or \( B \) or both is \( 10 - 2 = 8 \). Let \( x \) be the number who said both \( A \) and \( B \) were suitable. Using the formula: \[ \text{(Number who said A)} + \text{(Number who said B)} - \text{(Number who said both A and B)} = \text{(Total who said A or B)} \] We can plug in the numbers: \[ 7 + 5 - x = 8 \] Solving for \( x \): \[ 12 - x = 8 \implies x = 4 \] So, 4 said both \( A \) and \( B \) were suitable. (ii) Now, to find how many said \( A \) alone was suitable, we can use the information obtained. The total who said \( A \) is 7, and we know that 4 said both \( A \) and \( B \) were suitable. Thus, the number who said \( A \) alone is: \[ 7 - 4 = 3 \] Therefore, 3 said \( A \) alone was suitable. To summarize: 1. 4 interviewers said both \( A \) and \( B \) were suitable. 2. 3 interviewers said \( A \) alone was suitable.