College Algebra

General Questions

To determine how many **applicants are needed** to hire **30 new employees**, given successive attrition at each stage of the hiring pipeline, we must work **backwards** using **inverse percentage calculations**. This type of problem is common in **human resources analytics**, especially in modeling **recruitment funnel performance** or **conversion rates**.

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### **Problem Structure:**

We are told the following about applicant drop-off:

1. **10%** of applicants are rejected due to failing basic business requirements.

2. **12%** of the remaining applicants** fail a pre-screening assessment.

3. **23%** of those remaining** do not show up for interviews.

4. **5%** of the remaining applicants** fail a background investigation.

5. **Goal**: Hire **30 employees** (i.e., 100% of the final step output).

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### **Step-by-Step Mathematical Model**

Let:

- \( x \): the **initial number of applicants** needed

We apply the percentage success rates (not failure rates) at each step in **reverse order** to compute backward from the desired output of 30 hires.

#### Step 4: Background Investigation

Only **95%** pass the background check: \[\text{Let } a = \frac{30}{0.95} = 31.5789\]

#### Step 3: Interview Attendance

Only **77%** show up for the interview:

\[\text{Let } b = \frac{a}{0.77} = \frac{31.5789}{0.77} \approx 41.0174\]

#### Step 2: Pre-screening Assessment

Only **88%** pass the pre-screening:

\[\text{Let } c = \frac{b}{0.88} = \frac{41.0174}{0.88} \approx 46.6107\]

#### Step 1: Basic Business Requirements

Only **90%** meet the basic requirements:

\[x = \frac{c}{0.90} = \frac{46.6107}{0.90} \approx 51.79\]

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### **Final Answer:**

\[\boxed{52}\]

Approximately **52 applicants** must apply in order to successfully **hire 30 employees**, accounting for all stages of **attrition** in the recruitment process.

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### **Summary Table of Recruitment Funnel**

\[\begin{array}{|c|c|c|}\hline\textbf{Stage} &amp; \textbf{Success Rate} &amp; \textbf{Cumulative Applicants Needed} \\\hline\text{Final Hires} &amp; - &amp; 30 \\\text{Passed Background Check} &amp; 95\% &amp; 31.58 \\\text{Attended Interview} &amp; 77\% &amp; 41.02 \\\text{Passed Pre-screening} &amp; 88\% &amp; 46.61 \\\text{Met Basic Requirements} &amp; 90\% &amp; 51.79 \\\textbf{Initial Applicants} &amp; - &amp; \boxed{52} \\\hline\end{array}\]

This problem highlights the importance of **conversion rate optimization** in the hiring pipeline and can be generalized to any **multi-stage process** where each stage has an associated dropout rate.

Math

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?

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