One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers?
Answer & explanation
Answer: (b) 7, 8
The full booklet's page total must be just above 195. With 20 pages the total is 210, so the torn leaf carries numbers adding to 15 — pages 7 and 8.
- Sum of pages 1 to n is n(n + 1)/2. For n = 19 it is 190 (too small); for n = 20 it is 210.
- Missing sum = 210 − 195 = 15.
- A leaf carries two consecutive numbers, odd then even: 7 + 8 = 15.
- Check: n = 21 gives 231 − 195 = 36, which cannot be an odd + next-even pair (such pairs add to an odd number).
Remember · Missing leaf: find the first 1 + 2 + … + n above the given total; the gap is the two page numbers' sum.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·