Analyzing Entrance Exam Qualification Data

This question asks us to analyze the percentage distribution of students qualifying an Entrance Exam from different schools over two years, 2020 and 2021, based on the provided table. We are given the number of students qualifying from School G in both years, which is key to determining the total number of qualified students in each year. We need to find the combined number of students qualifying from Schools E and G in 2020 and express this number as a percentage of the number of students qualifying from School B in 2021.

We are given the following information:

• Number of students qualifying from School G in 2020 = 90
• Number of students qualifying from School G in 2021 = 135

Calculating Total Qualified Students in 2020 and 2021

From the table, School G represents 12% of the total qualified students in 2020 and 15% in 2021. We can use this information and the given absolute numbers for School G to find the total number of students who qualified in each year.

Total qualified students in 2020: Let $T_{2020}$ be the total number of qualified students in 2020. We know that 12% of $T_{2020}$ is 90. $ 12\% \text{ of } T_{2020} = 90 $ $ 0.12 \times T_{2020} = 90 $ $ T_{2020} = \frac{90}{0.12} = 750 $ So, 750 students qualified the Entrance Exam in 2020.

Total qualified students in 2021: Let $T_{2021}$ be the total number of qualified students in 2021. We know that 15% of $T_{2021}$ is 135. $ 15\% \text{ of } T_{2021} = 135 $ $ 0.15 \times T_{2021} = 135 $ $ T_{2021} = \frac{135}{0.15} = 900 $ So, 900 students qualified the Entrance Exam in 2021.

Number of Students Qualifying from Schools E and G in 2020

Now we need to find the number of students qualifying from Schools E and G in 2020.

• From the table, School E represents 18% of the total qualified students in 2020.
• Number of students from School E in 2020 = 18% of $T_{2020}$
• Number of students from School E in 2020 = $ 0.18 \times 750 = 135 $
• The number of students from School G in 2020 is given as 90.

Combined number of students from Schools E and G in 2020 = (Students from E in 2020) + (Students from G in 2020) Combined students (E + G) in 2020 = $ 135 + 90 = 225 $.

Number of Students Qualifying from School B in 2021

Next, we need to find the number of students qualifying from School B in 2021.

• From the table, School B represents 8% of the total qualified students in 2021.
• Number of students from School B in 2021 = 8% of $T_{2021}$
• Number of students from School B in 2021 = $ 0.08 \times 900 = 72 $

Calculating the Required Percentage

The question asks for the number of students qualifying from Schools E and G together in 2020 as a percentage of the number of students qualifying from School B in 2021.

Required Percentage = $ \left( \frac{\text{Combined students from E and G in 2020}}{\text{Students from B in 2021}} \right) \times 100 $ Required Percentage = $ \left( \frac{225}{72} \right) \times 100 $ Required Percentage = $ 3.125 \times 100 = 312.5 $

So, the number of students qualifying from Schools E and G together in 2020 is 312.5% of the number of students qualifying from School B in 2021.

Conclusion on Qualified Students Percentage

Based on our calculations using the provided data and the percentage distribution table, the number of students qualifying from Schools E and G together in 2020 is 312.5% of the number of students qualifying from School B in 2021. This matches one of the given options.

Revision Table: Key Calculations

Additional Information: Data Interpretation Skills

Data interpretation questions, like this one involving Entrance Exam results, often require understanding how to work with percentages and absolute values in a table.

• Percentage Distribution: A percentage distribution shows how a total is divided into parts. Each part is represented as a percentage of the whole. The sum of all percentages in a distribution should be 100%.
• Finding the Total: If you know the absolute number for a specific percentage within a distribution, you can find the total value. The formula is: $ \text{Total} = \frac{\text{Part (Absolute Value)}}{\text{Part's Percentage}} $. For example, if 12% is 90, the total is $ \frac{90}{0.12} $.
• Finding a Part: Once you know the total, you can find the absolute value for any other percentage in the distribution: $ \text{Part (Absolute Value)} = \text{Total} \times \text{Part's Percentage} $.
• Calculating Percentage of Another Number: To express a number (A) as a percentage of another number (B), use the formula: $ \left( \frac{A}{B} \right) \times 100 $.

Practicing with different types of tables and charts, such as bar graphs, pie charts, and line graphs, is essential for improving data interpretation skills for Entrance Exams. Pay close attention to the units and what each number or percentage represents.