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 ?
- (a) There is only one such number.
- (b) There are only two such numbers.
- (c) There can be more than one such number. ✓ UPSC's answer
- (d) No such number exists.
Why the answer is (c)
• Let the numbers be x and x + 10; the numbers strictly between them are the nine consecutive numbers x + 1 to x + 9.
• If x is a multiple of 5 (e.g. 5 and 15), only one multiple of 5 lies between them (10).
• If x is not a multiple of 5 (e.g. 1 and 11), two multiples of 5 lie between them (5 and 10).
• So the count is one or two depending on the numbers — it is not fixed, but there can be more than one, option (c).
Why the other options are wrong
- (a) There is only one such number.
- This is incorrect because if the smaller number is not a multiple of 5 (e.g., 1 and 11), there are two numbers (5 and 10) divisible by 5 between them.
- (b) There are only two such numbers.
- This is incorrect because if the smaller number is a multiple of 5 (e.g., 5 and 15), there is only one number (10) divisible by 5 between them.
- (d) No such number exists.
- This is incorrect because there is always at least one multiple of 5 between any two numbers differing by 10 (e.g., 10 is between 5 and 15).
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.