Analyzing College Data and Calculating AI Offerings

The question provides a table containing valuable data about colleges in four Indian states (A, B, C, D). This data includes the percentage of colleges in each state offering specific IT courses (Python, Java, Multimedia, and AI), as well as the percentage distribution of the total number of colleges across these states. The total number of colleges across all four states is given as 4000. Our goal is to find the total number of colleges that offer the AI course across all four states combined.

Here is the provided data table:

Step-by-Step Calculation of Total AI Colleges

To find the total number of colleges offering AI, we need to follow these steps:

1. Calculate the total number of colleges in each state based on the percentage distribution and the overall total (4000).
2. For each state, calculate the number of colleges offering AI based on the percentage given in the table.
3. Sum up the number of colleges offering AI from all four states.

Calculating Colleges per State

Total number of colleges = 4000

• State A: 35% of 4000 = $\frac{35}{100} \times 4000 = 0.35 \times 4000 = 1400$ colleges
• State B: 15% of 4000 = $\frac{15}{100} \times 4000 = 0.15 \times 4000 = 600$ colleges
• State C: 20% of 4000 = $\frac{20}{100} \times 4000 = 0.20 \times 4000 = 800$ colleges
• State D: 30% of 4000 = $\frac{30}{100} \times 4000 = 0.30 \times 4000 = 1200$ colleges

Let's quickly check if the total adds up: $1400 + 600 + 800 + 1200 = 4000$. This matches the given total number of colleges.

Calculating Colleges Offering AI per State

Now, we use the percentage of colleges offering AI in each state:

• State A: 56% of 1400 colleges = $\frac{56}{100} \times 1400 = 0.56 \times 1400 = 784$ colleges
• State B: 84% of 600 colleges = $\frac{84}{100} \times 600 = 0.84 \times 600 = 504$ colleges
• State C: 86% of 800 colleges = $\frac{86}{100} \times 800 = 0.86 \times 800 = 688$ colleges
• State D: 70% of 1200 colleges = $\frac{70}{100} \times 1200 = 0.70 \times 1200 = 840$ colleges

Calculating Total Colleges Offering AI Across States

Finally, we sum the number of colleges offering AI from each state:

Total AI Colleges = (AI colleges in A) + (AI colleges in B) + (AI colleges in C) + (AI colleges in D)

Total AI Colleges = $784 + 504 + 688 + 840$

Total AI Colleges = $1288 + 688 + 840$

Total AI Colleges = $1976 + 840$

Total AI Colleges = $2816$

Thus, the total number of colleges offering AI in all four states is 2816.

Revision Table: College Data and AI Offering Calculation

Sum of Colleges Offering AI = $784 + 504 + 688 + 840 = 2816$

Additional Information: Understanding Data Interpretation for Exams

Data Interpretation (DI) questions are common in many competitive exams. They test your ability to read, analyze, and draw conclusions from data presented in various formats like tables, charts (bar graphs, pie charts, line graphs), and caselets. Here are some key points related to solving DI questions:

• Read Carefully: Always read the question and the data source (table title, axis labels, footnotes) very carefully. Understand what the percentages or numbers represent.
• Identify the Goal: Clearly understand what is being asked. Are you calculating a total, an average, a percentage change, or a ratio?
• Break Down Complex Problems: For problems involving multiple steps, like this one, break them down into smaller, manageable calculations.
• Calculations: Practice basic arithmetic operations, percentages, ratios, and averages. Be comfortable with calculations involving large numbers or decimals.
• Check Units: Pay attention to units (e.g., percentage, absolute number, currency).
• Estimation: Sometimes, you can quickly eliminate options by estimating the result, although for precise calculations like this one, exact calculation is needed.
• Practice: The key to excelling in DI is practice with various types of data representations and questions.

This question specifically required calculating a value based on nested percentages – a percentage distribution of the total followed by a percentage of that resulting number. Mastering such calculations is crucial for data interpretation success.