Correct Option (3)
Both 1 and 2
Explanation
Given Data:
- Total participants = 100
- Number of Indian participants = 70
- Number of Non-Indian participants = 100 - 70 = 30
- Number of Vegetarian participants = 60
- Number of Non-vegetarian participants = 100 - 60 = 40
Analysis of Statement 1: "At least 30 Indian participants are vegetarian."
- To ascertain the minimum number of Indian participants who are vegetarian, we must consider the scenario where the number of Non-Indian vegetarians is maximized.
- The total number of vegetarian participants is 60.
- The maximum possible number of Non-Indian participants is 30. Therefore, the maximum number of Non-Indian vegetarians cannot exceed 30.
- If all 30 Non-Indian participants are vegetarian, then the remaining vegetarian participants must be Indian.
- Minimum Indian vegetarians = Total vegetarians - Maximum Non-Indian vegetarians = 60 - 30 = 30.
- In any other distribution where fewer than 30 Non-Indians are vegetarian, the number of Indian vegetarians would be greater than 30.
- Thus, the number of Indian participants who are vegetarian is always 30 or more. Statement 1 is correct.
Analysis of Statement 2: "At least 10 Indian participants are non-vegetarian."
- To ascertain the minimum number of Indian participants who are non-vegetarian, we must consider the scenario where the number of Non-Indian non-vegetarians is maximized.
- The total number of non-vegetarian participants is 40.
- The maximum possible number of Non-Indian participants is 30. Therefore, the maximum number of Non-Indian non-vegetarians cannot exceed 30.
- If all 30 Non-Indian participants are non-vegetarian, then the remaining non-vegetarian participants must be Indian.
- Minimum Indian non-vegetarians = Total non-vegetarians - Maximum Non-Indian non-vegetarians = 40 - 30 = 10.
- In any other distribution where fewer than 30 Non-Indians are non-vegetarian, the number of Indian non-vegetarians would be greater than 10.
- Thus, the number of Indian participants who are non-vegetarian is always 10 or more. Statement 2 is correct.
Since both Statement 1 and Statement 2 are factually correct based on the given data and logical deduction, option 3 is the correct answer.
Incorrect Options
Options 1, 2, and 4 are incorrect because a detailed analysis demonstrates that both Statement 1 and Statement 2 are valid. The minimum conditions specified in each statement are consistently met across all possible distributions of participants within the given constraints.