Numbers divisible by 5 between two naturals
Question
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?
Options
There is only one such number.
There are only two such numbers.
There can be more than one such number.
No such number exists.
Explanation
Let the two numbers defining the open interval be N and N+10. We must count multiples of 5 strictly between them. Case 1: If the boundary numbers are themselves multiples of 5 (e.g., 5 and 15), the only multiple of 5 strictly between them is 10. (Count = 1). Case 2: If the boundary numbers are not multiples of 5 (e.g., 1 and 11), the multiples of 5 strictly between them are 5 and 10. (Count = 2). Since the count can be either one or two depending on the boundaries, option (c) correctly states "There can be more than one such number."
Answer: (c).
Question details
Year
2025
Paper
CSAT
Question
Q60
Section
Numerical Ability
Sub-topic
Divisibility
Type
Number theory
Difficulty
Easy
Source hint
Number theory
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