The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?
Answer & explanation
Answer: (c) There can be more than one such number.
Two natural numbers 10 apart have nine numbers strictly between them. These contain one multiple of 5 when both ends are multiples of 5 (5 and 15) and two otherwise (3 and 13). So there can be more than one such number, as (c) says.
- Take 5 and 15: the only multiple of 5 strictly between them is 10 — one number.
- Take 3 and 13: the multiples of 5 between them are 5 and 10 — two numbers.
- The nine numbers between the two always include at least one multiple of 5, so the count is 1 or 2, never 0.
- Only (c), 'There can be more than one such number', holds in general.
- ✗ (a) True only when both numbers are multiples of 5 (e.g. 5 and 15); 3 and 13 have two such numbers between them.
- ✗ (b) True only when neither number is a multiple of 5; 5 and 15 have just one (10) between them.
- ✓ (c) The count can be 2 (3 and 13 give 5 and 10), so more than one such number is possible.
- ✗ (d) Nine consecutive numbers always include a multiple of 5, so at least one always exists.
Remember · When a count depends on the case, test a boundary case and a general case; pick the option true in every case.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·