UPSC Prelims 2025 CSAT, question 80

Topic: Number system

Q80

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 answer
(d) No such number exists.

Solution.

Answer: (c) There can be more than one such number.

Let the two natural numbers with difference $10$ be $a$ and $a + 10$ .
If $a$ is a multiple of $5$ (for example, $5$ and $15$ ), there is exactly $1$ multiple of $5$ strictly between them ( $10$ ); if $a$ is not a multiple of $5$ (for example, $6$ and $16$ ), there are $2$ multiples of $5$ strictly between them ( $10$ and $15$ ).
Therefore, there is always at least one and there can be more than one such number.