In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct ? 1. At least 30 Indian participants are vegetarian. 2. At least 10 Indian participants are non-vegetarian. Select the correct answer using the codes given below :
- (a) 1 only
- (b) 2 only
- (c) Both 1 and 2 ✓ UPSC's answer
- (d) Neither 1 nor 2
Why the answer is (c)
• Total participants = 100, Indians = 70, Non-Indians = 30.
• Total vegetarians = 60, Total non-vegetarians = 40.
• To find the minimum number of Indian vegetarians, assume the maximum number of Non-Indian vegetarians. Since there are only 30 Non-Indians, at most 30 can be vegetarians.
• Therefore, minimum Indian vegetarians = Total vegetarians (60) - Max Non-Indian vegetarians (30) = 30. Statement 1 is correct.
• To find the minimum number of Indian non-vegetarians, assume the maximum number of Non-Indian non-vegetarians. Since there are only 30 Non-Indians, at most 30 can be non-vegetarians.
• Therefore, minimum Indian non-vegetarians = Total non-vegetarians (40) - Max Non-Indian non-vegetarians (30) = 10. Statement 2 is correct.
• Since both statements are correct, option (c) is the answer.
Why the other options are wrong
- (a) 1 only
- Statement 2 is also correct, so selecting only statement 1 is incomplete.
- (b) 2 only
- Statement 1 is also correct, so selecting only statement 2 is incomplete.
- (d) Neither 1 nor 2
- Both statements are mathematically proven to be correct, so neither being correct is false.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.