Q. 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.
(d) No such number exists.
Correct Answer : (c) There can be more than one such number.
UPSC Prelims 2025 CSAT
Explanation :
1. Let the two natural numbers be n and n + 10.
2. Any number divisible by 5 has the form 5k. We want those 5k strictly between n and n + 10:
n < 5k < n + 10
Divide by 5:
n/5 < k < n/5 + 2
This is an interval of length 2 on the real line, so it can contain either one or two integers k.
3. Examples:
• If n = 5, then the numbers between 5 and 15 are 6,7,…,14. Only 10 = 5·2 lies between – that’s 1 multiple of 5.
• If n = 3, then the numbers between 3 and 13 are 4,5,…,12. Here 5 = 5·1 and 10 = 5·2 lie between – that’s 2 multiples of 5.
4. Conclusion: depending on n, there may be either 1 or 2 such numbers, so “only one” and “only two” are both false, and there is always at least one. Hence the correct statement is that you can have more than one such number.
