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:
Answer & explanation
Answer: (c) Both 1 and 2
Only 30 participants are not Indian. Even if all of them were vegetarian, at least 60 − 30 = 30 vegetarians are Indian; and even if all 30 were non-vegetarian, at least 40 − 30 = 10 non-vegetarians are Indian.
- Non-Indians = 100 − 70 = 30; non-vegetarians = 100 − 60 = 40.
- Fewest Indian vegetarians: make all 30 non-Indians vegetarian → Indian vegetarians = 60 − 30 = 30.
- Fewest Indian non-vegetarians: make all 30 non-Indians non-vegetarian → Indian non-vegetarians = 40 − 30 = 10.
- Both minimums hold, so both statements are correct.
- Check: 70 + 60 − 100 = 30 and 70 + 40 − 100 = 10.
- ✓ 1. At most 30 vegetarians can be non-Indian, so at least 30 of the 60 vegetarians are Indian.
- ✓ 2. At most 30 non-vegetarians can be non-Indian, so at least 10 of the 40 non-vegetarians are Indian.
Remember · For a guaranteed overlap, push the other group to the extreme: minimum overlap = A + B − total.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·