How many numbers are there between 100 and 300 which either begin with or end with 2?

Answer: (a) 110

All numbers from 200 to 299 begin with 2 — 100 numbers — and 20 numbers from 102 to 292 end in 2. Ten of those (202 to 292) are counted twice, so the total is 100 + 20 − 10 = 110.

1. Beginning with 2: 200 to 299 — 100 numbers.
2. Ending in 2: 102, 112, …, 292 — 20 numbers.
3. Both: 202, 212, …, 292 — 10 numbers.
4. Total = 100 + 20 − 10 = 110.

Remember · 'Either … or' counting: add both groups, then subtract the overlap once.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error