Analyzing Entrance Exam Qualification Data by School and Year

The problem provides data on the percentage distribution of students who qualified for an entrance exam from seven different schools (A through G) over two years, 2020 and 2021. We are also given the actual number of qualifying students from School G for both years.

The table showing the distribution is as follows:

We are given that the number of students qualifying from School G in 2020 is 90, and in 2021 is 135.

• In 2020, School G represents 12% of the total qualifying students.
• In 2021, School G represents 15% of the total qualifying students.

Calculating the Total Number of Qualifying Students Each Year

We can use the information about School G to find the total number of students who qualified in each year.

• For 2020: If 12% of the total students is 90, then the total number of students is $\frac{90}{12} \times 100$.
• Total qualifying students in 2020 = $\frac{90}{12} \times 100 = 7.5 \times 100 = 750$.
• For 2021: If 15% of the total students is 135, then the total number of students is $\frac{135}{15} \times 100$.
• Total qualifying students in 2021 = $\frac{135}{15} \times 100 = 9 \times 100 = 900$.

Calculating Students from Schools B, C, D in 2020

We need to find the total number of students qualifying from Schools B, C, and D in 2020. First, find the combined percentage for these schools in 2020.

• Percentage from School B in 2020 = 14%
• Percentage from School C in 2020 = 16%
• Percentage from School D in 2020 = 10%
• Total percentage for B, C, D in 2020 = $14\% + 16\% + 10\% = 40\%$.

Now, calculate the number of students corresponding to 40% of the total qualifying students in 2020.

• Number of students from B, C, D in 2020 = $40\%$ of $750 = \frac{40}{100} \times 750$.
• Number of students from B, C, D in 2020 = $0.40 \times 750 = 300$.

Calculating Students from Schools E, F, G in 2021

Next, we find the total number of students qualifying from Schools E, F, and G in 2021. First, find the combined percentage for these schools in 2021.

• Percentage from School E in 2021 = 16%
• Percentage from School F in 2021 = 13%
• Percentage from School G in 2021 = 15%
• Total percentage for E, F, G in 2021 = $16\% + 13\% + 15\% = 44\%$.

Now, calculate the number of students corresponding to 44% of the total qualifying students in 2021.

• Number of students from E, F, G in 2021 = $44\%$ of $900 = \frac{44}{100} \times 900$.
• Number of students from E, F, G in 2021 = $0.44 \times 900 = 396$.

Determining the Ratio

The question asks for the ratio of the number of students qualifying from Schools B, C and D in 2020 to that of Schools E, F and G in 2021.

• Ratio = (Number of students from B, C, D in 2020) : (Number of students from E, F, G in 2021)
• Ratio = $300 : 396$.

To simplify the ratio, we find the greatest common divisor (GCD) of 300 and 396. Let's simplify it step by step:

• Both numbers are divisible by 2: $150 : 198$
• Both numbers are divisible by 2: $75 : 99$
• Both numbers are divisible by 3: $25 : 33$

The simplified ratio is $25 : 33$.

Revision Table: Key Calculations

The ratio of the number of students qualifying from Schools B, C and D in 2020 to that of Schools E, F and G in 2021 is $25 : 33$.

Additional Information: Data Interpretation Strategies

Data interpretation questions like this require careful reading of the question and the provided data (tables, charts, graphs). Key steps often include:

• Understanding the Data: Look at what the rows, columns, and values represent. Understand if the values are absolute numbers, percentages, ratios, etc.
• Finding Base Values: If percentages or distributions are given, often you need to find the total or a base value to convert percentages into actual numbers, as we did here using School G's data.
• Identifying Required Information: Pinpoint exactly which schools, years, and calculations are needed for the question.
• Performing Calculations: Accurately calculate sums, averages, percentages, differences, or ratios as required. Be careful with percentage calculations (e.g., percentage of a total, percentage change).
• Simplifying Ratios/Fractions: Express the final answer in the simplest form if it's a ratio or fraction.
• Checking Options: Compare your calculated answer with the given options.

This question specifically tested the ability to use a known absolute value associated with a percentage to find the total, and then use the total to find the absolute values for other percentages, finally calculating and simplifying a ratio.