The following table shows the percentage (%) of colleges offering the four IT…
2022
The following table shows the percentage (%) of colleges offering the four IT courses on Python, Java, Multimedia and AI in four Indian States A-D, in a certain year. The table also presents the percentage-wise distribution of the number of Colleges in the four states. The total number of Colleges in the four states is 4000. Based on the data in the table, answer the questions 1-5.
State-wise Percentage of Colleges offering IT Courses
State | % of Colleges offering Python | % of Colleges offering Java | % of Colleges offering Multimedia | % of Colleges offering AI | % Distribution of Number of Colleges |
|---|---|---|---|---|---|
A | 86% | 74% | 59% | 56% | 35% |
B | 80% | 92% | 82% | 84% | 15% |
C | 74% | 88% | 84% | 86% | 20% |
D | 68% | 64% | 68% | 70% | 30% |
The total number of Colleges offering AI in all the four states is
Answer: B. 2816 — CONCEPTWhen a total is distributed across groups, first convert each group’s distribution percentage into its group count. For a category within a group,…
- A.
2784
- B.
2816
- C.
2864
- D.
2952
Show answer & explanation
Correct answer: B
CONCEPT
When a total is distributed across groups, first convert each group’s distribution percentage into its group count. For a category within a group, multiply that group count by the category percentage. Add the category counts across all groups.
APPLICATION
State A has 35% of 4000 = 1400 colleges; 56% of 1400 = 784 offer AI.
State B has 15% of 4000 = 600 colleges; 84% of 600 = 504 offer AI.
State C has 20% of 4000 = 800 colleges; 86% of 800 = 688 offer AI.
State D has 30% of 4000 = 1200 colleges; 70% of 1200 = 840 offer AI.
Add the four AI counts: 784 + 504 + 688 + 840 = 2816.
CROSS-CHECK
Compute the implied overall AI-offering rate: 2816 ÷ 4000 = 70.4%.
Independently compute the table’s weighted rate: (35 × 56 + 15 × 84 + 20 × 86 + 30 × 70) ÷ 100 = 70.4%. The matching rates confirm the count.
Therefore, the total number of colleges offering AI is 2816.