UPSC CSE 2025 · PYQ · Divisibility / Number Theory · medium
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.✓ Correct
D.No such number exists.
Explanation
Let the two natural numbers be n and n+10. The numbers divisible by 5 lying strictly between them depend on n. For example, if n = 1, the numbers between 1 and 11 divisible by 5 are just {5, 10} — two numbers. If n = 5, the numbers strictly between 5 and 15 divisible by 5 is just {10} — one number. If n = 4, numbers between 4 and 14 divisible by 5 are {5, 10} — two numbers. So the count varies between 1 and 2 depending on n. Hence 'there can be more than one such number' is the most accurate general statement.
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