Company B needs to hire 30 new employees

Company B needs to hire 30 new employees. Ten percent (10%) of applicants do not meet the basic business requirements for the job, 12% of the remaining applicants do not pass the pre-screening assessment, 23% of those remaining applicants do not show up for the interview, and 5% of those remaining applicants fail the background investigation. How many applicants need to apply in order to meet the hiring target?

The correct answer and explanation is :

To determine how many applicants need to apply to meet the hiring target of 30 new employees, we need to account for the percentages of applicants who drop out at each stage of the hiring process. The stages are:

1. Basic business requirements: 10% of applicants do not meet the basic business requirements.
2. Pre-screening assessment: 12% of the remaining applicants do not pass the pre-screening assessment.
3. Interview attendance: 23% of the remaining applicants do not show up for the interview.
4. Background investigation: 5% of the remaining applicants fail the background investigation.

Step-by-step breakdown:

Let the total number of applicants needed be $x$.

1. Step 1: Basic business requirements

• 10% of applicants do not meet the basic business requirements, so 90% of the applicants pass this stage.
• After this stage, the number of applicants left is:
  $0.9x$.

1. Step 2: Pre-screening assessment

• 12% of the remaining applicants do not pass the pre-screening assessment, so 88% of the applicants pass.
• After this stage, the number of applicants left is:
  $0.88 \times 0.9x = 0.792x$.

1. Step 3: Interview attendance

• 23% of the remaining applicants do not show up for the interview, so 77% of the applicants show up.
• After this stage, the number of applicants left is:
  $0.77 \times 0.792x = 0.61044x$.

1. Step 4: Background investigation

• 5% of the remaining applicants fail the background investigation, so 95% pass.
• After this stage, the number of applicants left is:
  $0.95 \times 0.61044x = 0.579918x$.

To meet the hiring target of 30 employees, the final number of applicants who pass all stages must equal 30:

$$
0.579918x = 30
$$

Solving for $x$:

$$
x = \frac{30}{0.579918} \approx 51.74
$$

Since the number of applicants must be a whole number, we round up to the nearest whole number:

$$
x = 52
$$

Final Answer:

Company B needs to have 52 applicants apply to meet the hiring target of 30 new employees.

Explanation:

The process accounts for each stage where applicants drop out, with each successive stage reducing the number of eligible candidates. By starting with a larger number of applicants (52), Company B ensures that after all stages of selection, they will have enough qualified candidates to meet their hiring target.