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Q60·CSAT · Prelims 2025

Numbers divisible by 5 between two naturals

NumericalDivisibilityNumber theoryEasy

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

a

There is only one such number.

b

There are only two such numbers.

c

There can be more than one such number.

Answer
d

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."

The number of multiples of K strictly inside an open interval of width W fluctuates by 1 depending on whether the interval boundaries align perfectly with multiples of K.

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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