Analyzing College B Employee Data

The problem provides a table with employee details for different colleges, including College B. We are given specific conditions for College B and asked to find the total number of employees.

From the table, we can extract the following known values for College B:

• Number of Teaching Females (TF_B): 215
• Number of Non-Teaching Females (NTF_B): 254

Calculating Female Employees in College B

The total number of female employees in College B is the sum of teaching and non-teaching females:

$$ F_{B} = TF_{B} + NTF_{B} $$

$$ F_{B} = 215 + 254 $$

$$ F_{B} = 469 $$

So, there are 469 female employees in College B.

Applying Given Conditions for College B

We are given three conditions regarding the employees in College B:

1. The number of non-teaching males (NTM_B) is 26 more than the teaching males (TM_B):

   $$ NTM_{B} = TM_{B} + 26 \quad \text{(Condition 1)} $$

2. The difference between the number of non-teaching males (NTM_B) and non-teaching females (NTF_B) is 122:

   $$ |NTM_{B} - NTF_{B}| = 122 \quad \text{(Condition 2)} $$

3. The number of males (M_B) is greater than the number of females (F_B):

   $$ M_{B} > F_{B} \quad \text{(Condition 3)} $$

Solving for Male Employees in College B

First, let's use Condition 2, substituting the known value of NTF_B = 254:

$$ |NTM_{B} - 254| = 122 $$

This absolute value equation gives two possible values for the number of non-teaching males (NTM_B):

• Case 1: $$ NTM_{B} - 254 = 122 $$

  $$ NTM_{B} = 254 + 122 = 376 $$

• Case 2: $$ NTM_{B} - 254 = -122 $$

  $$ NTM_{B} = 254 - 122 = 132 $$

Now, we use Condition 1 ($$ NTM_{B} = TM_{B} + 26 $$) to find the number of teaching males (TM_B) for each case:

• Case 1 (NTM_B = 376):

  $$ 376 = TM_{B} + 26 $$

  $$ TM_{B} = 376 - 26 = 350 $$

• Case 2 (NTM_B = 132):

  $$ 132 = TM_{B} + 26 $$

  $$ TM_{B} = 132 - 26 = 106 $$

The total number of male employees (M_B) is the sum of teaching males and non-teaching males ($$ M_{B} = TM_{B} + NTM_{B} $$):

• Case 1: $$ M_{B} = 350 + 376 = 726 $$
• Case 2: $$ M_{B} = 106 + 132 = 238 $$

Next, we use Condition 3 ($$ M_{B} > F_{B} $$) to determine which case is valid. We know that $$ F_{B} = 469 $$.

• Case 1: Is $$ M_{B} > F_{B} $$? $$ 726 > 469 $$. This is True.
• Case 2: Is $$ M_{B} > F_{B} $$? $$ 238 > 469 $$. This is False.

Therefore, Case 1 is the valid scenario based on the given conditions. The number of male employees in College B is 726.

Calculating Total Employees in College B

The total number of employees in College B is the sum of the total male employees and total female employees:

$$ E_{B} = M_{B} + F_{B} $$

Using the values from the valid Case 1:

$$ E_{B} = 726 + 469 $$

$$ E_{B} = 1195 $$

Based on the data provided in the table and the specified conditions, the calculated total number of employees in College B is 1195. However, the provided answer option text is 829. There appears to be a discrepancy between the result derived from the given conditions and the provided correct answer.

Revision Table: College B Employee Summary

Additional Information on Data Interpretation

Data interpretation questions often involve extracting information from tables or charts and using given conditions to calculate missing values. It's crucial to break down the problem into smaller steps:

• Understand the data presented in the table.
• Identify the specific information required by the question.
• Note down all conditions provided.
• Translate conditions into mathematical expressions.
• Solve the equations systematically.
• Verify if the solution satisfies all conditions.

Careful calculation and interpretation are key to accurately solving such problems.